Post on 16-May-2020
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Disentangling the Effects of Ecological and Environmental Processes on the Spatial Structure of
Metacommunities
by Sarah L. Salois
B.S. in Biology, Eastern Connecticut State University
A dissertation submitted to
The Faculty of
the College of Science of Northeastern University
in partial fulfillment of the requirements for the degree of Doctor of Philosophy
June 12, 2019
Dissertation directed by
Tarik C. Gouhier Professor of Marine and Environmental Sciences
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Dedication
To the memory of John and Noella Young who believed in me always and to my husband, Caleb, and our two children who inspire me daily.
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Acknowledgements
Let me start by acknowledging that this body of work could not have been achieved
without the support of my mentors, colleagues, friends and family both within and outside of
academia. I am forever grateful for all the encouragement and enthusiasm I have received from
the community of people I have grown to know along this journey.
I’d first like to thank Tarik Gouhier (my adviser) who guided me along this process and
whose standards and encouragement have been integral to my success. To the members of my
committee, Brian Helmuth, Jon Grabowski, Steve Vollmer and Ron Etter who have kept me on
track, I am grateful for all of your unique perspectives, insights and encouraging feedback which
have been fundamental to this dissertation as well as my professional development.
Thank you to my lab mates whose laughter and support I could not have survived
without. Thank you for being such great friends, always there to exchange ideas, lend a hand in
the field(ish) or with help with code. Each one of you contributes to the perfect equilibrium that
is the Gouhier lab, thank you all for keeping me sane and reminding me not to take myself too
seriously. May we continue to share pop-culture themed RColorBrewer palettes until the end of
days.
I’d like to express my gratitude to the Marine Science Center community, staff and
faculty both past and present. Each one of you has played a part in getting me to the finish line
and I truly value the hard work that goes into facilitating all the great research and education
coming out of the MSC that I have been so grateful to be a part of.
Finally, my deepest gratitude to my husband who has been patient and endlessly
supportive throughout the trials and tribulations that come along with a dissertation. I promise I
won’t do this again.
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Abstract of Dissertation
Identifying the relative influence of ecological and environmental processes on ecosystem
structure remains a challenge. This is partly because the inherent stochasticity and complexity of
nature, the product of multiple processes operating at different temporal and spatial scales, have
made it difficult to identify general rules that govern the assembly and dissolution of ecosystems.
Conversely, these same attributes have inspired a vast amount of theoretical and empirical
investigations of these natural systems, spanning multiple temporal and spatial scales. This
project is motivated by such seminal work and aims to combine both theoretical and empirical
tools to add to our understanding of the drivers of spatiotemporal dynamics in a changing world.
Through a combination of mathematical models, computer simulations and statistical analyses on
long-term ecological time series, this body of work aims to understand the nonlinearities of
marine systems across spatial scales. Specifically, this project investigates the mechanisms
governing community structure across spatial scales and examines the effects of interacting
ecological processes in complex and interconnected ecosystems in an era of global change. The
models developed for this thesis reveal the relative importance of dispersal, species interactions,
environmental heterogeneity as well as highlight the potential vulnerability of ecosystems to
climate change, and thus be a valuable extension to current forecasting methods and may provide
useful implications for the conservation and management of marine ecosystems.
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Table of Contents
Dedication 2
Acknowledgements 3
Abstract of Dissertation 4
Table of Contents 5
List of Figures 7
List of Tables 8
Introduction: The complexity of natural systems 9
Literature Cited 13
Chapter 1: Multifactorial effects of dispersal in an environmentally forced 18
metacommunity
Abstract 18
Introduction 19
Materials and Methods 23
Results 29
Discussion 36
Literature Cited 43
Tables 49
Figures 50
Chapter 2: Coexistence mechanisms collide across scales 54
Abstract 54
Introduction 55
Materials and Methods 58
Results 62
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Table of Contents (continued)
Discussion 65
Literature Cited 69
Figures 73
Chapter 3: Coastal upwelling generates cryptic temperature refugia 76
Abstract 76
Introduction 77
Materials and Methods 81
Results 87
Discussion 92
Literature Cited 98
Tables 104
Figures 106
Conclusions and Recommendations 111
Literature cited 114
Appendices 115
Appendix 1.1: Mechanistic schematics
Appendix 1.2: Robustness of metacommunity model results to 116
environmental stochasticity
Appendix 1.3: Robustness of metacommunity model results to 121
covariation in advection and diffusion rates
Appendix 3.1: Wavelet analysis 125
Appendix 3.2: Permutation-based ANCOVA tables 133
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ListofFigures
Chapter 1: Multifactorial effects of dispersal in an environmentally forced metacommunity
1.1. Metacommunity species richness at multiple spatial scales as a function of dispersal advection (a) and diffusion (b) for different environmental gradients
1.2 Species rank abundance as a function of dispersal advection rate (a) and diffusion rate (b)
1.3 Variation partitioning of community structure as a function of dispersal advection rate (a-c) and diffusion rate (d-f)
1.4 Variation partitioning results for an intertidal metacommunity
Chapter 2: Coexistence Mechanisms collide across scales
2.1 Schematic diagram of the spatially-explicit metacommunity model
2.2 Metacommunity species richness at multiple spatial scales as a function of dispersal diffusion and recruitment facilitation 2.3 Species extinction risk as function of dispersal rate
Chapter 3: Coastal upwelling generates cryptic temperature refugia
3.1 Hierarchicalclusteringofcorrelationsofwatertemperaturefrom timeseriesacross16sites 3.2 Hierarchicalclusteringofcorrelationsofwaveletpowerextracted fromwaveletanalysisacross16sites. 3.3 Timeseriesandscaleaveragedwaveletpowerfordailymicrohabitat watertemperatureforallsites. 3.4 Correlationasafunctionofdistance.Pairwisecomparisonsbetween siteswithintheCanaryCurrentSystem. 3.5 Coherenceandphasedifferenceasafunctionofdistance.
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ListofTables
Chapter 1: Multifactorial effects of dispersal in an environmentally forced metacommunity
1.1. ANOVA:effectsofpelagiclarvalduration(PLD)andzone onthespatialfraction
Chapter 3: Coastal upwelling generates cryptic temperature refugia
3.1 Kendall’scoefficientofconcordance(W)measuringdegreeof synchronybetweensites
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INTRODUCTION
Thecomplexityofnaturalsystems Complexity and variability are quasi-ubiquitous features of natural ecosystems that make it
difficult to link patterns and processes across scales. This inherent ecological complexity is the
product of multiple processes operating at different temporal and spatial scales. A central goal of
ecology is to reduce this complexity by partitioning the relative importance of processes
occurring at regional scales (e.g., landscape connectivity) and local scales (e.g., species
interactions)(Levins and Culver 1971, Peres-Neto and Legendre 2010, Dray et al. 2012).
Although abiotic processes are often thought to act at larger scales than biotic processes
(Chase and Leibold 2003, Boulangeat et al. 2012, Vellend et al. 2014), mapping abiotic and
biotic processes to specific spatial scales remains a hotly debated issue (Levin 1992, Cowen and
Sponaugle 2009, Christian Hof et al. 2011, Araújo and Rozenfeld 2014). Some theories suggest
that hierarchical or scale-dependent approaches are most useful for mechanistically linking
ecological patterns and processes(Willis and Whittaker 2002, Pearson and Dawson 2003, McGill
2010), while others advocate for the use of metacommunity theory to examine the interactions
between local and regional processes (Menge and Olson 1990, Leibold et al. 2004, Guichard
2005, Gotelli 2010, Gouhier et al. 2010).
Disentangling the effects of ecological and environmental drivers is even more complicated
in an era of global change because intensifying exogenous pressures can alter key processes and
cause both non-stationary and non-linear responses in ecosystems (Fridley et al. 2007, Baskett et
al. 2010, Amarasekare and Savage 2012, White et al. 2013, Andrello et al. 2015). For instance,
changes in climate are expected to have pronounced effects on seawater temperature leading to
changes in seasonality and patterns of connectivity in marine systems (Munday et al. 2009,
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Schiffers et al. 2013, Gerber et al. 2014, Andrello et al. 2015). Even slight fluctuations of this
type could create phenological mismatches, often resulting in deleterious ecological
consequences such as the observed seasonal disparity between larval release and resource
availability (Harley et al. 2006, Kordas et al. 2011, Francis et al. 2012). Anthropogenic impacts,
such as overharvesting or coastal development will only exacerbate these anticipated
consequences (Halpern et al. 2007, Condon et al. 2011, Roux et al. 2013, Watson et al. 2015,
Scyphers et al. 2015).
This dissertation aims to gain fundamental understanding of the mechanisms driving
biodiversity (chapter 1), coexistence (chapter 2) and environmental refugia (chapter 3) across
spatiotemporal scales. Together, these chapters provide critical insights about the assembly and
functioning of marine metacommunities in an era of global change.
Conceptual background: intertidal ecosystems as a model system
Intertidal ecosystems are ideal for developing and testing metacommunity theory because their
functioning has been linked to processes operating at multiple scales (Menge and Sutherland
1976, 1987, Lubchenco and Menge 1978, Menge 1978, 1992, Lubchenco 1980). Specifically,
local processes such as competition for space and predator prey dynamics work in concert with
regional processes including dispersal and environmental variability to modify community
assembly (Lubchenco and Menge 1978, Menge 1995, Bryson et al. 2014). Due to their location
at the interface of marine and terrestrial environments, intertidal ecosystems experience strong
differences in water and air temperature, desiccation stress and productivity along a well-defined
gradient of zonation. Environmental factors such as aerial and water temperature extremes have
been suggested as drivers of the upper range limits for intertidal species (Menge and Sutherland
1976, Harley and Helmuth 2003, Stickle et al. 2017), whereas ecological factors such as
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competition and predation have been associated with lower intertidal range limits (Connell 1961,
Lubchenco and Menge 1978, Sorte et al. 2017). Additionally, the rocky intertidal is composed
primarily of ectothermic invertebrates, many of which are sessile with characteristic pelagic
larval stages, during which the larvae can be transported over large distances by strong nearshore
currents (Siegel et al. 2003, Kinlan and Gaines 2003). These traits make these species
particularly sensitive to environmental perturbations such as temperature fluctuations, increased
pH and nutrient availability (Incze et al. 2010). For instance, recent work has shown that the Gulf
of Maine (GoM) is a ‘hotspot’ of change, with the sea surface temperature having risen faster
than 99.9% of the world’s oceans (Pershing et al. 2015). Although intertidal ecosystems are a
well-studied system, many questions remain regarding how the dynamics of community
composition and the processes that govern them will respond to a changing climate (Morrison et
al. 2012, Bryson et al. 2014, Sorte et al. 2017, 2018).
Significance of project
The overarching goal of this dissertation is to gain mechanistic insights about the spatiotemporal
dynamics that govern ecosystems in a changing world. In combining mathematical models,
computer simulations and statistical analyses on long-term ecological time series, this body of
work aims to disentangle the relative influence of environmental and ecological processes on the
dynamics of marine ecosystems. Incorporating empirical data from multiple long-term datasets
from intertidal systems on the East (Gulf of Maine) and the European Atlantic Coast (Canary
Current System), to parameterize and validate my models as well as conducting model
comparisons and analyzing model outputs has contributed to the identification of strengths and
limitations of some commonly used statistical frameworks. Specifically, this work addresses
prevailing scale-dependent/linear decomposition approaches commonly used to study ecological
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phenomena, which may not always capture the ubiquitous spatial heterogeneity and
nonlinearities found in nature, by making direct comparisons to cross-scale/nonlinear
frameworks.
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CHAPTER 1
The multifactorial effects of dispersal on biodiversity in environmentally forced
metacommunities
ABSTRACT
Disentangling the effects of dispersal and environmental heterogeneity on biodiversity is a
central goal in ecology. Although metacommunity structure can be partitioned into spatial and
environmental fractions, it remains unclear whether these statistical results can be used to infer
the relative importance of dispersal-limitation (spatial fraction) and environmental-forcing
(environmental fraction). Using an environmentally-forced spatially-explicit metacommunity
model, we show that the distinct effects of the mean (advection) and the standard deviation
(diffusion) of the dispersal kernel on biodiversity are not easily detectable via variation
partitioning alone. Although increasing dispersal ultimately leads to a decrease in the spatial
fraction due to reduced dispersal-limitation and greater species-sorting, the magnitude of the
spatial fraction depends on the complex interplay between the nature of dispersal and the type of
boundary conditions in the metacommunity. Indeed, metacommunities characterized by either
high or low dispersal can exhibit a small spatial fraction. A case study of a marine
metacommunity experiencing strong alongshore transport is consistent with these findings, as the
size of the spatial fraction is not associated with dispersal. Overall, our results suggest that
accounting for the nature of environmental-forcing as well as the multifactorial effects of
dispersal is critical for understanding how ecological and environmental processes give rise to
biodiversity across spatial scales.
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INTRODUCTION
Species abundance distributions are driven by a combination of abiotic and biotic processes
operating at multiple spatial and temporal scales (Leibold et al. 2004, Holyoak et al. 2005).
Although uncontroversial today, this synthetic perspective evolved from ardent and recurring
debates about the relative influence of biotic (Elton 1927, Nicholson 1933) and abiotic (Grinnell
1917, Davidson and Andrewartha 1948, Andrewartha and Birch 1954) processes on patterns of
species diversity and population dynamics (reviewed by Coulson et al. 2004). For instance,
pioneering work by Grinnell (1917) showed that species often ‘track’ the geographical
distribution of environmental conditions that characterize their habitat. In doing so, the
Grinnellian niche perspective emphasized the importance of environmental heterogeneity as a
driver of species abundance. This purely abiotic definition of the niche, which suggested a
unidirectional effect of the environment on species, was later extended by Charles Elton, who
highlighted the importance of biotic processes and the reciprocal feedbacks between species and
their environment in dictating community structure (Elton 1927). A similar but more
acrimonious argument emerged about the drivers of population dynamics, with Andrewartha and
Birch (1954) championing the role of density-independent abiotic factors such as temperature
and Nicholson (1933) arguing for the dominance of density-dependent biotic interactions such as
competition.
Although these debates initially focused on the relative importance of biotic and abiotic
processes at local scales, the role of regional factors such as dispersal began to garner greater
attention following the development of island biogeography (MacArthur and Wilson 1967). By
modeling how species diversity on islands could depend on the balance between regional
immigration from the mainland and local extinction rates, MacArthur and Wilson laid the
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foundation for metacommunity theory (Levins and Culver 1971, Hastings 1980, Tilman 1994), a
framework which depicts ecological systems as sets of discrete communities of interacting
species linked by dispersal (Leibold et al. 2004, Holyoak et al. 2005). Metacommunities are thus
ideal for understanding how biotic and abiotic processes operating at multiple scales interact to
give rise to patterns of biodiversity.
Modern theory has identified four main metacommunity ‘perspectives’ based on the relative
influence of local vs. regional (a)biotic factors on the distribution of species (Leibold et al. 2004,
Holyoak et al. 2005). The patch dynamic perspective stresses the importance of tradeoffs
between local and regional biotic processes as the drivers of community structure (Levins and
Culver 1971, Tilman 1994). For instance, an interspecific competition-colonization tradeoff can
allow an arbitrary number of species to persist on a single resource in a spatially-structured but
environmentally-homogeneous habitat (Tilman 1994). On the other hand, the species sorting
perspective focuses on the effect of spatial environmental heterogeneity in dictating the
distribution of species. Specifically, by assuming that dispersal allows species to reach patches
characterized by their preferred environmental conditions, this perspective emphasizes niche
separation due to local competitive exclusion over spatial rescue effects (Leibold et al. 2004,
Holyoak et al. 2005). The mass effects approach also considers patches to be environmentally-
heterogeneous but assumes that dispersal is sufficiently high to generate spatial dynamics that
override local competitive exclusion (Leibold et al. 2004, Holyoak et al. 2005). Indeed, when
dispersal is high, the movement of individuals from ‘source’ patches characterized by good
environmental conditions can allow species to persist in ‘sink’ patches characterized by poor
environmental conditions (Pulliam 1988, Amarasekare and Nisbet 2001, Holyoak et al. 2005).
Such source-sink dynamics can alter patterns of biodiversity in metacommunities (Mouquet and
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Loreau 2003) and erode the relationship between spatial environmental heterogeneity and the
distribution of species. Finally, the neutral perspective, which often serves as a null model,
assumes that all individuals are demographically equivalent and that community composition is
driven by the combination of limited dispersal and ecological drift (Hubbell 2001).
The metacommunity perspectives outlined above have provided the foundation for recent
theoretical developments identifying multiple dispersal-based coexistence mechanisms. These
coexistence mechanisms all rely on distinct connectivity patterns arising from interspecific
differences in spawning time, dispersal ability or dispersal direction. For instance, interspecific
differences in dispersal ability (Bode et al. 2011) or asymmetrical connectivity patterns
(Salomon et al. 2010) can promote coexistence between competing species when environmental
conditions are spatially-homogeneous. Interspecific differences in temporal variability have also
been identified as a coexistence mechanism in spatially-homogeneous environments (Berkley et
al. 2010). Here, differences in spawning time coupled with temporal variability in dispersal can
promote coexistence by creating ephemeral spatiotemporal niches that promote the long-term
coexistence of competing species (Berkley et al. 2010). Finally, Aiken and Navarrette (2014)
extended the results of Berkley et al. (2010) and Salomon et al. (2010) by showing that
differences in the dispersal properties of subordinate and dominant species could promote
coexistence in competitive metacommunities.
Although metacommunity theory has defined different perspectives based on the relative
importance of dispersal and environmental heterogeneity as drivers of biodiversity, testing this
theory will require identification of statistical signatures of these underlying mechanisms in
observational data. However, given the necessary scope and scale, it is logistically impractical to
conduct manipulative experiments in order to identify the drivers of metacommunity structure in
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the real world. One promising solution to this vexing problem is variation partitioning, a
statistical technique commonly used to decompose community variation into spatial and
environmental fractions (Borcard et al. 1992, 2004, Peres-Neto et al. 2006). Within this
framework, the environmental fraction essentially measures the degree of correlation between
local species abundances and abiotic factors such as temperature or rainfall. The spatial fraction
largely represents the ‘residual’ spatial variation in community structure not explained by the
abiotic factors. The size of the spatial fraction is most commonly interpreted as the effect of
dispersal, or more specifically, the degree of dispersal-limitation, where low dispersal rates or
geographical barriers can prevent species from reaching patches characterized by their optimal
environmental conditions (Cottenie 2005, Flinn et al. 2010, Tuomisto et al. 2012). Although this
statistical framework is powerful, there is still considerable debate about how to interpret the
‘spatial’ and ‘environment’ fractions in an ecologically meaningful way (Cottenie 2005, Gilbert
and Bennett 2010, Tuomisto et al. 2012, Legendre and Gauthier 2014). For instance, in analyses
of empirical and simulated data sets, dispersal limitation can lead to both large and small spatial
fractions (i.e., high and low ‘residual’ spatial variation in community structure respectively)
(Cottenie 2005, Gilbert and Bennett 2010). Hence, bridging the gap between metacommunity
theory and variation partitioning by identifying statistical signatures of biological and
environmental factors will promote our ability to predict and manage the dynamics of complex
and interconnected ecosystems.
Here, we use spatially-explicit models to explore the ability of variation partitioning to detect
a dispersal signal in environmentally-forced metacommunities. Specifically, we found that
although increasing advection (i.e., the mean of the dispersal kernel) or diffusion (i.e., the
standard deviation of the dispersal kernel) ultimately leads to a decrease in the spatial fraction,
23
the magnitude of the spatial fraction does not map to the dispersal rate directly. Indeed, large
spatial fractions can be associated with both high and low dispersal rates and the strength of the
environmental gradient amplifies this inconsistency. These results hold in the presence of
environmental noise as well as across a range of environmental gradients and are consistent with
observational data from an intertidal metacommunity along the West Coast of the United States.
Overall, our findings suggest that the interpretation of the spatial fraction does not map onto a
particular process, but rather depends on the complex interaction between dispersal, boundary
conditions and strength of environmental forcing.
MATERIALS AND METHODS
The model
To determine how environmental heterogeneity and different aspects of dispersal affect patterns
of species diversity and abundance, we developed a spatially-explicit metacommunity model
with lottery competition by extending Levins’ classical spatially-implicit framework (see
Appendix S1, Fig. S1; Levins 1969, Levins and Culver 1971). This type of model is well suited
for describing competition between sessile species with mobile dispersal stages in both terrestrial
(e.g., plants; Tilman 1994, Mouquet and Loreau 2003) and aquatic ecosystems (e.g.,
invertebrates; Gouhier et al. 2010b, 2011). Each metacommunity consists of L distinct sites
linked by propagule dispersal, a process that determines each of the S species’ potential
recruitment according to a Gaussian kernel whose advection and diffusion rates can be specified
(Appendix 1.1, Fig. S1.1c,d). Although all species share the same dispersal kernel, their realized
recruitment patterns depend on the match between a site’s environment and each species’
physiological requirements, depicted by a Gaussian distribution around an optimal
environmental value (Appendix 1.1, Fig. 1.1b). Environmental heterogeneity was implemented
24
as a simple linear gradient (Appendix 1.1, Fig. 1.1a). These processes were modeled using the
following set of coupled ordinary differential equations, which track the abundance 𝑁" of each
species i at site x along a one-dimensional array of size L:
d#$(&)d(
= 𝑟"(𝑥)𝐹(𝑒(𝑥), 𝑜")01 − ∑ 𝑁4(𝑥)5467 8 − 𝑚"𝑁"(𝑥) (Eq. 1)
Here, the first term on the right hand side represents the realized recruitment rate of species i at
site x, the second term in parentheses represents lottery competition for space, and the third term
represents species-specific background mortality. The realized recruitment rate is the product of
each species’ potential recruitment rate 𝑟"(𝑥) and survivorship F in that environment 𝑒(𝑥). The
potential recruitment rate 𝑟"(𝑥) is the convolution of the product of propagule production 𝑝"(𝑦)
and density 𝑁"(𝑦) at each source site y with the dispersal kernel k(x) at destination site x:
𝑟"(𝑥) = ∫ 𝑝"(𝑦)𝑁"(𝑦)𝑘(𝑥 − 𝑦)d𝑦?/AB?/A (Eq. 2)
Thus, the term 𝑟"(𝑥) denotes the total number of recruits arriving at each destination site x from
all other source sites y via dispersal. The dispersal kernel itself is a normalized Gaussian
distribution (i.e., sums to 1) with mean μ and standard deviation σ (Siegel et al. 2003):
𝑘(𝑥) = 7C√AE
𝑒B(FGH)I
IJI (Eq. 3)
Where μ represents alongshore advection and σ represents diffusion. We manipulated both μ and
σ independently for each simulation, allowing us to control the extent (advection) and scale
(diffusion) of dispersal. Each species’ propagule survivorship is represented by a Gaussian curve
centered around a species-specific environmental optimum 𝑜" (Appendix 1.1, Fig. 1.1b) such that
survivorship F of species i at site x is:
𝐹(𝑒(𝑥), 𝑜") = 𝑒B0K(F)GL$8
I
I
(Eq. 4)
25
Hence, the smaller the difference between a species optimum and the environment, the greater its
propagule survivorship and realized recruitment rate.
Spatial environmental variation was modeled using a simple linear gradient:
𝑒(𝑥) = M 𝑢𝑥 if𝑥 ≤ 𝐿/2−𝑢𝑥 if𝑥 > 𝐿/2 (Eq. 5)
Here, 𝑢 represents the slope of the linear environmental gradient. We simulated 10 different
levels of 𝑢 ranging from 0.02 to 0.16 in order to determine the robustness of our results to the
strength of the environmental gradient. We also ran additional simulations that included random
noise affecting local environmental conditions 𝑒(𝑥) within each site x using a white noise
(spatially-uncorrelated) process to determine the robustness of our results to different levels of
environmental stochasticity (See Appendix 1.2):
𝑒(𝑥) = 𝑢𝑥 + 𝑣(𝑥) (Eq. 6)
Here, 𝑣(𝑥) represents environmental stochasticity via a random deviate drawn from a normal
distribution with a mean of zero and a standard deviation ranging from 0 (no noise) to 1 (high
noise). Running simulations for 10 uniformly-spaced standard deviations between 0 and 1
allowed us to determine the robustness of our model results to variation in the linearity and
stochasticity of the environmental gradient (Appendix 1.2).
Model simulations
The model equations were solved numerically using an explicit Runge-Kutta (4, 5) formula in
MATLAB (function ode45) for 2,000 time steps. The metacommunity consisted of S = 20
species competing across L = 140 sites (absorbing boundary conditions) or L = 100 sites
(periodic boundary conditions). We varied the dispersal advection and diffusion rates
independently to simulate the dynamics of species ranging from direct developers, whose
propagules remain in their natal site (i.e., zero advection and diffusion), to long-distance
26
dispersers (i.e., high advection or diffusion). For simulations manipulating the advection rate 𝜇,
the diffusion rate was fixed at 𝜎 = √10. For simulations manipulating the diffusion rate 𝜎, the
advection rate was fixed at 𝜇 = 0. We followed existing approaches (e.g., Mouquet and Loreau
2003) and used our model to simulate the simplest and most generic metacommunity scenarios.
Specifically, initial abundances for all species were random across all sites, the same dispersal
kernel was used for each species and the propagule production rates 𝑝" were randomly selected
from a uniform distribution with a minimum value of 5 and a maximum value of 10. The
mortality rates 𝑚" were selected so that each species had the same production-to-mortality ratio
𝑝"/𝑚" in order to ensure coexistence in the absence of environmental heterogeneity and
dispersal. Additionally, each species’ environmental optimum 𝑜" was selected randomly from a
uniformly-spaced vector of 20 values ranging from the minimum to the maximum environmental
condition 𝑒(𝑥). Overall, adopting this approach allowed us to generate baseline and system-
agnostic results. Simulations were run under one of two scenarios to explore the effects of
boundary conditions. First, we used absorbing boundary conditions to simulate a finite-size
linear environment where propagules are able to leave the system. Second, we used periodic
boundary conditions to simulate an infinite-size environment without edge effects (e.g., Gouhier
et al. 2010a, 2010b, 2013). Here, the linear environmental gradient was thus altered in order to
avoid sudden spatial discontinuities at the ends of the spatial domain. Specifically, the
environmental gradient in our simulations increases linearly with slope u from the beginning of
the spatial domain (i.e., site 1) to the middle (i.e., site 50) and then decreases linearly from the
middle to the opposing end of the spatial domain (i.e., site 100) with slope -u. This ensures the
two ends of the spatial domain (sites 1 and 100), which are in fact nearest neighbors under
periodic boundary conditions, experience similar environmental conditions. To test the
27
robustness of the model results to covariation in advection and diffusion, we also ran additional
simulations where both aspects of dispersal (advection, diffusion) covaried as predicted under
climate change (e.g., Gerber et al. 2014; see Appendix 1.3). All analyses were performed on final
species abundances. Species whose final local abundances were lower than 10-8 were considered
to have gone extinct.
Model analysis
The model results were analyzed using two complementary approaches. First, we used species’
presence/absence information to partition biodiversity into local (α), between-community (β),
and regional (γ) diversity using standard methods (Whittaker 1972, Mouquet and Loreau 2003).
Here, regional diversity γ was measured as the total species richness across the entire
metacommunity, local diversity α was measured as the average species richness within each site,
and between-community diversity β was measured as the difference between regional and local
diversity. Second, we used partial redundancy analysis (RDA) to partition species abundances
across the metacommunity into their spatial (S|E), environmental (E|S), and shared (EÇS)
fractions (Borcard et al. 1992, 2004, Peres-Neto et al. 2006). This was achieved by relating the
matrix of species abundances Y to (i) the environmental matrix X1, which consisted of the
variables that characterized the environmental gradient, and (ii) the spatial matrix X2, which was
created via a spectral decomposition of the spatial structure of the metacommunity using the
principle coordinates of neighboring matrices (PCNM) method (Borcard et al. 2004). The
environmental fraction E|S thus represents the spatial variation in community structure that is
strictly due to the environment whereas the spatial fraction S|E represents the ‘residual’ spatial
variation in community structure that cannot be explained by the environment. This method is
particularly powerful because it can partition the spatial and environmental fractions of
28
metacommunity structure even when the shared fraction EÇS is large because the environment is
spatially-structured (Borcard et al. 1992, 2004, Peres-Neto et al. 2006). This is important given
that the environment is strongly spatially-structured in both our simulations and our test system,
the intertidal metacommunity along the West Coast of the US (Gouhier et al. 2010).
Empirical case study
We used community data from the rocky intertidal along the West Coast of the United States
(Schoch et al. 2006, Russell et al. 2006, Gouhier et al. 2010) to determine the empirical
relationship between the spatial fraction and dispersal. This is an ideal test system because it is
characterized by (i) strong latitudinal environmental gradients in sea surface temperature,
primary production and upwelling (Menge et al. 2004, Gouhier et al. 2010b, Menge and Menge
2013), and (ii) the relatively rapid southward advective California Current (Hickey 1979, Huyer
1983, Largier et al. 1993). Data were collected annually from 2000 to 2003 at 48 sites ranging
from southern California to northern Washington (32.7°N to 48.4°N). Community structure was
determined by averaging the abundance of each species across 10 randomly-placed 0.25m2
quadrats along 3-4 random transects at each site for the low, mid and high zone (see details in
Gouhier et al. 2010). Environmental variables included chlorophyll-a concentration (chl-a, in
mg/m3), upwelling index (m3/s/100 m of coastline) and mean annual sea surface temperature
(SST, in °C). Data were obtained from the sea-viewing wide field of view sensor (SeaWiFS;
NASA), sea level pressure maps (Pacific Fisheries Environmental Laboratory) and from a high-
resolution radiometer (NOAA), respectively (see Gouhier et al. 2010). Pelagic larval duration
(PLD) is commonly used as a proxy for dispersal ability for sessile marine organisms, as directly
assessing larval movement remains a challenge (Shanks et al. 2003, Siegel et al. 2003, Shanks
2009, Selkoe and Toonen 2011). For our empirical test, we used this approach to split the species
29
found in our surveys into four distinct groups based on their dispersal potential: direct developers
(0 days), low PLD (~8 days), intermediate PLD (~ 21 days) and high PLD (~ 70 days). We
conducted variation partitioning for each group of species across all zones in this empirical
dataset to determine the size of the spatial and environmental fractions. The approach we used
was identical to the one used for the model simulations, where species abundances across the
metacommunity were partitioned into their spatial (S|E), environmental (E|S), and shared (EÇS)
fractions (Borcard et al. 1992, 2004, Peres-Neto et al. 2006).
RESULTS
Patterns of biodiversity
We begin by analyzing the closed version of the metacommunity model (i.e., self-recruitment
only). Under this scenario, the following relationship between all pairs of species {𝑖, 𝑗} must hold
for coexistence to occur at equilibrium:
\$(&)]$(&)^(_(&),`$)
= \a(&)
]a(&)^(_(&),`a) (Eq. 7)
The ratio of mortality to realized recruitment must thus be identical across all species in order
for coexistence to occur within each site x. Hence, in the absence of dispersal, an arbitrary
number of species can coexist via a fitness equalizing tradeoff between mortality and realized
recruitment (sensu Chesson 2000). Because any species with a higher ratio is expected to
competitively exclude all other species locally, environmental heterogeneity promotes species-
sorting by generating low within-site diversity α, high between-site diversity β, and maximizing
regional diversity γ (Fig. 1a, b, dispersal advection and diffusion rates = 0). This is because each
species essentially monopolizes the site whose environmental conditions are closest to its
optimum.
30
In general, the introduction of dispersal between sites generates the species diversity patterns
commonly described in the literature (Mouquet and Loreau 2002, 2003, Shanafelt et al. 2015,
Thompson and Gonzalez 2016). Here, the type of dispersal (advection vs. diffusion) and the
nature of the boundary conditions (absorbing simulating a finite-size linear environment vs.
periodic simulating an infinite-size environment) determine the structure of biodiversity in the
metacommunity. As species are subject to the same linear gradient under each scenario
(absorbing or periodic), differences only occur at high dispersal rates, which lead to lower
recruitment rates (due to greater propagule loss) with absorbing boundary conditions and higher
recruitment rates with periodic conditions, as species are able to reach parts of the spatial domain
that are similar to their optimal environmental condition. Overall, the shapes of the species
diversity curves are largely driven by the nature of dispersal whereas the heights of the curves
are mediated by the boundary conditions (Fig. 1). In the absence of dispersal, our simulations
confirm our analytical results: self-recruitment generates a strong positive local feedback
between adult abundance and propagule production that promotes species abundance in sites
characterized by their optimal environmental conditions (Fig. 1). This promotes competitive
exclusion and species sorting, which lead to low local diversity (α), high between-community
diversity (β) and high regional diversity (γ). Increasing dispersal (0 <μ < 3, 0 < σ < 5) reduces the
degree of self-recruitment and species sorting by generating a positive regional feedback
between sites via spatial rescue effects (Brown and Kodric-Brown 1977). This leads to an
increase in local diversity, a sharp reduction in between-community diversity, and a moderate
decline in regional diversity (Fig. 1a-d). Further increasing dispersal (μ, σ ≈ 5, 30) spatially-
homogenizes the metacommunity, destroys all spatial rescue effects, and reduces diversity at all
31
scales as regionally dominant species are able to competitively exclude most species across the
metacommunity (Fig. 1a-d).
For advective dispersal, local diversity is thus maximized at intermediate rates when
advection is high enough to promote spatial rescue effects but not so high as to prevent self-
recruitment. Indeed, high advective dispersal rates will spatially couple distant sites experiencing
different parts of the environmental gradient, so a species growing in a site characterized by good
environmental conditions will receive relatively few recruits from unproductive sites
experiencing poor environmental conditions. Hence, even if the vast majority of these arriving
recruits survive, abundance at the site experiencing good environmental conditions will be
relatively low since the supply rate will be limited. Conversely, a site characterized by poor
environmental conditions might receive a large supply of recruits from sites experiencing good
environmental conditions, but because most of those recruits will not survive, local species
abundance will also be low.
Diffusive dispersal promotes higher overall levels of species diversity by maintaining the
local positive feedback between abundance and recruitment as the dispersal kernel remains
centered on the natal site. Hence, self-recruitment can allow species in sites experiencing good
environmental conditions to establish larger populations and subsequently subsidize populations
at sites experiencing poor environmental conditions via source-sink dynamics (Pulliam 1988). At
higher dispersal rates, these mass effects allow for increased abundances for species in non-
optimal environments. While these patterns hold regardless of the strength of the environmental
gradient (Fig. 1a-d), differences in the diversity-dispersal relationship emerge in
metacommunities with absorbing vs. periodic boundary conditions (Fig.1 a,b vs. c,d).
32
Diversity levels are generally higher under periodic than absorbing boundary conditions
because under the latter, all species experience an effective reduction in their recruitment rates as
propagules are lost from the metacommunity (Fig. 1). This is particularly true when increasing
advective versus diffusive dispersal, which increases the rate at which propagules are whisked
away from the metacommunity (Fig. 1a,c vs. Fig. 1b,d). Regional diversity is driven by between-
community diversity (β) at low dispersal in metacommunities with absorbing boundary
conditions, as spatial rescue effects allow most species in the metacommunity to persist.
Intermediate rates of advection (Fig. 1a,b: μ, σ = 6, 10) reduce regional species diversity by
replacing the local positive feedback between abundance and self-recruitment in closed
communities with a regional negative feedback that allows the same set of regionally-dominant
species (species with higher regional- scale realized recruitment rate F) to monopolize the
metacommunity regardless of local environmental conditions. In doing so, advection shifts
control of regional diversity (γ) from between-community (β) to local (α) diversity. Additionally,
the negative regional feedback generates relatively uniform abundances for the few regionally-
dominant species across the entire range of dispersal advection (Fig. 2a; μ > 5).
Initially, similar trends appear in metacommunities characterized by periodic boundary
conditions (Fig. 2c,d). Low levels of diffusive dispersal promote spatial rescue effects and
spatially homogenize the metacommunity, thus allowing local diversity (α) rather than between-
community diversity (β) to dictate regional diversity (γ). Intermediate rates of diffusive dispersal
fully spatially homogenize the metacommunity, thus promoting competitive exclusion.
Interestingly, further increasing diffusion leads to an additional peak in both local and regional
diversity (σ ~ 10 – 30, depending on environmental gradient). Here, species are able to persist in
more locations throughout the metacommunity due to an environmental rescue effect whereby a
33
portion of the propagules produced in optimal natal sites arrive in equivalently optimal sites far
from their origin. This secondary match between a species’ physiological optima and the local
environment creates a boost in fitness resulting in the resurgence of rare species (Fig. 2d). Hence,
the primary peak in species diversity due to spatial rescue and the secondary peak in species
diversity due to environmental rescue yield fundamentally different patterns of community
structure, with the former being characterized by a more uniform species abundance distribution
(many abundant species) and the latter a skewed species abundance distribution (many rare
species; Fig. 2d).
This environmental rescue occurs at diffusion rates where dispersal is strong enough to
dampen spatial rescue effects, but not strong enough to homogenize the whole system, thus a
secondary peak in diversity exists for all environmental gradients. For weaker gradients (slopes
of 0.02 to 0.05), the secondary peaks in local and regional diversity emerge at lower levels of
diffusion because it is easier for dispersal to spatially homogenize a system that is less
environmentally heterogeneous (Fig. 1d). Hence, we expect that the second peak should shift to
the left (to lower diffusion rates) with decreasing environmental variation slopes (i.e., weaker
environmental gradients). Conversely, increasing the slope of the environment leads to the
occurrence of an increasingly distinct secondary peak at higher diffusion rates.
Patterns of metacommunity structure
We applied variation partitioning to the model output in order to determine how different levels
of dispersal advection and diffusion affect the ecological interpretation of the spatial and
environmental fractions in metacommunities with either absorbing or periodic boundary
conditions. In environments characterized by either absorbing and periodic boundary conditions,
increasing the advection (μ) or the diffusion (σ) rate ultimately decreases the spatial fraction by
34
allowing species to increasingly find and monopolize the sites characterized by their optimal
environmental conditions (Fig. 3). Regardless of the nature of dispersal or the boundary
conditions, the introduction of dispersal promotes spatial rescue effects that erode the
relationship between the environment and community structure, resulting in a spatial fraction
explaining as much as 90% of the total variation in community structure. Despite these general
similarities, there are key differences in the effect of increased dispersal on the spatial fraction
that depend on the boundary conditions and the nature of dispersal.
For absorbing boundary conditions, increasing either aspect of dispersal (advection or
diffusion) beyond the levels required for spatial rescue generally promotes species sorting which,
in effect, reduces the spatial fraction. However, as previously stated, a few regionally dominant
species dominate regardless of environmental conditions, so the spatial fraction never explains
less than 40% of the total variation in community structure regardless of the extent of dispersal
(Fig. 3c,f).
Conversely, under periodic boundary conditions, increasing advection versus diffusion has
different effects on the sign and the magnitude of the change in the spatial fraction. The most
discernible difference between the advection and diffusion appears at low levels of dispersal
(Fig. 3; i vs. l: 0 < μ, σ < 8). Initially, increasing the dispersal advection rate increases the spatial
fraction, with space explaining anywhere from 40 to 100% of the variation in community
structure, whereas increasing the diffusion rate causes a reduction in the variation explained by
the spatial fraction from 80 to less than 10% depending on strength of the gradient. Increasing
the dispersal advection rate creates a spatial lag between local environmental conditions and their
effects on recruitment and community structure. This spatial lag disrupts the local positive
feedback between abundance and self-recruitment, replacing it with a regional negative feedback
35
that erodes the correlation between environmental conditions and community structure and thus
increases the spatial fraction (Fig. 3i). Apart from the initial increase under advective dispersal,
the predominant trend is a reduction in the spatial fraction. This decrease begins at intermediate
dispersal rates (μ > 8), which lead to spatial homogenization and the loss of spatial rescue
effects. The spatial fraction remains high relative to the spatial fraction observed under diffusive
dispersal because species are less able to exploit the periodicity of the environment and do not
experience environmental rescue, resulting in the presence of a few regionally dominant species,
as in absorbing conditions.
Under diffusive dispersal, the initial decrease in the spatial fraction is a consequence of high
species sorting, where species are able to reach their environmental niche and exclude their
inferior competitors locally (Fig. 3l). As the diffusion rate increases, environmental rescue
increases the degree to which species are able to persist at (multiple) optimal locations,
effectively increasing the variation explained by the environment and further reducing the spatial
fraction. Overall, these results demonstrate that altering the rates of advective vs. diffusive
dispersal can lead to very different patterns of spatial variation in community structure under
periodic boundary conditions.
Empirical case study
To test our model predictions, we applied variation partitioning to a dataset containing
abundances of rocky intertidal species in the high, mid and low zone along the West Coast of the
United States. Species were grouped based on their pelagic larval duration (PLD), which served
as a proxy for dispersal ability (Shanks et al. 2003, Shanks 2009, Selkoe and Toonen 2011). This
case study shows that the spatial fraction can map to different PLD values (Fig. 4). Indeed, we
found no relationship between the spatial fraction and the community’s mean group PLD
36
(ANOVA; df = 3, F = 2.498, p-value = 0.07518; Table 1, Fig. 4) and a significant interaction
between PLD and zone (ANOVA; df = 6, F = 4.408, p-value = 0.00194; Table 1). Hence, the
relationship between PLD and the spatial fraction depends on zone. For instance, large spatial
fractions were associated with high PLD in the low zone but low PLD in the high zone (Fig. 4).
This means that the size of the spatial fraction alone is not a reliable predictor of the extent of
dispersal. Additionally, there was a significant relationship between the spatial fraction and zone
(ANOVA; df = 2, F = 14.933, P-value < 0.0001; Table 1). Furthermore, PLD explained a smaller
proportion of the variance in the spatial fraction than zone (𝜂A = 0.075 vs. 𝜂A = 0.299, Table
1). This suggests that there are other factors affecting the size of the spatial fraction beyond
dispersal (e.g., differences in desiccation stress across zones). Overall, these empirical results are
consistent with the effects of dispersal predicted by our model: the spatial fraction is not a
measure of dispersal alone and should thus not be used as a direct proxy. Instead, one needs to
account for the strength and nature of environmental forcing as well as the type of dispersal in
order to correctly interpret the size of the spatial fraction.
DISCUSSION
Our empirical and theoretical results indicate that the effects of dispersal on patterns of species
diversity and abundance cannot easily be determined by applying statistical variation partitioning
to observational data collected across multiple scales. Indeed, although increasing dispersal
consistently leads to a reduction in the spatial fraction, as predicted by theory, this signature
trend is unlikely to be detected from statistical snapshots of observational data because the size
of the spatial fraction depends on the complex interaction between environmental heterogeneity,
boundary conditions and dispersal. Our results have important implications for managing
complex and interconnected ecosystems experiencing environmental variability.
37
The effects of dispersal on biodiversity across scales
The effects of dispersal on community stability (Holland and Hastings 2008, Gouhier et al.
2010), persistence (Huffaker 1958, Blasius et al. 1999) and biodiversity (Brown and Kodric-
Brown 1977, Tilman 1994) have been well established in theory and practice (reviewed by
Briggs and Hoopes 2004, Holyoak et al. 2005). When dispersal is too low, environmentally
heterogeneous communities become dominated by the strongest local competitors, thus
generating low local (α) diversity and high between-community (β) diversity. This type of
species-sorting is typically associated with low community stability and persistence because each
species is rare at the regional scale and thus vulnerable to the loss of the few locations where
they are found. Intermediate levels of dispersal promote both species coexistence and community
stability by allowing source-sink dynamics to emerge across the metacommunity (Mouquet and
Loreau 2003, Gouhier et al. 2010). Under this scenario, the increased movement of organisms
leads to high local diversity and low between-community diversity. Overall, these types of
spatial rescue effects will arise as long as dispersal is not high enough to fully synchronize the
dynamics of all communities. If dispersal is too high, the entire metacommunity behaves like a
single, well-mixed community with low local diversity due to competitive exclusion by the
regionally dominant species, zero between-community diversity and low stability (Mouquet and
Loreau 2003, Gouhier et al. 2010).
Our results based on manipulating dispersal diffusion rates are largely consistent with these
predictions. Increasing diffusion initially leads to high local diversity and lower between-
community diversity due to source-sink dynamics (Fig. 1b,d). Further increasing diffusion leads
to spatial-homogenization and species-sorting, with low local, between-community and regional
diversity (Fig. 1b,d). However, when environmental conditions are periodic in nature, increasing
38
diffusion even further leads to an unexpected spike of local and regional diversity by (Fig. 1d)
due to environmental rescue effects. High levels of dispersal open up the opportunity for species
to reach a secondary optimal location, promoting the persistence and subsequent resurgence of
rare species, thereby promoting both local and regional diversity. Ultimately, very high diffusion
leads to spatial homogenization and low local, between-community and regional diversity (Fig.
1d).
This dispersal-induced bimodal diversity pattern in periodic environments, which is robust to
(i) the strength of the environmental gradient (Fig. 1d) and (ii) the addition of environmental
stochasticity (Appendix 1.2), differs from the unimodal predictions based on classical theory
(Mouquet and Loreau 2003). The difference is likely due to the use of a spatially-implicit
approach by Mouquet and Loreau (2003) whereby dispersing propagules were redistributed
uniformly across the metacommunity. Hence, although they were able to manipulate the degree
of mixing by altering the dispersal rate, the scale of mixing remained constant and global. In our
spatially-explicit framework, however, varying the diffusion rate and boundary conditions alters
the degree and the scale of mixing by changing the breadth of the dispersal kernel and the
linearity of the environmental gradient. We suggest that our results stem from the simultaneous
effect of the diffusion rate on the degree of self-recruitment, the scale of dispersal and the size of
the metacommunity. Our advection results further reinforce the notion that some degree of self-
recruitment is necessary to generate the spatial rescue effects described by classical theory. We
showed a uniform reduction in local, between-community and regional diversity when dispersal
advection was sufficiently large to disrupt self-recruitment (Fig. 1a). Here, by replacing the local
positive feedback between abundance and self-recruitment with a regional negative feedback,
advection essentially reduces the fitness of all species thus resulting in all communities
39
becoming populated by the same few regional dominants. These patterns are expected to hold as
long as the advection-to-diffusion ratio is sufficiently high so as to prevent self-recruitment (see
Appendix 1.3). Overall, our results suggest that species diversity across scales and the relative
influence of local vs. regional processes depend on the complex interplay between the size of the
metacommunity, the degree of self-recruitment and spatial extent of dispersal in
environmentally-forced metacommunities.
Detecting the effects of dispersal in the real world
The impracticality of conducting manipulative experiments at the scales needed to document the
effects of dispersal on biodiversity has prompted much interest in the development of statistical
variation partitioning methods to decompose metacommunity structure into its spatial and
environmental fractions (Borcard et al. 1992, 2004, Dray et al. 2006, Peres-Neto et al. 2006).
According to these variation partition frameworks, the environmental fraction will be large if
dispersal is high enough to allow species to reach their environmental niche and exclude their
competitors at local scales (species sorting), whereas the spatial fraction will be large if dispersal
is low enough to allow spatial rescue effects without promoting local competitive exclusion
(mass effect). Hence the spatial fraction should be proportional to the degree of dispersal
limitation in the metacommunity. Although such variation partitioning methods are increasingly
being applied to empirical datasets in order to determine the relative influence of environmental
heterogeneity and dispersal on (meta)community structure in nature, the interpretation of the
spatial fraction remains controversial (Gilbert and Bennett 2010, Tuomisto et al. 2012). For
example, using simulated data, Gilbert and Bennett (2010) showed that variation partitioning
methods were unable to correctly identify the relative importance of dispersal and environmental
heterogeneity. However, their tests of variation partitioning methods were based on ‘model-free’
40
simulated data that did not incorporate the dynamical feedbacks between local competition and
regional dispersal over multiple generations.
Here, using a dynamic metacommunity model, we were able to show that dispersal advection
and diffusion leave similar yet distinct signatures that can be detected via variation partitioning
under certain scenarios. Our results extend and support the classical ecological interpretation of
the spatial fraction by showing that increasing advective or diffusive dispersal ultimately reduces
the size of the spatial fraction under both absorbing and periodic boundary conditions. Although
this trend (i.e., the negative correlation between the spatial fraction and dispersal) is clear and
consistent across all simulated scenarios, the size of the spatial fraction alone cannot be used to
infer the relative importance of dispersal because the former depends on a multitude of factors
including the strength of the environmental gradient, the nature of dispersal and the type of
boundary conditions. Our empirical results are consistent with our simulations in that the spatial
fraction varies significantly across zones, a proxy for environmental stress, but not across PLD, a
proxy for dispersal. Furthermore, the significant interaction between PLD and zone suggests that
PLD is not a consistent predictor of the spatial fraction.
Taken together, these results resolve an important discrepancy between theoretical
expectations and empirical observations: although increased dispersal will ultimately reduce the
spatial fraction (negative trend) under all scenarios, as predicted by theory, detecting this elusive
signal in nature is likely to be fraught with difficulties due to the fact that observational studies
provide snapshots of the spatial fraction rather than trends and the former are influenced not only
by dispersal, but by the strength of the environmental gradient and the nature of the boundary
conditions.
41
That being said, the more information available about the nature of dispersal and the size of
the metacommunity, the more insights can be gleaned about the mechanisms driving the patterns
in community structure. In finite-size metacommunities (simulated via absorbing boundaries and
a linear environment), the spatial fraction explains more than 40% of the variation in community
structure, suggesting that spatial rescue effects are driving coexistence patterns and diversity
levels. The added mortality associated with finite boundaries (propagules are leaving the system)
mitigates the differential impact of advective vs. diffusive dispersal on spatial community
structure. Conversely, in infinite-size metacommunities (simulated via periodic boundaries and a
periodic environment), species do not have to contend with added propagule loss, so the nature
of dispersal plays a much larger role. Here, a higher degree of self-recruitment can bolster the
ability of species to thrive locally and persist at the regional level. Thus, the mechanisms driving
the magnitude of the spatial fraction in periodic environments are the increased availability of
suitable environmental conditions and the high degree of self-recruitment due to diffusive
dispersal which, when combined, enable rare species to persist across the metacommunity via
both spatial and environmental rescue. Overall, our results suggest that although variation
partitioning methods could, in theory, be used to tease apart the relative importance of
environmental heterogeneity and dispersal on community structure, their direct applicability in
the real world is likely to be limited. Hence, while a negative relationship between dispersal and
the spatial fraction may be an indicator of increased connectivity in metacommunities, the size of
the spatial fraction alone is not sufficient to determine the extent of connectivity in natural
systems. Consequently, our results highlight the mistakes likely to be made when attempting to
infer ecological mechanisms from statistical snapshots of natural metacommunities via variation
partitioning.
42
Managing environmentally-forced and interconnected ecosystems
Metapopulation theory has long been used to inform conservation and management decisions
because of its ability to account for the effects of local and regional processes on the persistence
of species across scales (reviewed by Hanski 1998). Indeed, metapopulation theory is largely
responsible for identifying the role of connectivity in maintaining local populations. Although
promoting connectivity has become a key objective in the spatial management of interconnected
ecosystems (Botsford et al. 2001, 2003), too much connectivity can be detrimental to persistence
by synchronizing and destabilizing the dynamics of metacommunities (Gouhier et al. 2010a,
2013). Hence, determining when connectivity will promote or reduce persistence is critical in
order to effectively manage and conserve natural ecosystems (Earn et al. 2000).
Our results suggest exercising caution when attempting to evaluate the extent of connectivity
in a metacommunity via variation partitioning. Indeed, a small spatial fraction can emerge for
either low or high rates of advective or diffusive dispersal under both absorbing and periodic
boundary conditions. Hence, the size of the spatial fraction alone is not sufficient to infer the
extent of dispersal or connectivity in metacommunities. We suggest that applying variation
partitioning to system-specific dynamical models parameterized with real data can help improve
our ability to understand and manage natural systems by mapping statistical patterns in
metacommunity structure to their underlying ecological processes.
43
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Table 1.1 Summary of ANOVA model testing the effects of mean group pelagic larval duration (PLD) and zone on the spatial fraction obtained via variation partitioning. Source df MS F P-value Effect size ("#)
Mean PLD 3 0.2167 2.498 0.07518 0.075
Zone 2 1.2954 14.933 1.89e-05 0.299
Mean PLD x Zone 6 0.3824 4.408 0.00194 0.265
Residuals 36 0.0868 0.361
Note: Analysis was conducted on log10-transformed spatial fractions.
50
FIGURES
Figure 1.1 Metacommunity species richness at multiple spatial scales as a function of dispersal advection (a) and diffusion (b) for different environmental gradients. Red, blue and black lines depict local (α), between community (β) and regional diversity (γ), respectively. In addition to the color (red, blue, black) the translucence of each line represents the strength (slope) of the environmental gradient, which ranges from low (lighter hues) to high (darker hues). Results represent means from 10 replicate simulations. The vertical dashed line in panel (a) depicts when advection rates are high enough to prevent self-recruitment (μ > 2σ » 5).
0 5 10 15 350
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Dispersal diffusion rate (σ) Dispersal diffusion rate (σ)
(b)
(a)
51
Figure 1.2. Species rank abundance as a function of dispersal advection rate (a) and diffusion rate (b). The regional mean abundance of each species is plotted on a log scale as a function of species rank abundance. Color represents log abundance, which ranges from low (cool colors) to high (warm colors). Results represent means from 10 replicate simulations.
0 1 2 3 4 5 6 7 8Dispersal advection rate (7)
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Dispersal diffusion rate (σ)
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Dispersal diffusion rate (σ)
Spec
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52
Figure 1.3. Variation partitioning of community structure as a function of dispersal advection rate (a-c) and diffusion rate (d-f). Community structure was partitioned into three fractions: the environment ⟨𝐸|𝑆⟩, space⟨𝑆|𝐸⟩, and their joint influence or intersection ⟨𝐸 ∩𝑆⟩ (i.e., the fraction of the variation in community structure jointly influenced by space and the environment). Line color and translucence represent the strength (slope) of the environmental gradient, which ranges from low (lighter hues) to high (darker hues). Results represent means from 10 replicate simulations.
Com
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(l) Space (S | E)
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(a) Environment (E | S)
(c) Space (S | E)
(d) Environment (E | S) (g) Environment (E | S) (j) Environment (E | S)
(c) Space (S | E) (f) Space (S | E) (l) Space (S | E) (i) Space (S | E)
∩
(b) Intersection (E S) ∩ (e) Intersection (E S) ∩ (h) Intersection (E S) ∩ (k) Intersection (E S) ∩
53
Figure 1.4. Variation partitioning results for an intertidal metacommunity. Community structure was partitioned into three fractions: the environment ⟨𝐸|𝑆⟩, space⟨𝑆|𝐸⟩, and their joint influence or intersection ⟨𝐸 ∩𝑆⟩. The spatial fraction was plotted as a function of intertidal zone (low, mid, high). The color of the bar (white, light grey, dark grey, black) indicates mean group pelagic larval durations (PLD), a measure of dispersal ability (direct dispersers, low, medium, high). Overlapping horizontal lines indicate bars that are not statistically different at the alpha = 0.05 significance level. Analysis was conducted on log10-transformed spatial fractions.
Lowzone
Midzone
Highzone
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Direct DevelopersLow PLDIntermediate PLDHigh PLD
54
CHAPTER 2
Coexistence mechanisms collide across scales
ABSTRACT
Understanding how coexistence mechanisms operating at different scales give rise to
biodiversity is critical for both predicting and managing the dynamics of natural ecosystems in a
variable world. For instance, species interactions such as facilitation have been shown to
promote coexistence at local scales. At regional scales, dispersal across environmentally
heterogeneous landscapes can promote coexistence via spatial rescue effects that prevent species
from monopolizing their preferred habitat. Although a number of coexistence mechanisms have
been identified, relatively little is known about how they interact across scales to control local
and regional biodiversity. To address this issue, we developed a spatially-explicit
metacommunity model that included local (recruitment facilitation), regional (spatial
environmental heterogeneity) and tradeoff-based (competition-colonization) coexistence
mechanisms in order to determine their joint influence on patterns of diversity and extinction
risk. We found that recruitment facilitation, competition-colonization tradeoffs and
environmental heterogeneity interacted antagonistically to reduce biodiversity and promote
extinction risk at both local and regional scales. Our results suggest that classical approaches
focusing on a single spatial scale or a single coexistence mechanism may not yield fundamental
insights about the processes that structure natural ecosystems. Instead, our results call for a shift
from single- to multi-scale frameworks that account for interactions between coexistence
mechanisms in order to better understand the dynamics of complex and interconnected
ecosystems.
55
INTRODUCTION
Ecologists have long sought to explain Hutchinson’s “paradox of the plankton”, or how multiple
species can persist in natural systems despite competing for the same set of limiting resources
(Hutchinson 1961). Initial efforts to understand this phenomenon were primarily focused on
local scales, with studies investigating how species interacted in their local environments. For
instance, Connell (1961) showed how environmental differences between tidal zones influenced
interactions and community structure, with high (low) desiccation stress in the high (low) zone
leading to weak (strong) species interactions and dominance between by inferior (superior)
competitors. Following this work, Menge and Sutherland (1987) examined the roles of predation
and competition along a gradient of environmental stress in intertidal communities by developing
Environmental Stress Models (ESM). ESM suggested that community regulation depended on
the interaction between abiotic and biotic factors, with disturbance rather than species
interactions driving community structure under stressful environmental conditions. With
competition as the dominant driver under intermediate environmental conditions, and trophic
interactions playing a more prominent role under favorable environmental conditions. ESM set
the stage for studies investigating the relative influence of both abiotic and biotic factors in
understanding local species assemblages and coexistence. By incorporating facilitation, Bruno et
al. (2003) extended classic ESM by including the influence of intraspecific facilitative
interactions such as associative defenses on community structure under favorable environmental
conditions and the effects of interspecific facilitation under stressful environmental conditions.
That study highlighted the importance of positive interactions in structuring ecological
communities and introduced a reexamination of well-established paradigms about species
assemblages based solely on negative species interactions (e.g., competition, predation).
56
Together, this early work demonstrated the importance of incorporating information about both
environment and species interactions to understand coexistence at local scales.
Motivated by the fact that habitat patches do not exist in isolation, studies examining the
drivers of species coexistence expanded beyond local scales, focusing on the role of regional
scale processes. The theory of island biogeography began much of this work, investigating
regional processes such as colonization and patch size as drivers of biodiversity (MacArthur and
Wilson 1967). This theoretical framework showed that an island’s size and distance to the
mainland were critical determinants of species richness because they controlled, respectively, the
regional colonization rate and the local extinction rate. However, this framework focused
exclusively on the unidirectional effects of the mainland on islands and thus ignored both island-
to-island and island-to-mainland spatial feedbacks. Patch-dynamic models emerged as a way to
account for such feedbacks by examining the reciprocal effects of dispersal between local
patches on diversity at regional scales (Levins and Culver 1971, Hastings 1980, Tilman 1994).
For example, Levins and Culver (1971) showed that when environmental conditions were
homogeneous throughout the landscape, an interspecific competition-colonization tradeoff could
allow coexistence between species that were competitively superior but relatively sessile and
those that were competitively inferior but sufficiently mobile. By including spatial feedbacks
between patches, this framework highlighted the ability of tradeoffs across scales to promote
coexistence even when species competed for the same set of limiting resources (e.g., space). The
finding that two species could exhibit stable coexistence on a single resource via a competition-
colonization tradeoff was later extended to an indefinitely large number of species (Hastings
1980, Tilman 1994) despite the suggestion that doing so would be “formidable mathematically”
(Levins and Culver 1971). These and similar studies led to the development of metacommunity
57
theory, which sought to understand how local species interactions and regional dispersal interact
to govern the distribution of species across scales (Leibold et al. 2004, Holyoak et al. 2005).
Just as the inclusion of positive interactions in ESM affected predictions about
communities assembled, the integration of facilitation into metacommunity theory led to the
emergence of new and often less restrictive coexistence conditions (Guichard 2005, Gouhier et
al. 2011). For instance, Gouhier et al. (2011) found that recruitment facilitation could give rise to
coexistence even in the absence of a competition-colonization tradeoff. Specifically, the ability
of a subordinate species to facilitate the recruitment of a dominant species was found to promote
stable coexistence (and thus diversity) and buffer population growth by shifting patterns of
abundance from regional to local competitive processes. In addition to elucidating the effects of
positive species interactions, modern metacommunity theory has also shown how environmental
heterogeneity and dispersal can jointly influence biodiversity across scales (Loreau et al. 2003,
Mouquet and Loreau 2003, Bode et al. 2011, Salois et al. 2018). For instance, under spatially
variable but temporally constant environmental conditions, limited dispersal between discrete
populations due to either low rates (Mouquet and Loreau 2003) or small scales (Salois et al.
2018) tends to reduce local (α) diversity and increase between-community (β) diversity due to
species sorting, whereas intermediate dispersal tends to increase local diversity and reduce
between-community diversity by allowing the emergence of spatial rescue effects. Recent
theoretical advances have also demonstrated that spatiotemporal variation in dispersal can
promote coexistence when species experience sufficiently different connectivity patterns due to
asynchronous spawning times (Berkley et al. 2010, Aiken and Navarrete 2014).
Despite the large body of work identifying a variety of local and regional coexistence
mechanisms, little is known about how these processes interact. For this study, we created a
58
synthetic metacommunity which included both local (competition, recruitment facilitation) and
regional processes (dispersal, spatial heterogeneity) known to promote coexistence to determine
the consequence of their interaction on patterns of species diversity and abundance. Specifically,
we extended the patch-dynamic metacommunity framework by simulating species whose
competitive abilities were negatively correlated with their colonization rates in order to ensure
coexistence within a site. We then added recruitment facilitation, which controlled the degree to
which dominant species could colonize free space. Finally, we implemented spatial
environmental heterogeneity in the form of a linear gradient controlling recruitment success,
which each species having a different optimum.
MATERIALS AND METHODS
The metacommunity model
To determine how local and regional processes known to promote coexistence interact to affect
species diversity and abundance, we constructed a hierarchical metacommunity model whereby
local (within-site) dynamics are spatially-implicit and regional (among-site) dynamics are
spatially-explicit (Fig.1). Sites in the model are (i) arranged along a 1-dimensional array with
absorbing boundary conditions (e.g., a coastline; Fig.1a), (ii) characterized by different
environmental conditions (Fig. 1b) and (iii) interconnected by regional dispersal (Fig.1a,c).
Coexistence in the metacommunity can arise via three distinct mechanisms: a competition-
colonization tradeoff between species (Levins and Culver 1971, Hastings 1980, Tilman 1994),
recruitment facilitation (Menge et al. 2011, Gouhier et al. 2011) and regional environmental
heterogeneity (Mouquet and Loreau 2003). Competition between species is hierarchical so that
dominant species deterministically displace subordinate species (Levins and Culver 1971,
Hastings 1980, Tilman 1994). Recruitment facilitation in the model describes the dependency of
59
the dominant species on the subordinates, with obligate facilitation depicting full dependency
whereby dominant species can only colonize patches already occupied by their subordinates (see
Fig. 1a, Guichard 2005, Gouhier et al. 2011). This type of positive interaction is common in
intertidal systems where subordinate species often facilitate the recruitment of dominant species
by providing them with a rugose surface to settle onto and avoid disturbance (Connell and
Slatyer 1977; Berlow 1997; Halpern et al. 2007; Menge et al. 2011). More generally, this
formulation of facilitation corresponds to Connell & Slatyer’s (1977) classical facilitative model
of succession, whereby early succession species (i.e., subordinates) modify the substrate and
promote the subsequent colonization of late succession species (i.e., dominants). Overall, these
processes are modeled with the following set of ordinary differential equations that describe the
dynamics of S species ranked from dominant (species 1) to subordinate (species S) interacting at
each site, x, along a one-dimensional array consisting of L distinct sites:
d𝑁"(𝑥)d𝑡 = 𝑐"(𝑥)p q 𝑁4(𝑥) + (1 − 𝑓)
5
46"s7
t1 −q𝑁"(𝑥)5
"67
uv −𝑚"𝑁"(𝑥) − 𝑁"(𝑥)q𝑐4(𝑥)"B7
467
d𝑁5(𝑥)d𝑡 = 𝑐5(𝑥) t1 −q𝑁"(𝑥)
5
"67
u − 𝑚5𝑁5(𝑥) − 𝑁5(𝑥)q𝑐4(𝑥)5B7
467
Where the density 𝑁" of each species 𝑖 is mediated by the interplay between its realized
colonization rate (𝑐"), the amount of space available 01 − ∑ 𝑁"(𝑥)5"67 8, the degree of recruitment
facilitation (𝑓), natural mortality (𝑚"), and competitive displacement by dominant species
0−𝑁"(𝑥)∑ 𝑐4(𝑥)"B7467 8. Here, 𝑐"(𝑥) represents the realized colonization rate of species 𝑖 at site 𝑥.
This realized colonization rate is the product of each species’ potential recruitment rate 𝑟"(𝑥),
and fitness 𝐹 in that environment𝐸(𝑥) according to the following relationship:
𝑐"(𝑥) = 𝑟"(𝑥)𝐹(𝐸(𝑥), 𝑜")
60
Where the potential recruitment rate 𝑟"(𝑥) is the convolution of the product of propagule
production 𝑝" and density 𝑁" at site 𝑥 with the dispersal kernel 𝑘(𝑥):
𝑟"(𝑥) = w 𝑝"𝑁"(𝑦)𝑘(𝑥 − 𝑦)d𝑦?/A
B?/A
The term 𝑟"(𝑥) thus denotes the total number of recruits from species 𝑖 arriving at each site
from all other sites 𝑦 via dispersal. The dispersal kernel itself is a normalized (i.e., sums to 1)
Gaussian distribution with mean 𝜇 = 0 and variance 𝜎:
𝑘(𝑥) =1
𝜎√2𝜋𝑒B
(&By)IACI
Finally, each species’ fitness 𝐹 is represented by a bell-shaped curve around a species-specific
optimum 𝑜" such that the fitness of species 𝑖 at site 𝑥 is:
𝐹(𝐸(𝑥), 𝑜") = 𝑒B(z(&)B`$)I
A
Hence, the smaller the difference between a species optimum and the environment, the greater its
propagule survivorship and realized recruitment rate. Spatial environmental heterogeneity was
implemented via a simple linear gradient as follows:
𝐸(𝑥) = 𝑚𝑥 + 𝑣
Model simulations We simulated a range of recruitment facilitation scenarios via a uniformly-spaced vector of 50
values ranging from 0 (no facilitation) to 1 (full facilitation). We included a competitive
hierarchy and facultative dependency between species to model interactions commonly found in
marine systems between sessile species with larval dispersal (Connell 1961, Paine 1992, Menge
et al. 2011, Gouhier et al. 2011). Species within our metacommunity interacted in continuous
time over a spatially-heterogenous landscape of 140 sites that comprised a linear gradient of
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61
environmental conditions (i.e., a uniformly spaced vector of 140 values ranging from 0 to 1). We
varied the diffusion rate (𝜎) of the dispersal kernel across simulations to simulate an array of life
history strategies for propagules ranging from direct developers (𝜎 = 1 ×10B|) to long
distance dispersers (𝜎 = 30). For each simulation, the facilitation level and dispersal rate were
fixed and abiotic conditions were constant in time (slope 𝑚 = 0.05) but species-specific
environmental optima 𝑜" were selected randomly from a uniformly-spaced vector of 20 values
ranging from the minimum to the maximum environmental condition 𝐸(𝑥). Initial conditions for
all species paired random mortality rates with negatively correlated competitive abilities and
colonization rates in order to ensure coexistence under the competition-colonization tradeoff
(following the scheme described in Tilman 1994). Specifically, we set the equilibrium abundance
�̂�" of species 𝑖 to a value based on a geometric series such that �̂�" = 𝑧(1 − 𝑧)"B7 with 𝑧 = 0.15.
We then set each species’ mortality rate 𝑚" to a random value from the uniform distribution
𝑈(0,1) and computed the necessary colonization rate needed for coexistence 𝑐" =
∑ ]�a\as�7B∑ ]�a$G�a�� �\$
$G�a��
�7B∑ ]�a$G�a�� ��7B∑ ]�a$
a�� �. The model equations were solved numerically using an explicit Runge-
Kutta (4,5) formula in MATLAB (function ode45) for 2,000 time steps.
Model analyses
The model results were analyzed using two complementary approaches. First, we used species’
presence/absence information to partition biodiversity into local (α), between-community (β),
and regional (γ) diversity using standard methods (Whittaker 1972, Mouquet and Loreau 2003).
Regional diversity γ was measured as the total species richness across the entire metacommunity
and local diversity α was measured as the average species richness within each site. Between-
community diversity β was measured as the difference between regional and local diversity.
62
Next, extinction risk was calculated for each species across all dispersal-diffusion rates (s) and
facilitation levels (f). Specifically, for each combination of dispersal diffusion rate and
facilitation level, each species’ extinction risk was computed as the proportion of replicate
simulations where abundance fell below a minimum threshold of 10-6.
RESULTS
Diversity across scales
In the absence of dispersal (𝜎 ≈ 0), regional diversity (𝛾) across the metacommunity is largely
driven by high between-community diversity (𝛽) because local diversity (𝛼) is low, with each
site being dominated by the species whose physiological optimum most closely matches the local
environment (Fig. 2). The introduction of dispersal (𝜎 > 0) shifts the driver of regional diversity
from 𝛽 to 𝛼 diversity due to spatial rescue effects, which promote local species richness.
Eventually, at high levels of dispersal (𝜎 > 5), spatial rescue effects are lost resulting in a decay
of species richness as the system becomes homogenized due to increased mixing. Facilitation
works to amplify these trends as evidenced by a general decrease in species diversity across all
levels of facilitation and a sharp reduction at higher facilitation levels (Fig. 2a-c). In this case,
facilitation has a negative impact on species diversity, as it reduces species richness at all scales.
Hence, spatial environmental heterogeneity and recruitment facilitation, two mechanisms that are
often associated with coexistence, actually interact antagonistically when combined (Fig. 2). This
pattern emerges due to the fact that dominant and subordinate species do not have the same
optimum environment, yet under full facilitation the dominant species can only colonize sites
where the subordinate species is present. The dominant is thus co-dependent on both the
subordinate species and site-specific environmental conditions for recruitment. Because both
requirements can never be met in a single location (i.e., no location will be characterized by
63
optimal environmental conditions for both the dominant species and the subordinate species it
depends on), the dominant species must recruit in locations that are environmentally suboptimal,
which decreases its overall fitness.
Extinction risk Extinction risk provides a useful metric that complements patterns of diversity by highlighting
winning vs. losing species across the metacommunity in the presence of multiple coexistence
mechanisms. Overall, there is a U-shaped relationship between dispersal and extinction risk (Fig.
3). This general pattern of extinction risk occurs across all levels of facilitation, with the strength
of the signal dependent on each species’ competitive ranking. Dominant species experience a
shallower dip and faster recovery than subordinate species. This distinction is dampened as
facilitation increases (Fig. 3a vs. 3c). Regardless of species identity and facilitation, species
persistence is highest at intermediate dispersal values (0 < s < 10) due to spatial rescue effects,
resulting in high local diversity (α) driving high regional diversity (γ; Fig. 2) and low extinction
risk (Fig. 3).
In a purely competitive system (recruitment facilitation f = 0), the average local
extinction risk for the dominant species is high at all but intermediate levels of dispersal (Fig.
3a,b). At low dispersal rates (𝜎 ≈ 0), while the dominant species does not experience
competition for space, their low recruitment potential necessitates a reliance on spatial rescue
effects, which only occur at intermediate diffusion rates. At high rates of dispersal (𝜎 > 10), the
propagules produced by the dominant species become spread too thin across the spatial domain,
resulting in fewer of them landing in source sites, and thus eroding the spatial rescue of sink
populations and promoting extinction risk. The introduction of facilitation only serves to amplify
this effect of dispersal, with the dominant species losing the benefits of low-to-intermediate rates
64
of dispersal and suffering high extinction risk across the metacommunity (Fig. 3b,c). The
subordinate species performs much better across the whole range of dispersal because they have
much higher colonization potential due to the nature of the competition-colonization tradeoff.
Additionally, the introduction of recruitment facilitation competitively releases subordinate
species, thus decreasing extinction risk regardless of dispersal ability (Fig 3a vs. b,c).
The shifting burden of coexistence In classical competition-colonization tradeoff models (Levins and Culver 1971, Hastings 1980,
Tilman 1994), the burden of coexistence is always on the subordinate species, whose
colonization rates must be sufficiently larger than those of dominant species in order to persist.
However, our results show a shift in the burden of coexistence from the subordinate species to
the dominant. This shift emerges regionally via dispersal and locally via facilitation and becomes
amplified as the two processes interact. At regional scales, because the competition-colonization
tradeoff necessitates that dominant species produce fewer propagules than subordinates,
increased dispersal causes dominant species to spread their limited number of propagules across
more sites characterized by unfavorable environmental conditions, resulting in higher extinction
rates across the metacommunity (Fig. 3a). By increasing the dominant species’ extinction risk,
dispersal shifts the burden of coexistence away from the more productive and less extinction-
prone subordinate species. This is exacerbated by facilitation due to the dominant’s
irreconcilable co-dependency on the environment and subordinate species (Fig. 3b,c). At local
scales, facilitation drives this shift by reducing the available habitat for the dominant species. As
facilitation increases, the dominant species suffers even greater extinction risk with the added
dependency on the subordinate. This dependency generates a reduction in the recruitment of the
dominant species as they are increasingly confined to sites characterized by suboptimal
65
environmental conditions where the subordinate species are abundant. At intermediate to high
levels of dispersal and facilitation, these patterns become more pronounced as dispersal,
facilitation and environmental heterogeneity interact to promote the persistence of subordinate
species and the extinction of the dominant species. Indeed, when recruitment facilitation is
obligate (facilitation f = 1), only the most subordinate species is able to persist across the
metacommunity (Fig. 3a vs. c).
DISCUSSION
Diversity can be maintained via many types of coexistence mechanisms operating at different
scales (Levins and Culver 1971, Hastings 1980, Tilman 1994, Chesson 2000, Amarasekare et al.
2004, Aiken and Navarrete 2014). Although it is widely accepted that many of these coexistence
mechanisms likely operate simultaneously in nature (Levine et al. 2017, Letten et al. 2018), the
logistical constraints associated with documenting them across different spatial and temporal
scales have left their interactions relatively under-explored. Here, we have shown that in a virtual
metacommunity, coexistence mechanisms operating at different scales can interact
antagonistically to erode biodiversity and shift the burden of coexistence from competitively
subordinate to dominant species. These results have important implications for linking patterns
to their underlying processes across scales and for understanding how ecological communities
may disassemble and reassemble in response to environmental change.
Linking patterns to processes across scales Competition-colonization tradeoffs (Levins and Culver 1971, Tilman 1994), spatial
environmental heterogeneity (Mouquet and Loreau 2003), and recruitment facilitation (Gouhier
et al. 2011) can promote coexistence in metacommunities. However, instead of operating
additively to promote biodiversity, we found that these coexistence mechanisms actually reduced
66
biodiversity due to their antagonistic interaction across scales. Specifically, when facilitation was
combined with regional environmental heterogeneity and a competition-colonization tradeoff, a
shift occurred in individual species’ response to increased dispersal and species interaction
strength. Interspecific differences in environmental optima, when combined with spatial
environmental heterogeneity, led to spatial variation in fitness across species. Biodiversity was
maintained either regionally via high between-community but low within-community diversity
when dispersal was low due to species sorting, or locally via low between-community but high
within-community diversity due to spatial rescue effects when dispersal was high. The addition
of recruitment facilitation reduced the fitness of dominant species by inducing a co-dependency
on the environment and subordinate species that was unattainable due to interspecific differences
in environmental optima (“collision of coexistence mechanisms”).
The effects of this antagonistic interaction between coexistence mechanisms have
parallels to how habitat destruction competitively releases inferior species in metacommunities
(Nee and May 1992). Both mechanisms (habitat destruction, collision of coexistence
mechanisms) increase the regional abundance of the subordinate species and reduce that of the
dominant species. Similar to habitat destruction, recruitment facilitation is able to promote the
persistence of the inferior competitor by decreasing the number of patches that can be occupied
by the superior species. Unlike habitat destruction, this reduction in available patches occurs
both directly by effectively removing free space for dominant species and indirectly by making
dominants depend on subordinate species who do not share the same optimal environmental
conditions. This shift in the way in which species are interacting in space explains how
mechanisms found to promote coexistence when studied in isolation, can lead to extinction and
lower diversity at both local and regional scales when combined. Overall, our results suggest that
67
understanding the drivers of community structure in nature requires the integration of
coexistence mechanisms and their interactions across scales.
Accounting for interacting coexistence mechanisms to prioritize conservation efforts Landscapes are changing across all scales due to the direct and indirect effects of anthropogenic
pressures. While some ecosystems are becoming more heterogeneous in space via fragmentation
or changes in nutrient availability due to eutrophication (Hanski 2011, Hautier et al. 2014,
Gerber et al. 2014), others are becoming more homogenous due to large scale changes in climate
(Bertness et al. 2002, Pershing et al. 2015, Wang et al. 2015). Developing an understanding of
why and how communities shift across scales will be of particular importance in areas where
land use changes alter spatial heterogeneity and thus the competitive environment. Recent work
has identified the colonization ability of dominant species as a principal factor driving
community composition and species richness in marine intertidal systems (Bryson et al. 2014,
Morello and Etter 2018). Furthermore, Sorte et al. (2017) documented large declines in Mytilus
edulis populations (> 60%) along the Gulf of Maine, an area known for its rapid warming
(Pershing et al. 2015, Sorte et al. 2017). Unfortunately, increased extinction risk for dominant
species is not unique to intertidal systems in the Anthropocene (Bertness et al. 2002, Ellison et
al. 2005).
Our results demonstrate that such outcomes are to be expected when coexistence is
mediated by a competition-colonization tradeoff and recruitment facilitation, as dominant species
tend to be more susceptible to extinction (depending on dispersal ability), whereas subordinate
species are less prone to extinction (regardless of dispersal ability). It is thus crucial to include
coexistence mechanisms such as positive species interactions when attempting to both predict the
community-level effects of climate change and prioritize conservation efforts (Davis et al. 1998,
68
Suttle et al. 2007, Harley 2011). Determining how coexistence mechanisms interact in nature and
understanding the resulting effects on species extinction risk will require the quantification of
interspecific differences in recruitment and production at both local and regional scales. An
important next step will be to determine how the relative importance of different coexistence
mechanisms varies in space and time as communities become reorganized due to species
extinctions following environmental perturbations (Levine et al. 2017). Information of this kind
will be critical for prioritizing conservation efforts going forward. If for instance, the dominant
species is also a foundational species (e.g.: Spartina alternaflora, Mytilus edulis, Crassostrea
virginica, Zostera marina, etc.), changes in the dynamics, abundance or relative fitness of that
species could have wide ranging repercussions. As foundational species fundamentally shape and
modify species assemblages and habitats, increased extinction risk among these species can
cascade across scales by affecting species composition and modulating ecosystem processes
across whole landscapes. Additionally, because many foundational species provide key
ecosystem services, the ability to better understand shifts in the persistence of dominant species
would likely aide mitigation strategies in economically and ecologically important ecosystems.
Hence, incorporating multiple local and regional coexistence mechanisms is critical for
predicting their interactive effects on spatial patterns of biodiversity and prioritizing conservation
efforts in a rapidly changing world.
69
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FIGURES
Figure 2.1 Schematic diagram of the spatially-explicit metacommunity model. Panel (a) describes competition for space between a dominant (N1) and subordinate (N20) species along an environmental gradient. Each site x along the one-dimensional array is characterized by a particular environmental condition 0𝑒(𝑥)8, based its location, (𝑥"), along the linear gradient ranging from high (black: E+) to low (grey: E-). Sites exchange propagules via dispersal. In the absence of facilitation (𝑓 = 0), competition for space is based on classic competition-colonization tradeoffs where the dominant species can colonize both free space and any patch occupied by a subordinate species. Conversely, when facilitation is obligate (𝑓 = 1), the dominant species can only colonize sites occupied by a subordinate. Panel (b) describes how recruitment is modified by the environment, where propagule survivorship in a given site is determined by the match or mis-match between each species’ optimum (𝑜") and local environmental conditions 0𝑒(𝑥)8. Panel (c) depicts dispersal which was implemented via a Gaussian kernel whose standard deviation (𝜎) controls the degree of diffusion.
0.0
0.2
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Dominant (N1)Subordinate (N20)
Low diffusionIntermediate diffusionHigh diffusion
Environment at each site & '
Site location '
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Figure 2.2 Metacommunity species richness at multiple spatial scales as a function of dispersal diffusion and recruitment facilitation. Panels depict (a) local (α), (b) between-community (β) and (c) regional (γ) diversity. Color represents species richness, with cool colors representing low species richness and warm colors representing high species richness. Results represent means from 10 replicate simulations across 30 levels of dispersal and 50 levels of facilitation.
Species richness
Dispersal rate
Facilitation
Species richnessDispersal rate
Facilitation
Species richness
Dispersal rate
Facilitation
Species Richness
Dispersal rate
Facilitation
Spp. richness
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Dispersal rate
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(a) Local - ! (b) Between - " (c) Regional - #
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Figure 2.3 Species extinction risk as function of dispersal rate (a) without recruitment facilitation, (b) with intermediate recruitment facilitation, and (c) with full facilitation. Color represents species identity based on competitive ranking, with cool colors representing subordinate species and warm colors representing dominant species. Results represent means from 50 replicate simulations across 30 levels of dispersal and 3 levels of facilitation.
0.40.50.60.70.80.91.0
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Dispersal diffusion rate (σ)
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76
CHAPTER 3
Coastal upwelling generates cryptic temperature refugia
ABSTRACT
Natural systems are undergoing tremendous modification due to the rapidly changing
climatic conditions of the 21st century. Anticipated changes in the intensity, frequency and
duration of extreme events are expected to impact the biogeographical patterns of organisms
across the globe; therefore, ecological studies are increasingly focused on forecasting shifts in
the distribution and persistence of species. However, a consensus on which scales are needed to
accurately predict patterns of change and their underlying mechanisms has not yet been reached.
Here, we used wavelet analysis to document variation in daily water temperature at biologically-
relevant scales over 7 years and across 16 intertidal sites spanning 2,000 km of the Canary
Current System. We found that coastal upwelling promotes the emergence of both temporal and
spatial refugia during summer months when temperature stress is at its highest. In doing so, this
study highlights the importance of accounting for small-scale variation in water temperature to
accurately quantify temporal trends and identify spatiotemporal ecological refugia that could
promote persistence in a rapidly warming world.
77
INTRODUCTION
Ascribing ecological patterns to their underlying processes is fraught with difficulties because
the dynamics of natural systems are linked across time and space via the interplay of ecological
and environmental factors operating at multiple scales (Levin 1992). This inherent complexity
(May 1972, Menge and Sutherland 1987) has led to fundamental debates about the most
appropriate scale for studying ecological systems (Lawton 1999, Simberloff 2004, Ricklefs
2008). Some ecologists favor macroecology, where the focus is on large scales, claiming that
small-scale idiosyncrasies disappear at large scales making statistically consistent patterns more
likely (Lawton 1999). While macroecological studies may be useful for documenting patterns
that hold across large swaths of taxa and systems, these approaches are often unable to link these
general patterns to their causal mechanisms. For instance, a review by McGill et al. (2007)
highlighted dozens of mechanisms ranging from niche to neutral assembly processes that could
explain the “hollow curve”, the quasi-universal distribution of abundance observed across
communities dominated by a few abundant species and a multitude of rare ones. Because such
patterns often emerge in response to a myriad of processes based on fundamentally different
assumptions about the natural world, ascribing them to a specific mechanism is often difficult.
Hence, the search for universality can be characterized as a double-edged sword because
predictability often comes at the cost of understanding. Conversely, community ecology is
focused on local processes and patterns. This approach is amenable to experimental work which
has proven to be a valuable way to determine the mechanistic underpinnings of many ecological
patterns (Simberloff 2004). While the local scales of community ecology more readily lend
themselves to empirical work (as compared to the regional scales of macroecology), including
exhaustive communities via manipulative studies is not feasible, so a majority of work has
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focused on pairwise interactions between species which are then built into n-species models to in
effort to gain insights about population dynamics (McGill et al. 2006). This combined with the
fact that there are an intractably large number and types of species interactions simultaneously
occurring at the community level, make it hard to ‘scale up’ to whole communities from simple
community modules (Brose et al. 2005). Hence, while community ecology can often reveal the
mechanisms that underpin local patterns, these relationships often do not hold across systems and
scales (Ricklefs 2008). Metacommunity ecology attempts to bridge the gap between community
ecology and macroecology by integrating both local and regional processes in order to
understand ecosystem structure across scales (Leibold et al. 2004, Holyoak et al. 2005). This
framework evolved in response to findings that scale-dependent approaches of both
macroecology and community ecology were fundamentally limited by the shared assumption
that processes give rise to patterns at corresponding scales. More specifically, this approach
addressed the limitations of macroecology, which necessitates the exclusion of biotic interactions
(Pearson and Dawson 2003), environmental variables and spatial heterogeneity, common in
community ecology (Gilman et al. 2010). This cross-scale approach demonstrated that even in
the presence of strong regional processes, species interactions can have significant impacts on
the demographic properties of local populations, generating dynamical signals which can
propagate across scales via dispersal to control the spatial structure of metacommunities (Gotelli
2010, Gouhier et al. 2010b, Salois et al. 2018). While this framework has revealed great insights
about interconnected natural systems, it has done so largely via modeling and multi-scale surveys
as empirical tests and experimental data are hard to obtain.
Addressing the problem of scale is particularly important for understanding and
predicting the effects of climate change on the distribution of species, yet accurate and reliable
79
forecasts of the ecosystem-level effects of climate change remain one of the greatest
contemporary challenges (Helmuth et al. 2014, Pacifici et al. 2015, Gunderson et al. 2016).
Bioclimate envelopes, a type of species distribution model (SDMs), uses contemporary
relationships between environmental variables and abundances to make spatial predictions of
distributions of species in response to future climatic conditions (Pearson and Dawson 2003,
Gilman et al. 2010). Despite their power and simplicity, bioclimate envelope approaches make
assumptions that may fundamentally limit their forecasting ability in most systems (Davis et al.
1998, Araújo and Peterson 2012, Pacifici et al. 2015). Specifically, assuming that fine-scale
variation in climatic and environmental variables does not affect ecological patterns at larger
scales largely ignores evidence that cross-scale interactions between regional dispersal and local
processes can give rise to large-scale patterns (Gotelli 2010, Gouhier et al. 2010). Additionally,
even in the absence of such cross-scale interactions, measuring environmental variables at coarse
spatial and temporal scales can mask important variation that could influence organisms
(Helmuth et al. 2006, 2014, Vasseur et al. 2014, Dillon et al. 2016). For instance, using mean
trends of climatic variables often oversimplifies the complexity of environmental stressors by
averaging out meaningful variability (e.g., maximum and minimums) that can dictate organismal
performance and survival (Dillon et al. 2016). Disregarding important metrics (complexity) in
the spatial or temporal characteristics of climatic variables can result in range shift predictions
that are not reflective of either contemporary or projected directions of species distributions
(Seabra et al. 2015).
Similar mistakes can be made when attempting to characterize ecological refugia without
considering fine-scale variation and lead to errors when attempting to predict the effects of
environmental change. Helmuth et al. (2006) showed this empirically when they revealed the
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complex and counterintuitive way fine-scaled temperature varied in space and time along a
previously well described broad-scale temperature gradient. Specifically, they found that the
fine-scale variation of organismal body temperature differed greatly from that predicted by
broad-scale climatic patterns (Helmuth et al. 2006). Thus, ignoring ecologically relevant scales
by averaging out environmental variables (e.g. temperature) can mask refugia in space and time.
This is problematic because spatial and temporal refugia can promote persistence at local and
regional scales (Levins 1969, Brown and Kodric-Brown 1977, Chesson 2000). Temporal refugia
associated with temporal environmental variation can lead to variation in recruitment, buffered
population growth and other mechanisms (promoting temporal storage effects) enabling species
persistence and coexistence (Warner and Chesson 1985, Cáceres 1997, Chesson 2000). Spatial
refugia can arise from species-specific responses to spatially varying environmental variables.
For example, source-sink dynamics can arise due to spatial variation in environmental conditions
and promote regional species persistence as populations in locations characterized by favorable
environmental conditions (sources) can maintain populations in locations characterized by poor
environmental conditions (sinks) (Pulliam 1988, Gotelli 1991, Chesson 2000).
In order to identify fine-scale spatiotemporal temperature variation and its impact on the
frequency of temporal and spatial refugia in an upwelling system, we examined daily
microhabitat water temperature data spanning over 7 years from biomimetic limpets along
approximately 20 degrees of latitude within the Canary Current System (CanCs). We focused on
water temperatures in the intertidal, because these ecosystems experience some of the most
severe marine environmental conditions via large temperature fluctuations. These conditions
have resulted in strong (and well documented) relationships between thermal stress, fitness and
survival for the organisms who live there (Helmuth and Hofmann 2001, Helmuth et al. 2002,
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2006b, Lima and Wethey 2009), providing an excellent study system from which we can gain
greater understanding species response to external environmental forcing. Additionally, the
oceanographic variability associated with upwelling systems makes them model regions to
examine how coastal currents can govern temperature experienced at organismal scales now and
in the future as their duration and intensity is expected to increase under climate change (Wang
et al. 2015).
Here, we used wavelet analysis to evaluate intertidal microhabitat water temperature at
different spatiotemporal scales along the European Atlantic Coast. The goal of this study was to
compare how the same time series resolved in time and frequency can influence the
interpretation of water temperature trends and subsequent identification of ecological refugia in
space and time. Specifically, we used hierarchical clustering, pairwise correlations and wavelet
coherence of water temperature data across 16 sites to examine how temperature varied across
region characterized by differential (strong, weak, none) upwelling intensities. We found that
using simple raw time series alone masked underlying relationships between water temperature
and upwelling strength, whereas upwelling dependent spatiotemporal refugia emerged when the
same data was resolved in both time and frequency. These results highlight the importance of
considering both resolution and scale when projecting the ecological implications of trends
derived from climatic data.
MATERIALS AND METHODS
Microhabitat water temperature dataset
Data were acquired from a dataset comprised of daily intertidal microhabitat water temperatures
recorded via biomimetic temperature loggers (robolimpets; see Lima and Wethey 2009) along
the European Atlantic coast (as in Seabra et al. 2016 and Lima et al. 2016). Robolimpets are
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autonomous temperature sensing devices which are comprised of a lithium battery connected to a
circuit board encased within an empty limpet shell and designed to mimic the temperatures
experienced by actual limpets (Lima and Wethey 2009). These loggers were deployed to cover a
spectrum of microhabitats occupied by real limpets as in Seabra et al. (2011). Daily water
temperature data were recorded during high tide for loggers located in mid and low zones and
averaged per microhabitat when there was replicate data as described in Seabra et al. 2016. The
resulting timeseries from each of the 16 wave-exposed shores spanning from Southwest Scotland
to Southern Portugal (latitudes ranging from 37° - 55° N) were truncated to a common seven-
year period ranging from July 2010 to August 2017. These sites are located in the Canary
Current System (CanCS), one of the four coastal upwelling regions classified within the Eastern
Boundary Upwelling System (EBUS). Robolimpets were deployed throughout the CanCs, at
sites characterized by an upwelling gradient, experiencing a range of upwelling conditions from
strong to no upwelling. Robolimpets are a specific type of autonomous temperature logging
device, termed biomimetic logger, devised by Lima and Wethey (2009) to mimic the thermal
characteristics of the common intertidal limpet, Patella vulgata. Robolimpet temperature
measurements, like other biomimetic temperature loggers, have been shown to match
temperature trajectories of live organisms (here, limpets), thus providing temperature
measurements at an ecologically relevant scales (Helmuth 2002, Fitzhenry et al. 2004, Lima and
Wethey 2009).
Detecting spatiotemporal trends in microhabitat water temperature
In order to fully document the spatiotemporal trends in microhabitat water temperature, we
analyzed the raw water temperature time series using classical methods resolved in time as well
as methods capable of analyzing the time series in both the time and frequency domains.
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Raw Time Series
We computed a dissimilarity matrix of the raw temperature time series for each of the 16 sites
along the European Atlantic coast. Then we performed a hierarchical cluster analysis on the
dissimilarity matrix to identify how sites cluster based on Euclidean dissimilarity (distance) in
intertidal microhabitat water temperature.
Wavelet Analysis
We examined the 16 time series via wavelet analysis to determine if clusters based on the
variability of water temperature exhibited similar trends to those derived from clusters based on
the raw water temperature. Using wavelet analysis allowed us to examine the relative
contribution of each frequency (period) in the signal (time series) to the overall variance of
microhabitat water temperature over time (Torrence and Compo 1998, Cazelles et al. 2008). As
compared to traditional spectral analysis which is not resolved in time and more appropriate for
stationary (statistical properties of signal do not vary over time) time series, the wavelet
transform, resolved in both time and frequency was the analysis of choice for this study (Cazelles
et al. 2008). Additionally, the ability to relate scales to periodic components of a signal, is
particularly useful for analyzing ecological time series which are often nonlinear and non-
stationary(Recknagel et al. 2013, Vasseur et al. 2014). Here, we outline a brief summary of the
wavelet analysis used in this study and include more detailed description of the analyses in
Appendix 3.1.
We computed a continuous wavelet transform for each time series, using the Mortlet
wavelet as a base. This method decomposed the variance of water temperature ineach time
series over both the time and frequency domains and resulted in a wavelet power spectrum for
each of the 16 time series of microhabitats along the Eastern Atlantic Coast. In order to draw
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comparisons between and within regions of differential upwelling intensity in an upwelling
system, the resulting wavelet power spectra were grouped by upwelling regime (strong, weak, no
upwelling). From each wavelet transform, we extracted the resulting bias-corrected power, and
created a dissimilarity array on which we computed hierarchical cluster analysis to identify how
sites cluster based on Euclidean dissimilarity (distance) in the variability of intertidal
microhabitat water temperature (Appendix S1).
Identifying mechanisms driving patterns in time
Raw Time Series
As a baseline, all time series were truncated to a common time frame (07-18-2010 to 08-34-
2017) and grouped based on the upwelling regime each site was characterized by (e.g., strong,
weak or no upwelling) (Lemos and Pires 2004, Seabra et al. 2011, 2016). Daily water
temperature values were plotted as a function of time for each individual site as well as averaged
across sites for each upwelling region (Fig. 3, row 1). We calculated Kendall’s coefficient of
concordance (W) to measure the degree of synchrony between sites within each upwelling
region. Kendall's W is a non-parametric statistic that ranges from 0 to 1 and measures the level of
agreement between multiple ranked variables (Legendre 2005, Gouhier et al. 2010). Here, we
calculated Kendall’s W between time series for each site within a particular upwelling regime
(strong, weak, no upwelling) and we determined its significance using Monte Carlo
randomizations which shuffled the sites (columns) of the community matrix randomly (Legendre
2005, Gouhier and Guichard 2014). The Kendall’s W coefficient values reported are corrected
for tied ranks and the p-values are based on the randomization test (Table 1).
Waveletanalysis
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To investigate which scales or periods (1/frequency) dominated the patterns we detected in the
hierarchical clustering analysis, we calculated the scale-averaged wavelet power across all sites.
Specifically, wavelet transformations were truncated to a common time frame (07-18-2010 to
08-34-2017) and then subset into a series of standard arrays of scales into examine different
periodicities (annual [300-400 days], monthly [15-45 days], weekly [2-10 days]). To compute
the scale-averaged power, the wavelet power spectrum of water temperature was averaged across
each group of periods (annual, monthly, weekly). This metric represents the average variation of
the signal for each group of periods at each time point, allowing us to examine the variability of
water temperature at different temporal scales for each site. As with the raw time series data, we
then calculated Kendall’s Coefficient of Concordance (W) to measure the degree of synchrony
between sites within each upwelling regime (strong, weak, no upwelling) for each temporal scale
(annual, monthly, weekly). The Kendall’s W coefficient values reported are corrected for tied
ranks and the p-values are based on the randomization test (Table 1).
Identifying mechanisms driving patterns in space
In order to quantify the potential for spatial refugia in addition to temporal refugia, we calculated
the correlation and coherence in water temperature as a function of distance both within and
across upwelling regimes.
Raw time series
We used Pearson’s Correlation Coefficient (PCC) to measure the strength of the association of
microhabitat water temperature between each pairwise combination of sites (n = 16, 120 pairwise
combinations). Pearson’s correlation (r) is a parametric statistic that measures the strength of the
linear relationship between paired data, and ranges from -1 to 1. We performed a permutation-
86
based ANCOVA to determine if correlation in microhabitat water temperature was driven by
upwelling regime, geographical distance or their interaction (Fig. 4, see tables in Appendix 3.2).
Wavelet analysis
Due to the nonlinearity and non-stationarity of ecological time series, we decided to use a more
detailed metric to evaluate the associations of water temperature between sites across the CanCs.
Here, we used a bivariate extension of wavelet analysis (wavelet coherence) to assess the
temporal variability in the relationship between microhabitat water temperature and space.
Wavelet coherence is the cross-correlation of two time series in the time-frequency domain
(Grinsted et al. 2004, Cazelles et al. 2008), which allowed us to examine patterns of correlation
between pairs of sites. Specifically, we calculated the wavelet coherence for all pairwise
combinations of sites within and across upwelling regions (n = 120 pairwise combinations).
Next, we computed the average coherence between the two sites of interest across the entire time
series for each pairwise combination. These values were plotted as a function of geographical
distance (Fig. 5, column 1). Similarly, we calculated the mean and standard deviation of the
phase difference of coherence across the entire time series of each pairwise combination of sites
and plot those values against geographical distance (Fig. 5, columns 2,3, respectively). In
addition to calculating how correlations in fluctuations of water temperature between sites varies
over time at periods ranging from 2 to 890 days, we also made comparisons across different
periodicities (annual [300-400 days], monthly [15-45 days], weekly [2-10 days]) to examine
trends at biologically relevant scales. Mean coherence, mean phase difference and standard
deviation of phase difference were calculated for each subset of periodicities as described above.
We performed a permutation-based ANCOVA to determine if coherence in microhabitat water
87
temperature was driven by upwelling regime, geographical distance or their interaction (Fig. 5,
see tables in Appendix 3.2).
RESULTS
Detecting spatiotemporal patterns across a current system
The hierarchical clustering analysis on the raw time series was resolved only in time and resulted
in clusters which were very weakly associated with latitude and upwelling intensity (strong,
medium, weak, or none). However, including both time and frequency information in our
analysis revealed an improved ability to interpret these clusters. Including the added information
about the frequency of the signal allowed us to identify hidden similarities in the water
temperature time series that map onto upwelling conditions. This strong association suggests that
upwelling is a major driver of (dis)similarity in water temperature.
Identifying mechanisms driving patterns in time
Raw time series
As the previous analysis revealed that correlations in the wavelet power of intertidal microhabitat
water temperature are stronger than that of correlations in average daily water temperature, the
next step was to investigate which scales or periods (1/frequency) dominated these patterns. As a
baseline, time series were plotted individually and averaged according to groupings based on the
upwelling regime each site was characterized by (e.g.: strong, weak or no upwelling) (Fig. 3, row
1 *note need to fix edges). The main signal detected via the raw temperature timeseries is full
synchrony in water temperature across upwelling regimes (Table 1. W = 0.83, 0.89, 0.92 for
strong, weak or no upwelling sites, respectively), that is likely driven by seasonality. While there
is strong synchrony of temperature in the raw data regardless of upwelling intensity, seasonality
is least pronounced in sites categorized by strong upwelling. Here, upwelling disrupts this signal,
88
as sites in regions without upwelling reveal strong, predictable peaks in temperature in spring
and summer months as well as strong, predictable troughs in fall and winter months. These peaks
and troughs are less pronounced in regions that experience weak upwelling, as the difference in
temperature decreases slightly between the warm and cool seasons.
Wavelet analysis
In computing scale averaged power, the wavelet transform was decomposed into different
periodicities of interest (annual [300-400 days], monthly [15-45 days], weekly [2-10 days]) to
examine the variability of water temperature at different temporal scales. This analysis revealed
that the synchrony of variability of temperature is negatively correlated with the synchrony of
temperature at ecologically relevant scales. For instance, sites characterized by weak and no
upwelling displayed strong correlations in temperature (W = 0.89, 0.92, respectively) but weak
correlations in variability in temperature at monthly (W = 0.46, 0.39, respectively) and weekly
scales (0.46, 0.34, respectively). However, sites characterized by strong upwelling showed
weaker correlations in temperature (W = 0.83), yet strong synchrony in the variability of
temperature at monthly (W = 0.74) and weekly scales (W = 0.72). The systematic variation
across periodicities in strong upwelling sites suggests that upwelling brings consistent levels of
temperature variability to a system at scales relevant to organisms (Fig. 3,d:l), as variability in
temperature is occurring at the same temporal (subannual) scales, resulting in strong
synchronization between sites (Table 1, strong monthly, weekly > 0.7).
Conversely, in regions classified by weak or no upwelling, there is very little temporal variation
in water temperature that is consistent. Here, while sites are experiencing strong fluctuations,
they are out of phase (Table 1, weak/no monthly, weekly < 0.4), thus the magnitude of the
fluctuations are lost when the power is averaged across sites (Fig. 3h,i,k,l). The scale-dependent
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synchronization of the variability of intertidal microhabitat water temperature may have
important implications for spatial rescue effects. Knowledge about whether or not the variation
in temperature is systematic across a region classified by an upwelling regime may improve our
ability to forecast ecological impacts in the context of climate change. For instance, in upwelling
regimes where variation in temperature is systematic across the region at biologically relevant
temporal scales, we might predict that organisms will primarily rely on temporal refugia during
temperature extremes, since the variation in temperature will be highly synchronous across sites.
In our example, in strong upwelling regions, where sites are experiencing a high degree of
synchrony in the variability of water temperature (Fig. 3 g,j), organisms are most likely to benefit
from local (within-site) temporal rescue effects as temporal refugia will emerge simultaneously
during the summer when temperature extremes are most lethal. In contrast, in regions with weak
to no upwelling (Fig. 3 h,i,k,l), where variation in temperature is non-synchronous at relevant
time scales (monthly, weekly), organisms are less likely to experience this temporal refugia
during temperature extremes due to the anti-phase dynamics of temperature variability.
Identifying mechanisms driving patterns in space
Raw time series
Pairwise correlations on the raw water temperature timeseries revealed seasonality as the main
driver of correlation between sites. Generally speaking, there is high correlation between sites
within and between different upwelling regimes, with fairly weak decays in correlation with
distance (Fig. 4). Specifically, in sites that do not experience upwelling, no spatial pattern
emerges (N-N, r > 0.8 correlation over distances spanning >1300 km). Similarly, correlations in
temperature for sites experiencing no to weak upwelling (N-W and W-W) remain high withlittle
to no decay with distance (r = 0.9 - 0.7 over distances ranging from 250 km to 2000 km), a trend
90
again likely dictated by seasonality which is common to all sites within these regions. While sites
belonging to regions characterized by opposite upwelling regimes show lower correlations in
temperature (S-N, r < 0.6), again there is relatively no decay with distance as some sites are
dominated by season fluctuations and others by upwelling. These findings on correlations in raw
temperature time series combined with the previous analysis about variability of temperature
(above) suggests that sites experiencing little to no upwelling do not benefit from temporal
refugia (low synchrony of variability at weekly/monthly scales) nor spatial refugia (high spatial
synchrony of water temperature across 1000s of km). Conversely, the strong decay in correlation
with distance for sites in strong upwelling regimes (N-N, r = 0.85 – 0.5 over 500 km), would
suggest sites characterized by strong upwelling may benefit from spatial refugia (as temperatures
are not correlated at large distances) in addition to temporal refugia (high synchrony of
variability of temperature).
Wavelet analysis
Overall, regardless of upwelling regime, there is a general reduction in mean water temperature
coherence between sites when the analysis is restricted to monthly and weekly periods. When
mean coherence is calculated across all periods, the signal of upwelling is lost as upwelling
affects a very narrow band of frequencies (Fig. 5a) however, unlike in the correlations in time
series, we begin to see a slight decay in coherence with distance. Annual periods are dominated
by seasonality as we saw in the raw time series data (Fig. 5b). Coherence decreases significantly
as scale decreases, because the driving force (seasonality) is lost at monthly and weekly scales
(Fig. 5c,d). Both the mean and standard deviation of phase difference were calculated to parse
out the type of synchrony of coherence between sites. Examining the mean phase difference in
coherence is useful in clarifying the point at which the peaks and troughs in water temperature
91
are aligned in time. Likewise, the standard deviation of phase difference will reveal the degree of
phase locking over time. For reference, sites that experience full synchrony of water temperature
would have a value of zero for both the mean and standard deviation of phase difference. Here,
regardless of upwelling condition the mean phase difference is clustered around zero for all
periodicities (Fig. 5e:h) and does not decay with distance. Interestingly, there is a negative
correlation between the mean coherence and the spread of phase differences across scales (Fig.5
a:d vs. i:l). This trend is most pronounced at annual and weekly scales. For instance, at annual
scales, sites in regions without upwelling are highly correlated (Fig.5 b, R2 > 0.9) and in phase
(zero mean phase difference, Fig. 5 f) yet show a high degree of phase locking (low spread; Fig.
5 j, 0 < sd < 0.05). Similarly, at weekly scales, the mean coherence and spread of phase
difference are negatively correlated as well. Here, the mean coherence is low across all sites (Fig.
5 d, R2 < = 0.4) and declines slightly with distance, however the standard deviation of phase
difference is high across sites (Fig. 5 l, sd > 1.5) and increases with distance. This result suggests
that at there is less synchrony between sites than would be expected by looking at coherence
alone. Specifically, there is little to no phase locking at biologically relevant scales (monthly and
weekly), evidenced by the fluctuations becoming increasingly out of phase over larger distances,
indicating strong spatial heterogeneity in water temperature regardless of upwelling condition.
Together, the relatively low coherence in water temperature and low degree of phase locking
across 1000s of km indicates a high potential for spatial rescue across all sites, irrespective of
upwelling regime at biologically relevant temporal scales (monthly and weekly). These results
highlight the power of including information about the frequencies and scales at which we are
investigating trends. While we see a general negative correlation between mean coherence and
the spread of phase differences across periodicities, it is important to note how the temporal scale
92
of this information effects our interpretation. In considering only annual scales, one might
predict a low potential for spatial rescue effects as water temperature appears to be spatially
homogenous with sites both in phase and nearly phase locked. However, organisms are not
experiencing water temperature trends observed at annual scales and thus analyzing microhabitat
water temperature resolved in both time and frequency at biologically relevant scales revealed
hidden spatial rescue effects for non to weak upwelling sites that were masked when the analysis
was focused in the temporal domain alone (Fig. 4 vs 5). This analysis illuminated high potential
for spatial rescue effects across all upwelling regimes, with sites characterized by strong
upwelling also benefiting from temporal refugia.
DISCUSSION
Our results indicate that the resolution and scale at which environmental data is analyzed can
have profound effects on the ecological interpretation of the resulting spatiotemporal trends.
Many existing predictions about the ecological impacts of increased temperatures are based on
spatial or temporal averaging (Keppel et al. 2015, Molinos et al. 2015, Barceló et al. 2018).
While means can be informative, averaging over space and time can mask important signals
(e.g., variability, memory) occurring around the mean (Helmuth et al. 2014, Vasseur et al. 2014b,
Dillon et al. 2016). Indeed, our results highlight the importance of investigating trends in data
resolved in both frequency and time, as wavelet analysis revealed details about locations in the
Canary Current Upwelling System that went undetected when analyzing the raw time series. For
instance, including both time and frequency information in our analysis improved our ability to
interpret how sites clustered based on intertidal microhabitat water temperature. Specifically, we
identified upwelling as a major driver of (dis)similarity in water temperature, suggesting that
upwelling is a modulator of water temperature variation. The identification of a strong
93
correlation between upwelling and temperature (as compared to latitude) is just one example of
how important information can be missed via frequency and temporally unresolved analysis.
Additionally, analyzing water temperatures in both frequency and time revealed information
about the synchronization of variability of temperature within (and across) upwelling regime
illuminating the potential for spatial and temporal rescue effects. Specifically, we found that
synchronization of the variability of temperature is dependent on upwelling intensity, with strong
upwelling sites showing systematic variation in temperature. Ecologically, areas with a high
degree of synchrony in the variability of microhabitat water temperature are also areas with high
potential for temporal refugia. In addition to resolution, the spatial and temporal scales at which
data is analyzed can lead to dramatic differences in forecasts of ecological responses to climate
change.
The problem of scale in a changing world
Forecasting shifts in the biogeographical patterns of species in response to global change is often
done at spatial and temporal scales unreflective of scales relevant to species. For instance,
species range shifts are often classified at macroscales correlating species habitat or thermal
preferences to contemporary or projected climatic variables over large spatial scales (Pearson
and Dawson 2003, Araújo and Luoto 2007, Sandel et al. 2011, Pinsky et al. 2013, Molinos et al.
2015). While these macroscale models result in generalizations and forecasts which can account
for large swaths of taxa over large ranges of space (Keppel et al. 2012, Morelli et al. 2016), the
resulting coarse-scale species distribution predictions are likely be over (or under) estimates of
species response to a changing climate as body temperatures and thermal tolerances oforganisms
do not always correspond to those predicted by large-scale climate data (Helmuth and Hofmann
2001, Potter et al. 2013, Seabra et al. 2015).
94
Microclimates are increasingly being recognized for their importance for ecosystem
dynamics and processes (Potter et al. 2013, Morelli et al. 2016, Zellweger et al. 2019) as species
distributions obtained from macroclimate data is unrepresentative of the range of microclimates
most organisms experience (Helmuth et al. 2006b, Zellweger et al. 2019). Therefore,
microclimates have proven a more ecologically relevant scale at which to measure environmental
variables and examine climate-species interactions (Helmuth and Hofmann 2001, Seabra et al.
2011, 2015, Helmuth et al. 2016, Zellweger et al. 2019). Our results are consistent with these
findings. For instance, at coarse temporal scales (annual) microhabitat water temperature
appeared spatially homogenous with low variability, regardless of upwelling intensity.
Conversely, we found increased variability at ecologically relevant temporal scales (monthly and
weekly), that was dependent on upwelling intensity. The added information we gained with
increased resolution of our data indicates that examining environmental variables at finer
temporal and spatial scales will aid in our ability to forecast species persistence and survival
during extreme events.
Environmental refugia and persistence of ecological systems
Identifying ecological refugia is a common strategy used to predict species’ capacity to cope
with climactic change (Ashcroft 2010, Morelli et al. 2016). In natural systems, which are
environmentally variable, species that cannot acclimate will rely on spatial or temporal refugia to
persist. Historically, glacial and interglacial periods have provided a useful record from which to
gain insights on range contractions and expansions and define refuges for flora and fauna (Maggs
et al. 2008, Bennett and Provan 2008). From this work, ecological refugia came to be defined as
areas which facilitate the persistence of organisms in the face of climatic change. To this end,
recent studies have largely classified refugia by habitat (Keppel et al. 2012, Lima et al. 2016) or
95
climactic stability (Ashcroft et al. 2009, Barceló et al. 2018). A common hypothesis is that as
temperatures increase, species distributions should shift poleward. While intuitive, the data has
not supported this hypothesis for a wide variety of species (Molinos et al. 2015). This is likely
due to the fact that many of these projections of range shifts refer exclusively to those expected
in response to change in the mean climatic variable. Results from our study suggest that
identifying areas with potential for spatiotemporal rescue (via understanding how climatic
variables will vary in space and time) can provide insights as to where populations are more
likely to persist even when they seemingly cannot ‘keep pace’ with the climate.
To date, most approaches to defining ecological refugia have involved linking habitat
characteristics to climatic conditions (Keppel et al. 2015, Molinos et al. 2015, Barceló et al.
2018). This can be useful for mapping and forecasting climatic change, but not adequate for
defining the mechanisms behind ecological refugia important for predicting species persistence.
In particular, simply equating topological characteristics of a habitat to stability of climate may
result in liberal definitions of refugia that are not relevant to many species. Upwelling systems
have a high degree of spatial heterogeneity in temperature as sites throughout each region
experience a gradient of upwelling intensities, which has prompted generalizations about
upwelling regions as ‘climate refugia’ (Barceló et al. 2018). However, since upwelling systems
are both ecologically and economically important systems that are projected to change under a
changing climate, it is important to understanding the mechanisms driving potential for refugia to
better inform management and conservation objectives. By examining how the variability of
microhabitat water temperature changed across space within an upwelling system, we found that,
the strong spatial heterogeneity in water temperature led to out of phase dynamics (low degree of
phase locking), indicating a high potential for spatial refugia (via rescue effects) across the
96
upwelling system (regardless of upwelling intensity). Furthermore, locations characterized by
strong upwelling also had a high potential for temporal refugia. The ability to reveal cryptic
spatiotemporal refugia highlights the power of this approach in an era of global change where
climatic uncertainty will be the new normal. Understanding the variability of climatic variables
will be better tool for tackling environmental uncertainty and documenting areas of refuge than
current static approaches.
Changes in mean temperature and other environmental variables for the remainder of the
21st century are well documented and understood, yet less is known about how the variability of
environmental variables will change in time. For instance, while Seabra et al. found that the
mean sea surface temperature in Eastern Boundary Upwelling Systems has not increased at the
same rate as SST outside these regions (Seabra et al. 2019), we found that the variability of
temperature can be informative for elucidating ecologically relevant refugia potential, thus it
would be relevant to determine how the variability of temperature differs between upwelling
systems and neighboring regions. In fact, knowing more about the variability of temperature in
areas outside of Eastern Boundary Upwelling Systems, which are warming faster, would enable
the identification of areas with high or low potential for spatial or temporal refugia (due to high
synchronization of variability). It is also important to note that all upwelling systems are not
changing equivalently (Iles 2014, Wang et al. 2015), it will be important to quantify region-
specific variation in environmental variables of interest (e.g., temperature) and avoid
generalizing across locations that experience ‘similar’ upwelling intensities (e.g., strong
upwelling sites in Canary Current System vs California Current System). While understanding
general climatic trends (via computing global averages and climate velocity trajectories) has
resulted in important baseline understandings of how species ranges are likely to shift in space
97
and time, a better understanding of the mechanisms driving the patterns will improve our ability
to forecast changes in community composition and species assemblages. Since temperature
extremes are some of the most important drivers of population dynamics (Harris et al. 2018,
Salinas et al. 2019) and are becoming increasingly more common in an era of global change
(Fischer and Knutti 2015, Buckley and Huey 2016), it is imperative to adopt statistical
approaches that are able to decompose temperature variability at ecologically relevant scales to
accurately quantify the potential for temporal and spatial refugia in complex ecological systems.
98
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105
TABLES
Table 1. Kendall’s coefficient of concordance (W) measuring degree of synchrony between sites
within a specified upwelling region ranging from regions characterized by strong upwelling to
those without upwelling. This statistic was measured across sites for the raw time series as well
as for scale-averaged wavelet power at annual, monthly and weekly scales. Values represent
Kendall’s W corrected for tied ranks. Rows correspond to upwelling regime (strong, weak or no
upwelling). Columns correspond to values computed for the raw time series and resulting p-
value, and scale averaged power at annual (300-400 days), monthly (15-45 days) and weekly (2-
10 days) periodicities, respectively.
Raw TS P-value Annual P-value Monthly P-value Weekly P-value
Strong 0.8332525 0.001 0.9178599 0.001 0.7379248 0.001 0.7219196 0.001
Weak 0.8867467 0.001 0.9425014 0.001 0.4625272 0.001 0.4616176 0.001
No 0.9219468 0.001 0.8604674 0.001 0.3895519 0.001 0.3394520 0.001
106
FIGURES
Figure 1. Hierarchical clustering of correlations of water temperature from time series across 16 sites
54.9
7
53.7
5
48.5
4
52.1
3
50.3
1
53.3
2
45.6
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47.2
9
43.4
8
43.5
7
43.4
1
37.0
7
41.8
4
43.0
4
37.5
2
39.0
1
Cluster Dendrogram
hclust (*, "ward.D2")
Latitude (°N )
Dis
sim
ilarit
y
0
100
200
300
400
500Strong
Medium
Weak
None
Upwelling Strength
107
Figure 2. Hierarchical clustering of correlations of wavelet power extracted from wavelet analysis across 16 sites.
37.0
7
37.5
2
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47.2
9
43.4
1
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48.5
4
45.6
1
54.9
7
43.0
4
39.0
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41.8
4
050
015
0025
00
Latitude (CanCs)
Dis
sim
ilarit
y
54.9
7
53.7
5
48.5
4
52.1
3
50.3
1
53.3
2
45.6
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9
43.4
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43.5
7
43.4
1
37.0
7
41.8
4
43.0
4
37.5
2
39.0
1
hclust (*, "ward.D2")
Latitude (°N )
Dis
sim
ilarit
y
0
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2000
2500
54.9
7
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48.5
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ilarit
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Upwelling Strength
108
Figure 3. Time series and scale averaged wavelet power for daily microhabitat water temperature for all sites. Columns represent upwelling regime (strong, weak or no upwelling). The first row is the raw time series, and subsequent rows represent scale averaged power at annual (300-400 days), monthly (15-45 days) and weekly (2-10 days) periods. Bold black lines represent means across all sites, grey lines each individual site. Orange background refers to spring/summer seasons and fall/winter are represented by a blue background.
2011 2013 2015 2017
(a)
Wat
er te
mpe
ratu
re
°C( )
Strong Upwelling
05
10152025
2011 2013 2015 2017
(b)
Scal
ed A
vera
ged
Powe
r (lo
g 2)
02468
10
2011 2013 2015 2017
(c)
Scal
ed A
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g 2)
02468
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2011 2013 2015 2017
(d)
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02468
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2011 2013 2015 2017
(e)
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05
10152025
2011 2013 2015 2017
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2011 2013 2015 2017
(i)
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ries
05
10152025
2011 2013 2015 2017
(j)
Annu
al
02468
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2011 2013 2015 2017
(k)
Mon
thly
02468
10
2011 2013 2015 2017
(l)
YearW
eekl
y
02468
10
Spring/Summer Fall/Winter
109
Figure 4. Correlation as a function of distance. Pairwise comparisons between sites within the Canary Current System. P-value reported from ANCOVA results for interaction between upwelling intensity and distance.
p = 0.003 **
Distance Between Sites (km)
Cor
rela
tion
0 500 1000 1500 2000
0.0
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110
Figure 5. Coherence and phase difference as a function of distance. Pairwise comparisons between sites within CanCs on wavelet coherence data. Columns represent mean coherence, mean phase difference and standard deviation of phase difference (from left to right). Rows represent all periods (2-889), annual (300-400 days), monthly (15-45 days) and weekly (2-10 day) periods. P-values reported from ANCOVA results for interaction between upwelling intensity and distance.
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111
CONCLUSIONS AND RECOMMENDATIONS
By using mathematical and statistical theory to address classical issues of scale, the models and
analyses described in this thesis have revealed the relative importance of ecological (dispersal,
species interactions) and environmental (heterogeneity and fine-scale abiotic fluctuations)
variables while highlighting the vulnerability of ecosystems to a changing and variable climate.
Implementing a metacommunity framework enabled me to address the mechanistic goals of
community ecology while still recognizing the large-scale patterns and processes important in
macroecology. Specifically, this work has examined the complex and variable interactions
between patterns and process across scales by investigating the roles of heterogeneity in
dispersal, species interactions and environmental forcing on metacommunity composition,
persistence and biodiversity across scales.
Chapter one emphasized the role of dispersal in structuring communities and indicated
how signatures of dispersal in real communities can be empirically detect by integrating
metacommunity models and empirical data. System-specific models which include information
about the size of metacommunity, spatial extent of dispersal and degree of self-recruitment of
species of interest combined with survey data can clarify the mechanistic underpinnings of
spatial variation in a metacommunity.
Chapter two highlighted the importance of considering the interaction of ecological
processes. This work addressed the fact that multiple coexistence mechanisms are operating
simultaneously and at different scales in natural systems. Quantifying interspecific differences in
recruitment and production at both local and regional scales can help to define the ‘winners’ and
‘losers’ when coexistence mechanisms act antagonistically in a metacommunity.
112
Chapter three quantified the uncertainty surrounding the effects of climate variability on
marine species in an upwelling system. Analyzing temporally- and frequency- resolved data of
water temperatures revealed how coastal upwelling promotes spatial and temporal temperature
refugia for intertidal species.
Together, this work has highlighted the importance of considering the scale and
resolution at which ecological systems are studied. Natural extensions of this work would
include how the relative importance of some of the mechanisms investigated in this study (e.g.,
interspecific differences in recruitment and production, variability of climatic stressors, spatial
extent of dispersal) might vary in space and time as ecological communities become reorganized
due to species invasions and extinctions following environmental and anthropogenic
perturbations. Specifically, one could explore the impacts of variability, memory and extremes
for multiple climatic variables by extracting trends from climate models and incorporating these
different projected carbon emission scenarios in metacommunity and metaecosystem models.
Insights about the roles of connectivity in natural systems gleaned from this work will
likely be critical for understanding the links between humans and ecological systems in an era
where human activity is increasingly altering the natural flow of organisms and matter within
and across ecosystems. Extending the models and frameworks used for this project could be
useful in understanding the relative importance of direct and indirect drivers of abundance and
distributions of species as well as highlighting the potential vulnerability or persistence of
geographical ‘hot spots’ to climate change. This type of information could be valuable in an
applied setting, and aid in the understanding of the spatiotemporal distribution of fishing activity
or key harvested and protected species in marine ecosystems. For instance, statistical approaches
from this dissertation are applicable to many types of survey data (e.g., biomass, abundance,
113
acoustic survey data) and could aid in determining statistical relationships between economically
important species and environmental variables at ecologically relevant scales. Furthermore,
developing a metacommunity (or metaecosystem) model with environmentally dependent
parameters (e.g., thermal breadths) could reveal underlying mechanisms driving the statistical
relationships derived from actual data. These types of approaches could also be useful in
determining to what extent species distributions are driven by direct (environmental) or indirect
(fishing pressure) factors. Combining both statistical and dynamical models is an ideal way to
push this work forward and could prove a useful tool in understanding important ecological
shifts in many applied subsets of ecology (e.g., conservation, fisheries). This dissertation is
further evidence that the complex, variable nature of ecosystems necessitates the use of
frameworks that are dynamic in space and time, as these approaches will be invaluable for
improving our ability to generate accurate forecasts and devise successful large-scale
conservation, mitigation, and management strategies (Gouhier et al. 2013, Holsman et al. 2016,
Young et al. 2019).
114
LITERATURE CITED
Gouhier, T. C., F. Guichard, and B. A. Menge. 2013. Designing effective reserve networks for
nonequilibrium metacommunities. Ecological Applications 23:1488–1503.
Holsman, K. K., J. Ianelli, K. Aydin, A. E. Punt, and E. A. Moffitt. 2016. A comparison of
fisheries biological reference points estimated from temperature-specific multi-species
and single-species climate-enhanced stock assessment models. Deep Sea Research Part
II: Topical Studies in Oceanography 134:360–378.
Young, T., E. C. Fuller, M. M. Provost, K. E. Coleman, K. St. Martin, B. J. McCay, M. L.
Pinsky, and Handling editor: Mitsutaku Makino. 2019. Adaptation strategies of coastal
fishing communities as species shift poleward. ICES Journal of Marine Science 76:93–
103.
115
APPENDICES
Appendix 1.1: Mechanistic schematics
Figure 1.1i: The spatially-explicit metacommunity model. (a) Each site x along the one dimensional array is characterized by a particular environmental condition e(x), based its location along the linear gradient which ranges from high (E+) to low (E-). Simple lottery competition determines which species (N) occupy each patch within a site. Sites exchange propagules via dispersal. (b) The environment modifies realized recruitment, with propagule survivorship in a given patch depending on the similarity between each species’ optimum oi and local environmental conditions e(x). (c, d) Dispersal is implemented via a Gaussian kernel whose mean, μ, and standard deviation, σ, control advection and diffusion, respectively.
(a) Species 1Species 2Species 3
0.0
0.2
0.4
0.6
0.8
1.0
o1 o2 o3Environment at each site (e(x))
Prob
abilit
y of
pro
pagu
le s
urvi
val (
F (e
(x) ,
oi))
(b)
Low advectionMedium advectionHigh advection
Site location (x)
Pote
ntia
l rec
ruitm
ent (
r i(x)
)
0.01
0.02
0.03
0 20 40 60 80 100
(c)
−40 −20 0 20 40
Low diffusionMedium diffusionHigh diffusion
Site location (x)
(d)
Dis
pers
al (k
) N2
x1
xn
E +
E -
N2
N1 N1
N1
N1
116
Appendix 1.2: Robustness of the metacommunity model results to environmental stochasticity
Robustness of metacommunity model results
To determine the robustness of model results to variation in the linearity of the
environmental gradient, stochastic noise was added to our simple linear gradient. Below, we
present model results from simulations from one environmental gradient (u = 0.1), identical to
those described in the main text and Appendix 1.3 in every respect except for the addition of
environmental stochasticity. The recovery of our results under different levels of environmental
noise demonstrates that these findings are robust and do not require strictly linear environmental
gradients (Fig 1.2i -1.2ii).
Patterns of biodiversity
We found that the effects of increasing dispersal advection on biodiversity and
metacommunity structure described in the main text held under different levels of environmental
stochasticity for both absorbing and periodic conditions (Fig. 1.2i a-f, g-l). Briefly, increasing the
dispersal advection rate replaces the local positive feedback between abundance and self-
recruitment with a regional negative feedback that allows regionally dominant species to
monopolize the metacommunity, shifting control of regional diversity (γ) patterns from between-
community (β) to local (α) diversity (Fig. 1.2i a-c, g-i). Again, the negative regional feedback
generated relatively uniform abundances for the few regionally-dominant species across the
entire range of dispersal advection rates. Additionally, dispersal advection reduces local,
between-community and regional diversity by increasing the rate at which propagules are lost
from the finite-size metacommunity. These results hold across all levels of environmental noise.
The effects of increasing dispersal diffusion on biodiversity and metacommunity structure
described in the main text also hold under different levels of environmental stochasticity for both
117
periodic and absorbing conditions (Fig. 1.2i d-f, j-l). Indeed, increasing dispersal diffusion
initially leads to high local diversity and lower between-community diversity due to spatial
rescue effects, while higher rates of dispersal diffusion leads to increased spatial homogenization
and species-sorting resulting in low local, between-community and regional diversity. Again, as
in the main text, we see a bimodal effect of dispersal diffusion under periodic boundary
conditions, with low rates of diffusion (0 < σ < 5) leading to peaks in local and regional diversity
due to spatial rescue effects and intermediate rates of diffusion (10 < σ < 18) leading to a
prominent secondary peak in local and regional diversity as an effect of environmental rescue
(Fig. 1.2i j-l). Here again, species are able to exploit a secondary match between their
physiological optima and the local environment, resulting in a fitness boost and the subsequent
resurgence of rare species.
Patterns of (meta)community structure
Applying variation partitioning to simulations where dispersal rates varied yielded results
that were qualitatively identical to those described in the main text (Fig. 1.2ii a-f, g-l).
Specifically, increasing either the dispersal advection or diffusion rate ultimately resulted in
decreases in the spatial fractions for both absorbing and periodic boundaries conditions, as in the
main text. The initial introduction of dispersal (whether it be advection or diffusion) works to
erode the correlation between environmental conditions and community structure via spatial
rescue effects leading to a larger spatial fraction. However, as dispersal rate increases (for both
advection and diffusion), the spatial fraction decreases in communities with absorbing and
periodic boundary conditions. The mechanisms behind the decrease mirror those from the main
text; high rates of dispersal lead to spatial homogenization and the loss of spatial rescue effects,
or environmental rescue increases the correlation between the environment and community
118
structure. These results are robust to intermediate levels of environmental noise but begin to
erode at higher levels of noise (Fig. 1.2ii a-f, g-l).
Similarly, applying variation partitioning to simulations where dispersal diffusion rates
varied yielded results that were qualitatively identical to those described in the main text (Fig.
1.2ii c, f, i, l). Specifically, increasing the dispersal diffusion rate resulted in smaller spatial
fractions by spatially homogenizing the metacommunity and promoting species-sorting. In doing
so, dispersal diffusion generates a strong correlation between environmental conditions and
community structure leading to small spatial fraction. These results are fairly robust to across all
levels of environmental noise (Fig. 1.2ii a, d, g, j vs. c, f, i, l).
119
Figure 1.2i. Metacommunity species richness at multiple spatial scales as a function of dispersal advection (a-c) and diffusion (d-f) for different noise levels and boundary conditions. Red, blue and black lines respectively depict local (α), between community (β) and regional diversity (γ). Results represent means from 10 replicate simulations.
Periodic BoundariesAbsorbing Boundaries
Dispersal advection rate (μ) Dispersal advection rate (μ)Dispersal diffusion rate (σ) Dispersal diffusion rate (σ)
0 5 10 15 20 25 30 350
5
10
15
20 DiversityRegional (γ)Between (β)Local (α)
(a) Low Noise
0 5 10 15 20 25 30 350
5
10
15
20(b) Medium Noise
0 5 10 15 20 25 30 350
5
10
15
20 (c) High Noise
0 10 20 30 40 500
5
10
15
20(d) Low Noise
0 10 20 30 40 500
5
10
15
20(e) Medium Noise
0 10 20 30 40 500
5
10
15
20 (f) High Noise
0 5 10 15 20 25 30 350
5
10
15
20 (g) Low Noise
Spec
ies
richn
ess
0 5 10 15 20 25 30 350
5
10
15
20(h) Medium Noise
Spec
ies
richn
ess
0 5 10 15 20 25 30 350
5
10
15
20 (i) High Noise
Spec
ies
richn
ess
Dispersal advection rate (µ)
0 10 20 30 40 500
5
10
15
20(j) Low Noise
0 10 20 30 40 500
5
10
15
20(k) Medium Noise
0 10 20 30 40 500
5
10
15
20 (l) High Noise
Dispersal diffusion rate (σ)
0 5 10 15 20 25 30 350
5
10
15
20 (g) Low Noise
Spec
ies
richn
ess
0 5 10 15 20 25 30 350
5
10
15
20(h) Medium Noise
Spec
ies
richn
ess
0 5 10 15 20 25 30 350
5
10
15
20 (i) High Noise
Spec
ies
richn
ess
Dispersal advection rate (µ)
0 10 20 30 40 500
5
10
15
20(j) Low Noise
0 10 20 30 40 500
5
10
15
20(k) Medium Noise
0 10 20 30 40 500
5
10
15
20 (l) High Noise
Dispersal diffusion rate (σ)
0 5 10 15 20 25 30 350
5
10
15
20 DiversityRegional (γ)Between (β)Local (α)
(a) Low Noise
Spec
ies
richn
ess
0 5 10 15 20 25 30 350
5
10
15
20(b) Medium Noise
Spec
ies
richn
ess
0 5 10 15 20 25 30 350
5
10
15
20 (c) High Noise
Spec
ies
richn
ess
Dispersal advection rate (µ)
0 10 20 30 40 500
5
10
15
20(d) Low Noise
0 10 20 30 40 500
5
10
15
20(e) Medium Noise
0 10 20 30 40 500
5
10
15
20 (f) High Noise
Dispersal diffusion rate (σ)
Spec
ies
Ric
hnes
sSp
ecie
s R
ichn
ess
Spec
ies
Ric
hnes
s
120
Figure 1.2ii Variation partitioning of community structure as a function of dispersal advection rate (a-c, g-i) and diffusion rate (d-f, j-l) for different noise levels and boundary conditions. Community structure was partitioned into three fractions: the environment ⟨𝐸|𝑆⟩, space⟨𝑆|𝐸⟩, and their joint influence or intersection ⟨𝐸 ∩𝑆⟩ (i.e., the fraction of the variation in community structure jointly influenced by space and the environment). Line color represents the level of environmental noise, which ranges from low (cool colors) to high (warm colors). Results represent means from 10 replicate simulations.
Com
mun
ity v
aria
nce
Expl
aine
d (R
2 adj)
Periodic BoundariesAbsorbing Boundaries
Com
mun
ity v
aria
nce
Expl
aine
d (R
2 adj)
Com
mun
ity v
aria
nce
Expl
aine
d (R
2 adj)
Dispersal advection rate (μ) Dispersal advection rate (μ)Dispersal diffusion rate (σ) Dispersal diffusion rate (σ)
0.0
0.2
0.4
0.6
0.8
1.0
Com
mun
ity v
aria
nce
expl
aine
d (R
adj
2)
(g) Environment (E | S)
0.0
0.2
0.4
0.6
0.8
1.0C
omm
unity
var
ianc
eex
plai
ned
(Rad
j2
)(h) Intersection (E ∩ S)
0 5 10 15 20 25 30 35Dispersal advection rate (µ)
0.0
0.2
0.4
0.6
0.8
1.0
Com
mun
ity v
aria
nce
expl
aine
d (R
adj
2)
(i) Space (S | E)
Dispersal advection rate (µ)
(j) Environment (E | S)
(k) Intersection (E ∩ S)
0 10 20 30 40 50Dispersal diffusion rate (σ)
(l) Space (S | E)
Dispersal diffusion rate (σ)
0.0
0.2
0.4
0.6
0.8
1.0
Com
mun
ity v
aria
nce
expl
aine
d (R
adj
2)
(a) Environment (E | S)
0.0
0.2
0.4
0.6
0.8
1.0
Com
mun
ity v
aria
nce
expl
aine
d (R
adj
2)
(b) Intersection (E ∩ S)
mu
0 2 4 60.0
0.2
0.4
0.6
0.8
1.0
Com
mun
ity v
aria
nce
expl
aine
d (R
adj
2)
(c) Space (S | E)
Dispersal advection rate (µ)
(d) Environment (E | S)
(e) Intersection (E ∩ S)
0 10 20 30 40 50Dispersal diffusion rate (σ)
(f) Space (S | E)
Dispersal diffusion rate (σ)
121
Appendix 1.3: Robustness of the metacommunity model results to covariation in advection and diffusions rates
Robustness of metacommunity model results
To determine the robustness of our model results to covariation in advection and
diffusion rates, we ran additional simulations where both aspects of dispersal (advection and
diffusion) were positively correlated as predicted under climate change (e.g., Gerber et al. 2014).
We found that the effects of increasing dispersal advection on biodiversity and metacommunity
structure described in the main text held when dispersal diffusion also increased under both
boundary conditions (Fig. 1.3i- 1.3ii). Briefly, increasing the dispersal advection rate replaced
the local positive feedback between abundance and self-recruitment with a regional negative
feedback that allowed regionally dominant species to monopolize the metacommunity, shifting
control of regional diversity (γ) patterns from between-community (β) to local (α) diversity (Fig.
S1). Again, the negative regional feedback generated relatively uniform abundances for the few
regionally-dominant species across the entire range of dispersal advection rates. These results
held across all levels of environmental gradient (1.3ia,b).
Similarly, applying variation partitioning to simulations where dispersal advection and
diffusion rates covaried yielded results that were qualitatively identical to those described in the
main text (Fig. 1.3ii). Specifically, increasing the dispersal advection rate resulted in smaller
spatial fractions due to the same mechanism whereby the loss of spatial rescue effects (absorbing
boundaries) or the emergence of environmental rescue effects (periodic boundaries) decreased
the correlation between community structure and spatial structure. Overall, these results suggest
that the effect of dispersal advection on biodiversity and metacommunity structure will hold as
long as the advection rate is sufficiently larger than the diffusion rate so as to significantly limit
self-recruitment.
122
LITERATURE CITED
Gerber, L. R., M. D. M. Mancha-Cisneros, M. I. O’Connor, and E. R. Selig. 2014. Climate
change impacts on connectivity in the ocean: Implications for conservation. Ecosphere
5:art33.
123
Figure 1.3i: Metacommunity species richness at multiple spatial scales as a function of dispersal (advection and diffusion covaried) (a,b) for different noise levels. The first panel (a) contains results from simulations with absorbing boundary conditions and the second column refers to simulations with periodic boundary conditions (b). Red, blue and black lines depict local (α), between community (β) and regional diversity (γ), respectively. In addition to the color (red, blue, black) the translucence of each line represents the strength (slope) of the environmental gradient, which ranges from low (lighter hues) to high (darker hues). Results represent means from 10 replicate simulations.
0 2 4 6 8 100
5
10
15
20Sp
ecie
s ric
hnes
s
Dispersal rate
DiversityRegional (γ)Between (β)Local (α)
(a)
0 2 4 6 80
5
10
15
20
Spec
ies
richn
ess
Dispersal rate
(b)
124
Figure 1.3ii: Variation partitioning of community structure as a function of dispersal (advection and diffusion covaried). The first column contains results from simulations with absorbing boundary conditions (panels a-c) and the second column refers to simulations with periodic boundary conditions (panels d-f). Community structure was partitioned into three fractions: the environment ⟨𝐸|𝑆⟩, space ⟨𝑆|𝐸⟩, and their joint influence or intersection ⟨𝐸 ∩𝑆⟩ (i.e., the fraction of the variation in community structure jointly influenced by space and the environment). Line color and translucence represent the strength (slope) of the environmental gradient, which ranges from low (lighter hues) to high (darker hues). Results represent means from 10 replicate simulations.
0.0
0.2
0.4
0.6
0.8
1.0
Com
mun
ity v
aria
nce
expl
aine
d (R
adj
2)
(a) Environment (E | S)
0.0
0.2
0.4
0.6
0.8
1.0
Com
mun
ity v
aria
nce
expl
aine
d (R
adj
2)
(b) Intersection (E ∩ S)
0 2 4 6 80.0
0.2
0.4
0.6
0.8
1.0
Com
mun
ity v
aria
nce
expl
aine
d (R
adj
2)
(c) Space (S | E)
Dispersal rate
(d) Environment (E | S)
(e) Intersection (E ∩ S)
0 5 10 15 20 25 30 350 10 20 30
(f) Space (S | E)
Dispersal rate
125
Appendix 3.1: Wavelet analysis
Background
Ecological time series have proved a valuable tool for understanding the dynamics of ecosystems
(Benincà et al. 2009, Wootton and Forester 2013) and have traditionally been analyzed via
spectral analysis. Spectral analysis reveals what frequencies (i.e., spectral components) exist in a
signal (i.e., the times series) via a decomposition of the variance (power) of the signal into its
different frequencies (periods) obtained by a transform (e.g., Fourier Transform, Hilbert
transform, etc.) (Cazelles et al. 2008). While spectral analysis has been a fundamental tool in
understanding the variability of time series by giving information about how much of each
frequency exists in a signal, it does not tell us when in time these frequency components exist.
Thus, spectral analysis assumes that the statistical properties of a time series are stationary (do
not change in time) which becomes particularly important when analyzing ecological time series,
which are largely found to be non-stationary (Benincà et al. 2008, Cazelles et al. 2008, Rouyer et
al. 2008a, Gouhier et al. 2010). Wavelet analysis provides a solution, as it is a more sophisticated
time-resolved method. Thus, we used wavelet analysis to determine how fluctuations in
microhabitat water temperature varied within and across sites at 16 locations along the European
Atlantic Coast. Here, we provide a summary of the wavelet methods we used in the main text
and provide reference to many published guides for further details (e.g., Torrence and Compo
1998, Grinsted et al. 2004, Cazelles et al. 2008, Iles et al. 2012). All of our analyses were
conducted with the Biwavelet-package for R written by T. Gouhier.
Wavelet analysis
Wavelet analysis is able to resolve both the time and frequency domains of a signal, via the
wavelet transform. Specifically, a transforming function (mother wavelet) is passed through a
126
signal via windows 𝜏 across a series of scales 𝑠. For this study we chose to the Morlet wavelet,
which represents a sine wave modulated by a Gaussian function (Fig. S1-2; (Torrence and
Compo 1998):
𝜓�(𝑡) = 𝜋B7/�𝑒"���𝑒B�I/A
Where 𝑖 is the imaginary unit, 𝑡 represents nondimensional time, and 𝜔� = 6 is the
nondimensional frequency (Torrence and Compo 1998). The continuous wavelet transform of a
discrete time series 𝑥(𝑡) with equal spacing 𝛿𝑡 and length 𝑇 is defined as the convolution of 𝑥(𝑡)
with a normalized Morlet wavelet (Torrence and Compo 1998a, Grinsted et al. 2004b):
𝑊&(𝑠, τ) = �𝛿𝑡𝑠 q𝑥(𝑡)𝜓�
�B7
(6�
∗ �(𝑡 − τ)𝛿𝑡
𝑠 �
where * indicates the complex conjugate. By varying the wavelet scale 𝑠 (i.e., dilating and
contracting the wavelet) and translating along localized time position τ, one can calculate the
wavelet coefficients 𝑊&(𝑠, τ) across the different scales 𝑠 and positions τ. These wavelet
coefficients can be used to compute the bias-corrected local wavelet power, which describes how
the contribution of each frequency or period in the time series varies in time (Torrence and
Compo 1998a, Liu et al. 2007, Cazelles et al. 2008):
𝑊&A(𝑠, τ) = 2�|𝑊&(𝑠, τ)|A
Where 2� is the bias correction factor (Liu et al. 2007). The local wavelet power spectrum can
then be visualized via contour plots (Grinsted et al. 2004b, Cazelles et al. 2008).
The scale 𝑠 of the Morlet wavelet is related to the Fourier frequency 𝑓 (Maraun and Kurths
2004, Cazelles et al. 2008):
127
1𝑓 =
4𝜋𝑠𝜔� + 2 + 𝜔�A
When 𝜔� = 6, the scale 𝑠 is approximately equal to the reciprocal of the Fourier frequency 𝑓:
𝑠 ≈1𝑓
Hence, in all equations the scale can be converted to the Fourier frequency
𝑓 ≈1𝑠
or period
𝑝 =1𝑓 ≈ 𝑠
Zero-padding and the cone of influence
While the continuous wavelet transform can be approximated by using discrete Fourier
transforms to compute T convolutions for each scale 𝑠, it is more efficient to use discrete Fourier
transforms to calculate all T convolutions simultaneously (Torrence and Compo 1998). However,
method will introduce errors in the estimation of the local wavelet power spectrum at both the
beginning and end of a finite time series (Torrence and Compo 1998, Cazelles et al. 2008). This
occurs because the Fourier transform assumes that the data is periodic, thus the end of a time
series is padded with zeros before the wavelet transform is computed and then they are removed.
In effort to sufficiently deal with these edge effects, generally enough zeros are added in order
for the total length T of the time series to reach the next-higher power of two (Torrence and
Compo 1998, Cazelles et al. 2008). This procedure does reduce reliability in the estimation of the
local wavelet spectrum (by a factor of 𝑒BA in the region where the zero padding (via artificial
discontinuities at endpoints of data), thus this region is termed the ‘cone of influence (COI),
128
demarcating the area below as susceptible to edge effects (Torrence and Compo 1998a, Cazelles
et al. 2008).
Statistical significance testing
In order to determine the statistical significance of the wavelet spectrum obtained from a time
series, one must first formulate an appropriate null hypothesis. Here, the null hypothesis is that
the observed time series is generated by a stationary process with a given background power
spectrum 𝑝(𝑘) (Torrence and Compo 1998b, Grinsted et al. 2004a). Since many ecological and
environmental time series exhibit strong temporal autocorrelation (i.e. high power associated
with low frequencies; e.g. Beninca et al. 2009, see Ruokolainen et al. 2009 for review), we used
a first order autoregressive model [AR(1)] to generate a temporally autocorrelated time series or
red noise, which served as our null hypothesis. Specifically, the power spectrum 𝑝(𝑘) of our red
noise process was calculated with (Gilman et al. 1963):
𝑝(𝑘) =1 − 𝛼A
1 + 𝛼A − 2𝛼 cos(2𝜋𝑘 /𝑁)
where the autocorrelation coefficient 𝛼 at time lag 1 is estimated from the observed time series
and 𝑘 = 0,… , #A represents the frequency index. The observed wavelet spectrum can be
compared to the wavelet spectrum of the red noise process by means of a chi-square test. The
distribution of the local wavelet power spectrum of a red noise process is ¥¦F(�,§)I¥
CI, which is
distributed according to 7A𝑝(𝑘)𝒳A
A, with 𝑘 representing the frequency index,𝜎A representing the
variance of the time series and 𝒳AA representing the chi-square distribution with 2 degrees of
freedom (Torrence and Compo 1998). The value of𝑝(𝑘) is the mean wavelet power spectrum
at frequency 𝑘 that corresponds to the wavelet scale 𝑠 (Torrence and Compo 1998b). Using this
129
equation, one can construct 95% confidence contour lines at each scale using the 95th percentile
of the chi-square distribution 𝒳AA (Torrence and Compo 1998b).
Hierarchical cluster analysis
In order to determine how sites cluster based on Euclidean dissimilarity (distance) in intertidal
microhabitat water temperature we computed the wavelet spectra 𝑊&(𝑠, 𝜏) for each time series
𝑥(𝑡) and extracted a matrix containing the bias-corrected power obtained via the method
described by Liu et al. (2007). We then computed the dissimilarity between all time series via an
𝑁 ∗ 𝑝 ∗ 𝑡 array of wavelet spectra, where 𝑁 is the number of wavelet spectra to be compared
(𝑁 = 16), 𝑝 is the number of periods in each wavelet (𝑝 = 106), and 𝑡 is the number of time
steps in each wavelet spectrum (𝑡 = 2595). We then performed a hierarchical cluster analysis on
the set of dissimilarities for all sites being clustered. This clustering analysis works by assigning
each site to its own cluster and then iteratively joining the two most similar clusters, until there is
just a single cluster. Here, at each stage distances between clusters were recomputed according to
the version of the Ward clustering algorithm that necessitates the dissimilarities to be squared
before cluster updating (Murtagh and Legendre 2014).
Wavelet coherence
Wavelet coherence quantifies the coherence of fluctuations (strength of the covariation) between
two signals (Torrence and Compo 1998a, Grinsted et al. 2004b), thus is essentially the time-
resolved correlation between two time series (Cazelles et al. 2008, Rouyer et al. 2008b, 2008a).
Specifically, this method requires taking the wavelet transforms 𝑊&(𝑠, 𝜏) and 𝑊©(𝑠, 𝜏) of each
time series 𝑥(𝑡) and 𝑦(𝑡) and then calculating the cross-wavelet via (Torrence and Compo
1998a, Grinsted et al. 2004b):
𝑊&,©(𝑠, 𝜏) = 𝑊&(𝑠, 𝜏)𝑊©∗(𝑠, 𝜏)
130
where * indicates complex conjugation. The wavelet coherence is then defined as:
𝑅&,©A (𝑠, 𝜏) =¥⟨𝑠B7𝑊&,©(𝑠, 𝜏)⟩¥
A
⟨𝑠B7|𝑊&(𝑠, 𝜏)|A⟩ ⟨𝑠B7¥𝑊©(𝑠, 𝜏)¥A⟩
Where ⟨∙⟩ denotes smoothing in both time 𝜏 and scale 𝑠 and 0 ≤ 𝑅&,©A (𝑠, 𝜏) ≤ 1. Here, the time
smoothing is done via a filter derived from the absolute value of the wavelet function at each
scale, normalized to have a total weight of unity, which is a Gaussian function 𝑒G�I
I®I for the
Mortlet wavelet. The scale smoothing is done with a boxcar function of width 0.6, which
corresponds to the decorrelation scale of the Morlet wavelet (Torrence and Webster 1998,
Torrence and Compo 1998, Grinsted et al. 2004).
Statistical significance testing
The statistical significance of wavelet coherence can be tested by using Monte Carlo
randomization techniques (Torrence and Compo 1998a). Following the approach detailed by Iles
et al. (2012), 1,000 pairs of surrogate time series were generated using the same first order
autoregressive coefficients as our observed time series. Wavelet coherence was computed for
each pair of surrogate time series, in effort to generate a distribution of wavelet coherence. From
this distribution, we obtained the 95% significance level for each scale by computing the 95th
percentile of the wavelet coherence distribution.
131
LITERATURE CITED
Benincà, E., J. Huisman, R. Heerkloss, K. D. Jöhnk, P. Branco, E. H. Van Nes, M. Scheffer, and
S. P. Ellner. 2008. Chaos in a long-term experiment with a plankton community. Nature
451:822–825.
Benincà, E., K. D. Jöhnk, R. Heerkloss, and J. Huisman. 2009. Coupled predator–prey
oscillations in a chaotic food web. Ecology letters 12:1367–1378.
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Appendix 3.2: Permutation based ANCOVA tables
Raw Time Series: Correlation Table 3.2i. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the pairwise correlation of variably of temperature for 16 along the Canary Current System. Upwelling intensity ranged from strong to no upwelling. P-values from permutation test (Pperm) are reported for each factor in our analysis. Effect DF F P Pperm Upwelling 5 108.99 < 0.0001 0.001
Distance 1 8.69 0.0039 0.001
Upw x Dist 5 8.32 < 0.0001 0.003
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Wavelet Coherence: Mean coherence Table 3.2ii. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean coherence across all periodicities. Upwelling intensity ranged from strong to no upwelling. P-values from permutation test (Pperm) are reported for each factor in our analysis. Effect DF F P Pperm Upwelling 5 46.46 < 0.0001 0.001
Distance 1 94.68 < 0.0001 0.001
Upw x Dist 5 7.29 < 0.0001 0.001
Table 3.2iii. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean coherence at annual periods. Effect DF F P Pperm Upwelling 5 71.17 < 0.0001 0.001
Distance 1 3.08 0.0823 0.088
Upw x Dist 5 4.42 0.0011 0.002
Table 3.2iv. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean coherence at monthly periods. Effect DF F P Pperm Upwelling 5 18.30 < 0.0001 0.001
Distance 1 145.14 0.0039 0.001
Upw x Dist 5 4.54 0.0009 0.004
Table 3.2v. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean coherence at weekly periods. Effect DF F P Pperm Upwelling 5 11.07 < 0.0001 0.001
Distance 1 57.91 < 0.0001 0.001
Upw x Dist 5 4.82 0.0005 0.003
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Wavelet Coherence: Mean phase difference Table 3.2vi. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean phase difference of coherence across all periodicities. Upwelling intensity ranged from strong to no upwelling. P-values from permutation test (Pperm) are reported for each factor in our analysis. Effect DF F P Pperm Upwelling 5 8.08 < 0.0001 0.001
Distance 1 0.12 0.7342 0.72
Upw x Dist 5 2.24 0.0554 0.048
Table 3.2vii. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean phase difference of coherence at annual periods. Effect DF F P Pperm Upwelling 5 10.27 < 0.0001 0.001
Distance 1 2.15 0.1450 0.148
Upw x Dist 5 0.77 0.5729 0.595
Table 3.2viii. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on mean phase difference of coherence at monthly periods. Effect DF F P Pperm Upwelling 5 11.32 < 0.0001 0.001
Distance 1 14.46 0.0002 0.002
Upw x Dist 5 2.48 0.0363 0.041
Table 3.2ix. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the mean phase difference of coherence at weekly periods. Effect DF F P Pperm Upwelling 5 6.04 < 0.0001 0.001
Distance 1 16.35 < 0.0001 0.001
Upw x Dist 5 3.62 0.0046 0.007
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Wavelet Coherence: Standard deviation of phase difference Table 3.2x. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the standard deviation of phase difference of coherence across all periodicities. Upwelling intensity ranged from strong to no upwelling. P-values from permutation test (Pperm) are reported for each factor in our analysis. Effect DF F P Pperm Upwelling 5 42.36 < 0.0001 0.001
Distance 1 115.63 < 0.0001 0.001
Upw x Dist 5 5.30 0.0002 0.001
Table 3.2xi. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the standard deviation of phase difference of coherence at annual periods. Effect DF F P Pperm Upwelling 5 27.86 < 0.0001 0.001
Distance 1 9.03 0.0033 0.002
Upw x Dist 5 3.77 0.0035 0.005
Table 3.2xii. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the standard deviation of phase difference of coherence at monthly periods. Effect DF F P Pperm Upwelling 5 21.65 < 0.0001 0.001
Distance 1 121.79 < 0.0001 0.001
Upw x Dist 5 4.81 0.0005 0.002
Table 3.2xiii. Results of permutation-based ANCOVA testing the effects of upwelling intensity and distance on the standard deviation of phase difference of coherence at weekly periods. Effect DF F P Pperm Upwelling 5 14.26 < 0.0001 0.001
Distance 1 87.50 < 0.0001 0.001
Upw x Dist 5 3.14 0.0110 0.022