Snails at three scales: Interplay of

stream hydrology and hydraulics with

the morphology, dispersal and

distribution of Elimia proxima

Ben Strauss

A Dissertation

Presented to the Faculty

of Princeton University

in Candidacy for the Degree

of Doctor of Philosophy

Recommended for Acceptance

by the Department of

Ecology and Evolutionary Biology

November 2007

c© Copyright by Ben Strauss, 2007.

All Rights Reserved

Abstract

This thesis quantifies effects of hydraulic environment and flooding disturbance on

the ecology and evolution of benthic stream macroinvertebrates from organismal to

landscape scales, utilizing the snail Elimia proxima as a model species.

Recent research has complicated views about the nature of flow environments near

stream beds and of the organismal shapes best equipped to cope with them. Analy-

sis of intraspecific morphological variation in field populations exposed to contrasting

environments is a largely untapped source of potential insight. I measured shell shape

and size in E. proxima sampled from hydraulically diverse locations. At every site,

small shells were stubbier than large shells, consistent with the changing hydrody-

namic demands snails likely face as they grow, and providing what may be the first

evidence for this theoretically predicted ontogenetic shift. Sites subject to greater

hydraulic stress were associated with smaller mature snails; and evidence also sug-

gests that snails at stressful sites begin with bluffer shells but grow more streamlined

when compared to snails in gentler locations. All of these findings are consistent with

adaptive plastic or genetic variation to reduce exposure to hydrodynamic forces.

At the next scale, I explored the consequences of hydraulic environment and flood

history for snail dispersal by conducting long-term mark-release-resurvey experiments

at multiple sites with flow records, and developing maximum likelihood models to fit

subsequent observations. Findings suggested that hydrodynamically stressful envi-

ronments impede upstream migration and enhance the downstream transport caused

by floods. Previous research has demonstrated transport of benthic invertebrates by

floods, but appears to lack quantitative estimates of relationships between environ-

ment, flood size and dispersal impacts, as provided here.

Finally, I examined the relationship between stream hydrology and hydraulics

and the landscape-scale distribution and abundance of E. proxima. In a geographic

survey, the probability of site occupancy varied negatively with indicators of hydraulic

iii

stressfulness and flooding likelihood. A negative relationship between these factors

and density was evident only in the aftermath of a major regional flood event. Several

lines of evidence suggested, however, that hydraulic resistance to upstream migration

plays a more important role in setting distributional limits than floods.

iv

Acknowledgements

My cup overflows with the list of people who helped me bring this project to fruition.

To begin with, I must thank my advisor, Simon Levin, for his consistent patience

and support for my endeavor, from my unconventional arrival at Princeton, through

my selection of a project not much aligned with his current interests, and to the end.

Committee members Peter Grant, Steve Pacala, Ignacio Rodriquez-Iturbe and Dan

Rubinstein each provided comments and guidance which have made their way into

the final product. Henry Horn and Tom Doak generously helped with key equipment

and facilities, and conversations with Marissa Baskett, Adi Livnat, and especially

Jeremy Lichstein sparked my thinking. However, my greatest intellectual debt goes

to my good friend Jonathan Dushoff, who took the time to understand the nuts and

bolts of my project, and not only helped me with challenging statistical analyses,

but also prodded strategic evaluation of my overall approach in each chapter. I don’t

know what the department will be without him.

When I began my research, I had no idea that I would spend as much time think-

ing about hydrology and the physics of fluid flow as about snails. Fortunately, the

departments of engineering at Princeton are filled with friendly and accessible faculty

and staff. Lex Smits introduced me to fluid mechanics, and Mike Vocaturo provided

extensive laboratory access and assistance for building instruments. Jim Smith shared

his expertise in stream hydraulics, and gave me access to his computer workstation

and licensed flow modeling software; Mary Lynn Baeck provided vital assistance in

getting it all to work. Finally, Ignacio Rodriguez-Iturbe, of my committee, helped

orient me to key concepts and methods in landscape-scale hydrology. Outside of

Princeton, Mimi Koehl, Josef Ackerman, David Hart, and Steven Vogel, all biologists

who study life in moving water, gave me insight and encouragement.

Most field research stands on the shoulders of field assistants, and mine was no

exception. I owe Janet Prevey, Katie Burke, and especially Heidi Zellie and John

v

Ludlam truly special thanks. Together we camped, drove endless miles, worked in

the rain, and counted more snails than you can imagine.

The Highlands Biological Station was my home base for field research, and also a

financial supporter. Other financial support came from the Howard Hughes Medical

Institute, the Pew Program in Biocomplexity, and the Department of Ecology and

Evolutionary Biology.

Rob Dillon got me into this mess by introducing me to Elimia proxima. Jim

Paintiff gave a lot of his time to help me learn to raise snails in tanks, even if my

experiments there didn’t bear fruit. And countless other people helped this project,

in small and large ways. I apologize if I have failed to mention you; it does not mean

that I did not appreciate your generosity.

Finally, no major undertaking like this could be possible without the emotional

support and patience of family and friends alike. Besides department friends already

mentioned, I’d like to give special thanks to Rick Duke for helping me make my final

press toward completion. My mother, father, sister and brother-in-law have tolerated

long periods of absence and silence with grace; and my sweetheart Danna, I am sure,

has suffered most of all, but never gave a hint of it, and has been a vital support and

refuge for me through and through.

Thank you to everybody.

vi

To my loving family,

and to Danna.

vii

Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

1 Introduction 1

2 Hydraulic environment and morphological variation 6

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Study organism, sites and sampling . . . . . . . . . . . . . . . 9

2.2.2 Stream hydraulics . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.3 Hydrodynamic forces . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.4 Morphometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.5 Statistical analysis . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.1 Reynolds number . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.2 Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.3 Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4.1 Variation in shell size . . . . . . . . . . . . . . . . . . . . . . . 23

2.4.2 Variation in shell shape with size . . . . . . . . . . . . . . . . 28

2.4.3 Variation in shell shape with environment . . . . . . . . . . . 29

viii

2.4.4 Variation in relative foot size . . . . . . . . . . . . . . . . . . 32

2.4.5 Broader context . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3 Influences of hydraulic environment and flooding on dispersal 34

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2.1 Mark-release-resurvey experiments . . . . . . . . . . . . . . . 36

3.2.2 Hydraulic environment and flow history reconstruction . . . . 37

3.2.3 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.4.1 Effects associated with shear velocity . . . . . . . . . . . . . . 53

3.4.2 Quantitative implications . . . . . . . . . . . . . . . . . . . . 59

3.4.3 Conclusion and consequences . . . . . . . . . . . . . . . . . . 60

4 Relationships of hydrology and hydraulics to distribution and abun-

dance 61

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.2.1 Snail surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.2.2 Bankfull shear velocity . . . . . . . . . . . . . . . . . . . . . . 64

4.2.3 Precipitation parameters . . . . . . . . . . . . . . . . . . . . . 66

4.2.4 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

ix

Chapter 1

Introduction

The physical environment organisms experience influences their ecology and evolu-

tion, but also depends on organismal biology. Morphology, behavior, movement, dis-

persal and distribution all shape and are shaped by environmental experience, from

short to long temporal and spatial scales.

Benthic stream invertebrates, and stream-obligate snails in particular, offer a con-

venient system for studying environment-organism interactions across many scales.

Stream biologists widely agree that the hydraulic forces imparted by flowing water

are a dominant factor in the biology of many lotic organisms (see, e.g., [1, 33, 65]).

At a small physical scale, the hard shells of snails lend themselves to fine measure-

ments capable of distinguishing subtle morphological variation, which may indicate

adaptation or plastic response to different flow regimes. At an intermediate scale,

the pseudo-linear geometry of streams, the conspicuousness of snails, and the ease of

labeling shells facilitates dispersal tracking studies in which movement can be related

to gross hydraulic environment and flow history. And at the largest scale, some of the

same factors make mapping geographic distribution relatively efficient, for relation to

flow environment.

Rapidly flowing water presents important challenges for benthic stream fauna.

1

Strong currents and forces near the streambed can raise the energetic cost of locomo-

tion [65], immobilize organisms [42], or dislodge them from the substrate [47]. These

effects interact with the complex and changeable geometry of near-bed hydraulic

environments to influence energetics [5], microhabitat use [44], and movement and

dispersal [48, 33].

Given such ramifications and their clear significance for fitness, many benthic

macroinvertebrates should possess morphological adaptations for coping with high

flow velocities. The literature documents diverse candidate traits. For example,

various species utilize hooks [9], suckers [22], or byssal threads [1] to attach firmly to

the substrate, or silk to build shelters or sticking pads [29]. In particular, authors

have argued for over a century that the streamlined or dorsoventrally flattened shapes

common among fast-water benthic fauna, such as the mayfly Baetis, evolved to reduce

drag [66]. In another enduring notion (e.g. see [41, 29]), Ambuhl [3] claimed that the

low profile conferred by these shapes allows organisms to hide from strong currents

altogether. The same benefit would accrue to sufficiently small organisms, regardless

of shape.

More recent work has complicated these interpretations of the significance of size

and shape. The best hydrodynamic shape for an organism appears to depend upon

its size and the distribution of flow velocities it encounters, with streamlining most

important for larger organisms experiencing faster flows, and stubby shapes more

adaptive for smaller individuals in slower flows [72]. One such contrast may unfold

across development, because different shapes should be preferred by the same individ-

ual as it grows in size, flow exposure and Reynolds number (the latter two being likely

consequences of size increase) [64]. Conventional wisdom holds that benthic macroin-

vertebrates stay essentially the same shape throughout ontogeny despite generally

growing by an order of magnitude [64, 1, 45], but this claim remains untested.

Chapter 2 exploits a common approach for detecting and exploring potential adap-

2

tations, but one that appears largely absent from the literature on benthic stream

fauna and flow. I measured and analyzed intraspecific variation in target traits with

respect to variation in the environment. Specifically, I related size and shape of the

snail Elimia proxima to hydraulic environment across multiple sites and streams, to

test for variation consistent with adaptive plastic or genetic responses to reduce ex-

posure to strong hydrodynamic forces. I also related shape to size within sites to

explore whether snails shift from bluffer to more streamlined forms during ontogeny.

At a larger physical scale, dispersal exerts a key influence on many population

genetic and demographic processes. Unfortunately, it is difficult to fully characterize,

especially with respect to relatively long distance transport events which, despite their

general rarity, have important consequences for the spread of genes and populations

[8].

Streams offer promising systems for the study of dispersal, its influences and

its effects. Organisms confined within their banks occupy a landscape of reduced

dimensionality where movement can be tracked and characterized along a single up-

stream/downstream axis. While branching tributaries increase spatial complexity in

the upstream direction to a degree, downstream dispersal is essentially confined to

be linear. Thus, detecting long moves (downstream, as expected after floods) should

be easier than in other systems. Furthermore, flow gauges (or, where they are ab-

sent, rainfall history) provide a record of events capable of precipitating flood-driven

dislocations.

A rich account of dispersal must also detail the major relationships between envi-

ronment and dispersal. Streams offer ample variation for the study of such influences.

Stream beds present highly heterogeneous flow environments that strongly influence

the paths and costs of travel available to benthic fauna [48, 65]. At the same time,

the gross features of streams, including substrate composition, slope, and discharge

levels, shift dramatically as they descend from headwaters toward alluvial plains [18].

3

These features have direct consequences for the near-bed hydraulic environment [56]

which, in turn, bears directly on dispersal.

Chapter 3 investigates dispersal in Elimia proxima, a stream-dwelling prosobranch

snail common in the southern Appalachian Mountains of the United States. Proso-

branchs are not known to voluntarily enter stream drift, so long distance downstream

displacements are likely caused by floods. I conducted mark-release-resurvey exper-

iments at sites spanning a range of hydraulic environments and flood histories, and

developed a series of nested models to fit my observations, in an attempt to elucidate

the importance of floods in shaping snail dispersal, and to register the influence of

hydraulic environment on snail-driven and flood-driven dispersal alike. While a num-

ber of studies document changes in site-specific species abundance and composition

following spates (e.g. [53, 63]), and others anecdotally report long-distance displace-

ments [11, 55], I am unaware of previous attempts to isolate and quantify the effect

of natural floods on the dispersal of benthic stream macroinvertebrates.

Influences of environment on dispersal may scale up to affect geographic patterns

of density and occurrence. The final components of my research program, described in

Chapter 4, explored for relationships between hydraulics, hydrology and the distribu-

tion and abundance of the snail Elimia proxima. I conducted an extensive geographic

survey of snail presence and absence, and an intensive survey of snail density at a

smaller set of focal sites. I estimated bankfull shear stress U∗bk at each location

following methods from earlier chapters, but required new means for characterizing

flooding hydrology because most watercourses were not gauged. As a rough proxy, I

employed publicly available weather data to estimate precipitation parameters in the

basin draining through each survey point. Finally, I related bankfull shear stress and

precipitation parameters to snail distribution and abundance.

Several months after initial density surveys, Hurricanes Frances and Ivan dropped

25-75 cm of rain over most of the study region in a span of two weeks, causing century

4

floods in some area streams. A month later, I resurveyed most of my sites to assess

consequences and see whether they varied according to U∗bk.

Benthic snails in streams offer a convenient system for studying environment-

organism interactions across many scales. Stream biologists widely agree that the

hydraulic forces imparted by flowing water are a dominant factor in the biology of

many lotic organisms. At a small physical scale (but longer temporal ones), stream

flow characteristics likely influence evolution and plasticity of organism shape and

size. The hard shells of snails lend themselves to fine measurements capable of dis-

tinguishing subtle morphological variation. At intermediate scales, hydrology and

hydraulics

5

Chapter 2

Hydraulic environment and

morphological variation

2.1 Introduction

Rapidly flowing water presents important challenges for benthic stream fauna. Strong

currents and forces near the streambed can raise the energetic cost of locomotion

[65], immobilize organisms [42], or dislodge them from the substrate [47]. These

effects interact with the complex and changeable geometry of near-bed hydraulic

environments to influence energetics [5], microhabitat use [44], and movement and

dispersal [48, 33].

Given such ramifications and their clear significance for fitness, many benthic

macroinvertebrates should possess morphological adaptations for coping with high

flow velocities. The literature documents diverse candidate traits. For example,

various species utilize hooks [9], suckers [22], or byssal threads [1] to attach firmly

to the substrate, or silk to build shelters or sticking pads [29]. Authors have argued

for over a century that the streamlined or dorsoventrally flattened shapes common

among fast-water benthic fauna, such as the mayfly Baetis, evolved to reduce drag

6

[66]. In another enduring notion (e.g. see [41, 29]), Ambuhl [3] claimed that the low

profile conferred by these shapes allows organisms to avoid strong currents altogether

by hiding in a viscous sublayer of much reduced flow at the stream bottom. The same

benefit would accrue to sufficiently small organisms, regardless of shape.

More recent work has questioned these interpretations of the significance of size

and shape. One important area of uncertainty concerns the hydraulic environment

that benthic organisms experience. Advances in understanding of turbulent open

channel flows have ruled out Ambuhl’s concept of a substantial protective sublayer

blanketing natural stream beds [56, 33], and fine-scale water speed measurements

taken around exposed animals set in turbulent laboratory flumes indicate that even

small and streamlined organisms confront appreciable currents in that setting [66, 67].

However, we still lack a good understanding of near-bed flows in natural streams,

and especially within the complex topography of the roughness layer, underneath the

peaks of the roughness elements (e.g. rocks, pebbles, debris) that cover large areas of

many stream bottoms [33]. The effects of these elements keep intact the possibility

that dorsoventral compression or small size could help benthic macroinvertebrates

avoid strong currents.

Another important complication concerns what shapes best handle the hydrody-

namic forces that organisms face. The answer depends substantially upon an indi-

vidual’s Reynolds number, Re, a dimensionless parameter that scales with body size

and current speed (see Vogel [72] for a thorough discussion). Streamlined shapes

reduce drag at relatively high Re, a clear benefit, but they also expose organisms to

lift, which becomes more important the more Re increases. At low Re, lift is not a

concern, but viscous forces become significant and favor bluffer (stubbier) shapes for

total drag reduction. The best shape for an organism therefore depends upon its size

and the distribution of flow velocities it encounters, with many tradeoffs involved.

One such tradeoff may unfold across development, because different shapes should

7

be preferred by the same individual as it grows in size, flow exposure and Re (the

latter two being likely consequences of size increase) [64]. Conventional wisdom holds

that benthic macroinvertebrates stay essentially the same shape throughout ontogeny

despite generally growing by an order of magnitude [64, 1, 45], but this claim remains

untested.

This study exploits a common approach for detecting and exploring potential

adaptations, but one that appears largely absent from the literature on benthic stream

fauna and flow. I measured and analyzed intraspecific variation in target traits with

respect to variation in the environment. Specifically, I related size and shape of the

snail Elimia proxima to hydraulic environment across multiple sites and streams,

to test for variation consistent with adaptive plastic or genetic responses to reduce

exposure to strong hydrodynamic forces. I also related shape to size within sites to

explore whether snails shift from bluffer to more streamlined forms during ontogeny.

Snails make strong candidates for this type of investigation because their hard

shells lend themselves to fine measurements capable of distinguishing subtle varia-

tion. Prior work has explored morphological variation in snails across elevational

gradients in streams, but has employed only a simple shape metric (height-to-width

ratio) subject to bias from variation in the mean size of each sample population,

and has failed to characterize hydraulic environment [30, 59]. The marine literature,

however, does includes examples of apparently adaptive size and shape variation,

wherein intertidal snails at wave-exposed sites are more streamlined and smaller than

conspecifics in nearby protected areas [70, 69] (but see [60]).

8

2.2 Methods

2.2.1 Study organism, sites and sampling

E. proxima (synonym: Goniobasis proxima) is an operculate prosobranch snail (fam-

ily: Pleuroceridae) common in small softwater streams throughout much of southern

Appalachia [15]. Its habitat ranges from low-gradient piedmont creeks to moderately

steep mountain headwaters as high as one thousand meters. E. proxima is small (shell

<20 mm long) and can reach densities of hundreds per square meter (pers. obs.). It

is dioecious and iteroparous, reaching sexual maturity after at least one year, and

surviving up to four or five years in the field. In springtime, fertilized females ce-

ment eggs onto rocks; the eggs develop directly and hatch into benthic young [15, 16].

Growth is indeterminate but slows with size [68].

For this study, I sampled from upper, middle and lower sites in each of five streams

in western North Carolina and northern Georgia between June 12 and July 7, 2004

(see Table 2.1). Within each stream, I spaced the sites as widely as possible in order

to obtain the greatest range of stream slopes and flows and, consequently, hydraulic

environments. Upper sites were located within 1.25 km of the upstream limit to snail

distribution in each stream, at the second highest elevation where snails exceeded a

preset density criterion (≥100 found in a 5-minute search within a 10 m segment;

segments were checked every 50 m from the limit). Lower sites were located at the

lowest accessible points above junctions with rivers or major disturbances such as

heavy development or dams. Middle sites were chosen to be roughly midway between

upper and lower sites.

Each site was a relatively uniform length of stream, or reach, roughly twelve times

its estimated wetted width at bankfull flow, and thus ranged from 60-270 m long.

Bankfull flow is flow occupying full channel capacity, a level which can typically be

estimated visually in the field as corresponding to the strongest break in streambank

9

Table 2.1: Site locations and basic characteristics. Buck, Curtis, Long, Snow, andTal abbreviate Buck Creek, Curtis Creek, Long Creek, Little Snowbird Creek, andTallulah River. Site indicates elevation ranking (1 is highest), UTM-E and UTM-Ngive Universal Transverse Mercator coordinates (North American Datum 1983, Zone17, in meters), Dist indicates stream distance from highest site in stream (km), Areagives basin area drained (km2), and U∗bk is estimated bankfull shear velocity (m s−1).

Stream Site UTM-E UTM-N Dist Area Slope U∗bk

Buck 1 263049 3883664 0.0 14.67 0.013 0.2692 261013 3886420 3.7 22.36 0.006 0.1963 261223 3889745 8.0 38.79 0.010 0.274

Curtis 1 392503 3953516 0.0 0.78 0.106 0.4892 391655 3950993 4.2 10.64 0.064 0.5693 393286 3946380 11.0 39.24 0.021 0.403

Long 1 243932 3905867 0.0 2.03 0.075 0.4772 243690 3907360 2.0 8.60 0.027 0.3603 244159 3911076 6.4 15.68 0.012 0.261

Snow 1 237275 3906109 0.0 37.06 0.011 0.2862 238515 3907303 2.8 42.90 0.018 0.3753 238143 3908726 5.4 48.99 0.014 0.338

Tal 1 266728 3877561 0.0 6.50 0.059 0.5092 266818 3870486 8.8 42.31 0.006 0.2243 267896 3864791 17.2 99.04 0.004 0.206

slope [18, 27]. I established a coordinate grid and placed quadrats randomly to sample

for snails within two meters of either stream bank. I collected all specimens with shells

≥5 mm in the longest dimension until obtaining at least forty combined from at least

six quadrats at each site.

2.2.2 Stream hydraulics

Evaluating the morphology of benthic organisms in light of their hydraulic envi-

ronment must begin with characterizing that environment. The mean E. proxima

shell height in my full sample was 4.30 mm, and the maximum was 7.96 mm. Cur-

rent velocities in the first centimeter above natural stream bottoms are difficult to

measure, poorly known and complex. Turbulent flows should theoretically exhibit

logarithmic velocity gradients that increase with distance from the flow boundary

[18]. However, field measurements above stones in gravel-bed [32] and torrenticulous

[39] streams have yielded many different velocity profile shapes in the first several

10

millimeters (starting from 1 mm in height: constant, linear, logarithmic, exponential

and wedge-shaped), and velocities at 2 mm did not correlate with velocities at 10 mm

[32] (most benthic stream biology research does not even include measurements as

close to stream bottom as the latter). Such measurements are very difficult using

available technologies in a field setting; an extensive literature search uncovered only

two studies reporting multiple velocity readings under 10 mm per profile, the two

cited here, which describe flows over fewer than ten natural stones between them—a

very small database in need of expansion.

Detailing the flow environments experienced by benthic macroinvertebrates thus

remains problematic, not only in light of the spatial variability of currents over het-

erogeneous stream bottoms, but also the temporal variability from fluctuating stream

discharge. However, appropriately chosen metrics should correlate with moments of

the distribution of near-bed flows in a stream reach, and allow gross comparisons

among conditions at different sites or levels of discharge.

The metric employed in this study is shear velocity estimated at the reach scale,

defined as

U∗ =√

gRZ, (2.1)

where g is gravitational acceleration, R is reach mean hydraulic radius, and Z is reach

slope. Mean stream depth D generally approximates R well. Shear velocity reflects

the resistance of a stream bed against flow, and thus near-bed hydraulic forces too

[18]. It exerts a strong influence on the substrate (grain size and sorting) [56]; and

local U∗ (over a point) can be used to predict mean water velocity as a function of

height in ideal turbulent flow [18]. Thus, for a gross metric, U∗ seems to come as close

as possible to characterizing the velocities small benthic fauna experience; in turn,

these velocities drive the magnitude of hydrodynamic forces encountered.

R and D vary with stream discharge, so to compare U∗ among reaches, a standard

flow level should be chosen. Bankfull flow is a common standard well-characterized in

11

the hydrological literature; it represents a significant flood stage that returns roughly

twice every three years. Empirically parameterized power laws can be employed

to estimate a wide range of stream reach attributes during bankfull flow, including

bankfull mean depth Dbk (but not Rbk) [51]. In this study, I estimated reach bankfull

shear velocity values U∗bk using field-measured slopes, drainage areas calculated from

digital elevation models (DEMs), and values of Dbk estimated from these areas and

power law coefficients and exponents for the mountains of western North Carolina

[31].

Area drained and slope

To determine upstream drainage area A for study sites, I downloaded 30 m horizontal

resolution United States Geological Survey (USGS) DEMs covering the complete wa-

tersheds of all study streams, and used the software package TauDEM in conjunction

with ArcGIS to generate stream networks based on topography. I overlayed these

networks onto USGS digital maps with labeled water bodies and visually confirmed

close correspondence with the networks I had generated. In the field, I used a global

positioning satellite (GPS) device to determine coordinates for each study reach, and

matched these to nearest stream points in the DEM-based network. All points were

within 70 m of target streams and locations matched properly with key landmarks

(e.g. stream junctions, bridges, roads). I then used TauDem to calculate watershed

area drained through the GPS-matched stream point at each site.

To determine stream bottom slope Z at each site, I made field measurements along

the thalweg (deepest part of the channel) using a digital clinometer (±0.1 degrees)

and surveying rods, dividing each reach into multiple segments at stream bends to

ensure good estimates for reach horizontal length, the slope denominator. I also

estimated reach slopes using DEM data. I employed field measures in analysis except

for the one site not surveyed (Tal-2). To estimate a field value for that site, I used

12

the regression relationship between DEM and field slope values for the other fourteen

sites (R2 = 0.927).

2.2.3 Hydrodynamic forces

Flowing water imposes three forces on benthic organisms that may damage them, dis-

lodge them or inhibit locomotion: drag, lift, and acceleration reaction [13]. Among

these, acceleration reaction appears to be relatively unimportant for organisms as

small as E. proxima [14]. This is true even in intertidal environments, where acceler-

ations from breaking waves (see [13]) exceed by several-fold documented turbulence-

driven accelerations in streams (see [32]). Here, I focus on lift and drag.

A body in flow experiences both lift and drag proportional to the square of fluid

velocity acting upon it [72]. Therefore, an organism can avoid both forces quite

effectively by avoiding high-velocity flows. Shorter shells extend less into the velocity

profile that increases vertically from stream bottom. I compared shell heights across

sites (focusing on the largest snails) to test whether hydraulically more severe sites

were associated with shorter shells.

Drag has two components. Pressure drag is an inertial force that results from

the difference in pressure between the front and rear of an object with respect to the

direction of flow, and increases with the object’s area projected normal to flow. I

compared the frontal area of snails across sites (again focusing on the largest snails)

to test for variation reducing exposure at more stressful sites. Skin friction results

from viscous forces applied by fluid as it flows around an object, and increases with

the object’s exposed area [72]. I did not quantify this area directly. However, given a

particular frontal area, and assuming no differences in shell texture, snails with longer

shells (and thus more streamlined forms) should have greater area exposed to flow.

Similarly, lift increases with the projected area of a body parallel to flow, so longer

and more streamlined shapes are relatively prone to lift [72]. I measured snail shell

13

lengths to help explore morphological variation potentially related to skin friction and

lift.

The shape that minimizes the total force experienced by an organism exposed to

a particular flow velocity depends upon the relative importance of pressure drag, skin

friction and lift. This ranking, in turn, is determined in large part by the organism’s

Reynolds number, computed as

Re =Ul

ν, (2.2)

where U gives mean fluid velocity through the organism’s projection normal to flow,

l is a characteristic body length, and ν is the kinematic viscosity of the flowing fluid.

At Re < 102, skin friction is important and bluff shapes minimize drag, while at

Re > 104, pressure drag predominates and streamlined shapes minimize total drag.

Little is known about the best shapes for drag reduction in between these values [72].

Streamlining in benthic organisms is essentially equivalent to dorsoventral flattening,

assuming the body is held close to or pressed against the substrate.

Lift complicates the picture, because it increases with Re and with streamlining

or flattening [72]. Lift generally exceeded drag in tests of several aquatic larvae with

strong dorsoventral flattening, at flows from 0.5-1.2 m s−1; however, the converse held

for the mayfly Baetis, which is roughly tubular in shape [74]. E. proxima is grossly

bluff and, like Baetis, presents a fairly circular projection when oriented to oncoming

flow, so the influence of drag forces likely outweighs that of lift in the evolution of E.

proxima shell form.

In any case, characterizing Re is clearly critical for making interpretations about

the effects of body shape on hydrodynamic forces experienced. I estimated Re’s

for newly hatched (ca. 1 mm long, pers. obs.) and large specimens (>10 mm) of

E. proxima at multiple flow velocities (and 20C) to develop a sense of whether its

hydrodynamic demands change qualitatively during ontogeny. In the absence of my

own direct field measurements of flow speed at the relevant heights, I used assorted

14

values from the literature in an attempt to develop an envelope of possibility. I

also built an apparatus that allowed me to subject live snails to gradually increasing

flows up to 2.49 m s−1 through a 12.7 mm diameter pipe in an attempt to determine

the maximum relevant Re for large snails (i.e. the highest Re at which a snail can

withstand dislodgement).

To help evaluate whether snails shift from bluffer to more streamlined forms

through ontogeny, as they grow in size and Re, I considered plots of shell height

against shell length (or aperture length as a proxy—see below) for the sample for

each site (see, e.g., Figure 2.3). To compare shapes of snails among sites, in an

attempt to look for effects of hydraulic environment, I contrasted these plots; see

Statistical Analysis below for more detail. A simple comparison of height-to-length

ratios among sites would be biased if mean shell sizes were to vary among sites and

shell shape change with size (both conditions were met in this study).

In a final set of tests, I measured snail foot sizes and plotted these against shell

size across sites to explore whether snails at rougher sites had relatively large feet, a

condition likely to enhance resistance against hydrodynamic forces experienced. Mul-

tiple studies have found tenacity to scale linearly with foot attachment area in marine

snails [37], and Littorina from wave-exposed sites grow larger feet than conspecifics

from protected locations, adjusting for body size [69].

2.2.4 Morphometry

To measure the dimensions most relevant to the drag forces an object might expe-

rience, it is first necessary to determine the object’s likely orientation with respect

to flow [72]. Huryn and Denny [40] studied orientation patterns in three species of

Elimia and found that each kind turned to face flow above a critical water velocity

(0.2-0.4 m s−1). Like the snails in the orientation study, E. proxima have elongate

coniform shells. Following from this, I assumed snails orient into flow under the

15

Figure 2.1: Shell length measurements. Aperture length AB and shell length BC.Shell height was the maximum segment length perpendicular to the plane of thepage, determined using photographs oriented orthogonally to the example here (seeFigure 2.2).

Figure 2.2: Snail measurements II. Shell width EF and height GH. Snail picturedwith shell opening facing up (in upper right hand quadrant of image). Not to scalewith Figure 2.1.

16

high-velocity conditions of greatest interest to this study—conditions that threaten

to dislodge snails or inhibit locomotion. Accordingly, I measured length along the

long axis of the shell, and frontal area as the area projected perpendicularly to it.

To determine length, I took scaled standardized digital photographs of snails with

major axis parallel to the plane of the lens. In essentially all mature specimens,

however, some portion of the spire of the cone is missing (pers. obs.), presumably due

to corrasion. Thus each snail can be conceptually associated with a directly observable

“realized” shell length and an “ideal” shell length—full length in the absence of

corrasion. Realized length and its corollary, realized shape, are more likely to influence

the microhabitat distribution of snails because they affect actual forces experienced.

Ideal length and shape, however, almost certainly have a closer relationship with snail

genotype. If hydrodynamic forces influence variation in snail shape among sites via

natural selection, ideal shape should give a stronger signal than realized shape.

I used shell aperture length as a proxy for ideal length, assuming these co-oriented

linear measures to be directly proportional to each other. To build confidence in the

quality of this indicator, I regressed log-transformed ash-free dry mass (AFDM ) of

snail soft tissue against log aperture length in a sample of 28 snails collected from

Buck Creek in mid-February 2004, chosen haphazardly but to represent a wide range

of sizes, and found a close relationship (R2 = 0.970). AFDM is a robust measure of

snail mass because it excludes both shell and inorganic particles of sediment commonly

found in the digestive tract. I calculated AFDM for each snail as the difference in mass

between its soft tissue after oven drying at 80C to constant mass, and the inorganic

remains left after subsequent treatment in a muffle furnace (600C for 24 hours). Before

obtaining AFDM, I photographed each snail for aperture length measurement in the

same manner as photographs for full shell length, described above, and then carefully

cracked each shell with pliers to allow removal of soft tissue for oven drying.

To extract aperture length from my photographs (see Figure 2.1), I manually

17

identified the apex A of the shell aperture in each image and programmed an algorithm

to find the longest line segment AB connecting this point to the outside edge of the

base of the aperture. The same algorithm then measured realized shell length by

calculating the distance from the secondary aperture base point B, once determined,

to a manually selected point C at the apex of the centerline of the entire shell.

To quantify shell area, I took scaled standardized digital photographs of snails

with major axis normal to the plane of the camera lens, against a simple contrasting

background. For height, I programmed an algorithm to measure width as the longest

segment EF across the frontal area projection starting from a manually specified point

F at the outermost edge of the shell’s aperture, as shown in Figure 2.2. (Live snails

generally hold EF parallel to the surface on which they are attached.) The program

then calculated shell height as length of the longest segment GH perpendicular to

width.

Finally, to measure foot size, I constructed a glass-bottomed arena in which snails

could move freely under about 20 mm of water. The arena mounted on top of a

box-like base with a flat bottom, an open top and one open side. From inside the

base, I took digital photographs of each snail’s foot sticking against the glass above,

but only once the snail emerged from its shell and began to move. I then used the

magnetic lasso tool (settings: width 4 pixels, edge contrast 10%, frequency 85) in

Adobe Photoshop Elements 4.0 to trace and fill the snail’s foot in each image for easy

calculation of area (excluding the snail’s head).

2.2.5 Statistical analysis

To test for effects of hydraulic environment on size, I fit linear models separately

relating shell height or projected area to the random factor stream and to U∗bk,

avoiding pseudoreplication by comparing effects to variation at the level of individual

sites, the experimental unit. In separate analyses, I used the full unrestricted data

18

set, the largest quartile of snails from each site, or the largest ten percent of snails

from each site, because size constraints should be easiest to detect comparing largest

size classes. Using the same approach, I also tested for effects of temperature (for

each stream, measured at three locations at all three sites on the same morning before

sun struck the water, to ensure within-stream comparability; June 17–July 6, 2004).

I analyzed variation in shape by separately regressing snail height or foot area on

aperture length or shell length, one set of four regressions per site. I employed all

available data, using no size restrictions. When paired variables differed in units (i.e.

area vs. length), I log-transformed them prior to analysis.

To test for variation in shell shape with size (and potentially ontogeny), I compared

the intercepts of the regressions of shell height on length for each site to zero. I also

compared the grand intercept to zero, developed from individual intercepts weighted

by the inverses of the squares of their standard errors. Positive intercepts indicate

that bluffness decreases with size, when bluffness is defined as the height-to-length

ratio. (This interpretation follows from considering a fitted regression, H = aL + b,

with H for height and L for length. Then the height-to-length ratio can be expressed

(aL + b)/L, with derivative −bL−2 with respect to L. Thus, for intercepts b > 0, the

height-to-length ratio is a decreasing function of L.)

To test for effects of hydraulic environment (or temperature) on shape, I used

linear models to compare fitted regression features across sites, and sought to explain

variation with the random factor stream and with U∗bk (or temperature). I compared

regression slopes and intercepts, and regression heights at fixed small and large sizes.

Each regression feature estimate was weighted by the inverse of the square of its

standard error. For the fixed sizes, I used the tenth and ninetieth percentile values

of aperture length or shell length (depending upon the analysis) for the entire pooled

sample of snails, allowing comparison of shell shapes across sites at standard sizes

requiring no extrapolation at most sites to compute an estimate.

19

2.3 Results

2.3.1 Reynolds number

Hart et al. [32] measured flow velocities from 1-10 mm in height over stones colonized

by black fly (simuliid) larvae, which are rheophilic and appear to prefer faster-moving

water than E. proxima (pers. obs.). The swiftest currents observed might thus set

reasonable bounds on the highest velocities E. proxima are likely to encounter under

normal conditions. At 1 mm, the fastest flow observed was 0.56 m s−1, which would

correspond to Re ≈ 600 for a 1 mm snail (this calculation, as the others, assumes a

water temperature of 20C, relatively high for E. proxima, thus making Re estimates

relatively high). Re dips to 100 at flows of 0.1 m s−1 for snails this size—still likely

swifter than normal given their low profile (ca. 1 mm) and apparent preference for

stream edge habitats (pers. obs.).

At 3 mm, almost half the height of the largest snail in my sample, the fastest

flow Hart et al. observed was 0.69 m s−1, corresponding to Re ≈ 10, 000 for that

snail (14.5 mm long). In the apparatus I constructed, several snails over 10 mm long

withstood pipe flows up to 2.49 m s−1 for one minute without dislodging, at Re from

roughly 25,000-35,000.

2.3.2 Size

Neither shell height nor frontal area related significantly to U∗bk or temperature in

the analysis of complete samples. However, mean shell size decreased with increasing

hydraulic stress (U∗bk) in tests incorporating only the largest 25 or 10 percent of snails

at each site. Both effect strength and significance increased with increasing restriction

(i.e. 25 percent, 10 percent) of the test samples. Shell size varied positively with

temperature in tests including only the top decile. Table 2.2 presents full details.

20

Table 2.2: Shell size and environment. Columns show effects and significance of U∗bkor temperature on size in different data sets, from separate linear models of shellheight or frontal area as a function of these factors. Stream effects were significantbut are not shown. Effects were compared to variation at the level of individual sites;for all tests shown, df = (1, 9).

Data set ntot Eff-U∗bk p-value Eff-Temp(C) p-value

Shell heightAll snails per site 647 −0.719 0.401 −0.000 0.999Top quartile p.s. 166 −2.378 0.009 ** 0.191 0.110Top decile p.s. 66 −3.741 0.001 ** 0.402 0.004 **

Shell frontal areaAll snails per site 647 −7.321 0.215 0.284 0.696Top quartile p.s. 166 −21.698 0.004 ** 1.783 0.080 .Top decile p.s. 66 −35.107 0.001 ** 3.781 0.006 **

Table 2.3: Site-by-site slope and intercept values for individually fitted linear modelsof shell height as a function of aperture length.

Stream Site n Slope Intercept Intercept–95% CIBuck 1 48 0.722 0.867 0.531−1.203

2 58 0.773 0.616 0.073−1.1603 56 0.719 0.761 0.354−1.168

Curtis 1 62 0.813 0.589 0.092−1.0852 54 0.707 1.006 0.446−1.5653 50 0.843 0.537 0.108−0.966

Long 1 13 0.734 0.654 0.203−1.1062 20 0.759 0.567 0.102−1.0313 26 0.781 0.467 −0.182−1.116

Snow 1 38 0.754 0.639 0.276−1.0032 18 0.838 0.378 −0.328−1.0853 42 0.754 0.658 0.210−1.107

Tal 1 49 0.790 0.657 0.217−1.0972 58 0.839 0.370 −0.196−0.9353 55 0.840 0.339 −0.064−0.742

21

3 5 7

3

5

7

Aperture length

She

ll ht

Buck Creek

3 5 7

3

5

7

Aperture length

She

ll ht

Curtis Creek

3 5 7

3

5

7

Aperture length

She

ll ht

Long Creek

3 5 7

3

5

7

Aperture length

She

ll ht

Little Snowbird Creek

3 5 7

3

5

7

Aperture length

She

ll ht

Tallulah River

Figure 2.3: Plots and models of shell height (mm) vs. aperture length. Filled trianglesand solid lines correspond to the site with the greatest value of U∗bk in each stream(the hydraulically most stressful site); hollow circles and dashed lines correspond tothe intermediate-value U∗bk site; and hollow triangles and dash-dot lines correspondto the lowest-value U∗bk site. Long diagonals give y = x.

22

2.3.3 Shape

Large snails had more streamlined shells than small ones, both within sites, and when

all sites were considered collectively. In other words, intercepts of within-site shell

height vs. length regressions universally exceeded zero. These findings were statis-

tically significant at most individual sites, and stronger when sites were considered

collectively (p < .001, df = (1, 13)). Table 2.3 shows regression results for shell height

vs. aperture length for each site, including 95 percent confidence intervals around in-

tercept values. Figure 2.3 illustrates the same regressions. Results for shell height vs.

shell length were qualitatively the same.

Hydraulic environment, as well as size, appeared to affect shell shape. U∗bk exerted

a positive influence on regression intercepts and heights at tenth percentile values of

aperture and shell lengths; this effect was statistically significant in most cases (see

Table 2.4 and, e.g., Figure 2.4). Thus, small shells were bluffer at hydraulically more

stressful locations. At the same time, U∗bk exerted a generally significant negative

effect on model slopes (see Table 2.4 and, e.g., Figure 2.5). This indicates that snails’

transition across the size axis from bluffer shapes (when small) to more streamlined

ones (when large) was faster at hydraulically rougher sites. In other words, shell

height increased more slowly with aperture or shell length at stressful sites.

Hydraulic environment had no significant effect on foot size relative to shell size

(Table 2.4), and temperature had no significant effect on any shape relationship.

2.4 Discussion

2.4.1 Variation in shell size

This study augments a body of observations that benthic organisms tend to present

lower profiles in hydraulically more stressful environments. Many lotic insects, for

23

0.2 0.3 0.4 0.5 0.6

0.4

0.6

0.8

1

1.2

U*

Inte

rcep

t, S

hell

ht ~

Ape

rtur

e le

ngth

Figure 2.4: Site-by-site aperture length–shell height intercept vs. U∗bk. Symbol size isproportional to site sample sizes. Note consistent upwards trend within each stream.Filled triangles = Buck Creek sites; filled diamonds = Long; filled circles = Curtis;hollow triangles = Tal; hollow squares = Snow.

24

0.2 0.3 0.4 0.5 0.6

0.75

0.8

0.85

U*

Slo

pe, S

hell

ht ~

Ape

rtur

e le

ngth

Figure 2.5: Site-by-site aperture length–shell height slope vs. U∗bk. Note consistentdownwards trend within each stream. Same symbolic key as Figure 2.4.

25

Table 2.4: Effects of hydraulic environment on shell shape and foot–shell relationship,assessed through effects on features of within-site regressions relating paired size met-rics. 10th and 90th indicate regression heights at the tenth and ninetieth percentiles,respectively, of the independent variable as computed for the entire sample acrossall sites. Besides factors shown, all models also included stream as a random factor.df = (1, 10).

Regression ntot Estimate Eff-U∗bk p-valueShell ht vs. aperture len 647 Slope -0.297 0.027 *

Intercept 1.253 0.006 **10th 0.420 0.018 *90th −0.349 0.289

Shell ht vs. shell len 646 Slope -0.268 0.050 *Intercept 2.055 0.029 *10th 0.433 0.12390th −0.993 0.079 .

Ln(foot area) vs. ln(aperture len) 544 Slope -0.004 0.994Intercept −0.080 0.90410th −0.024 0.88490th 0.009 0.972

Ln(foot area) vs. ln(shell len) 543 Slope -0.228 0.628Intercept 0.571 0.57310th 0.138 0.65590th −0.025 0.930

example, are smaller than their lake-dwelling relatives [29]. Multiple snail species

have been found to be smaller in fast-flowing stream habitats than slow ones [10, 43],

and in wave-exposed habitats than in protected ones [69]. This consistent pattern

provides one reason to suspect a causal relationship between hydraulic environment

and E. proxima size.

What mechanisms might drive such a relationship? While Ambuhl’s thesis [3]

that a substantial viscous sublayer blankets stream bottoms has been discredited,

some investigators may have carried the opposite notion too far, namely that strong

turbulent flows essentially reach the bed across most of a stream, and velocity mea-

surements 20 mm high or higher can approximate near-bed currents [40]. The high

diversity of velocity profile shapes present in the tiny existing sample of very near-

bed field profiles [32, 39] suggests that low height might commonly reduce the mean

flow velocity to which an organism is exposed through its projected area. Further,

26

these empirical profiles were taken extending from the upper surfaces of stones, and

do not account for the diversity of flow patterns and refuges likely to exist amongst

roughness elements on stream beds. Smaller animals can find refuge in dead water

zones behind smaller obstacles (e.g. note the dead zone–obstacle size relationship in

[67]), and fit into smaller crevices under and among rocks and debris.

Thus, small size is probable to benefit organisms in hydraulically stressful envi-

ronments both by reducing the mean velocity faced in many contexts when organisms

are exposed, and by providing more access to flow refuges. These effects in turn have

likely positive ramifications for daily incremental fitness (e.g. energetics, foraging ac-

cess) and survival of catastrophic floods.

In light of these potential benefits, and the corresponding disadvantages of larger

size, the observed differences among E. proxima populations might be driven by

selected genetic differences or adaptive plasticity. Alternatively, reduced growth rates,

increased mortality rates, or increased rates of flood entrainment driven by severe

hydraulic conditions could account for the same observations, even if not influenced

by organism size. Size is a very general trait, and determining the causal bases of

variation in natural populations is a perennial challenge.

Temperature figures prominently in much of the literature on body size, and thus

makes an important alternative factor to explore. Thermal regime influences growth

and mortality in an enormous range of organisms, and can also exert an indirect influ-

ence through effects on food supply. In this study, June and July water temperature

correlated positively with mean shell size of the largest decile at each site. Higher sites

were colder than lower ones, and rankings within streams remained stable throughout

the year except for winter months, when they equalized (pers. obs.).

However, at least several considerations suggest that temperature gradients did

not drive the size variation observed here. First, temperature associated more weakly

than hydraulics with size. Second, this was true despite the fact that hydraulic envi-

27

ronment varied nonmonotonically within streams, creating a more complex template

than temperature for populations to track (relevant if genetic variation drove the size

variation observed). And finally, although thermal gradients have been widely found

to coincide with size clines in ectotherms, colder temperatures paradoxically associate

with larger individuals in the great majority of cases [4, 58, 71]—the opposite from

the case here.

Alternative explanations cannot be exhausted in a correlative study, but hydraulic

environment appears at least more strongly linked to size than temperature does.

Further research to suggest a causal connection between shell size and hydraulics

might include experimental manipulation of shells or flow environment (while keeping

the other constant—e.g. augmenting shell height and tracking any changes in behavior

in a flow-controlled arena).

2.4.2 Variation in shell shape with size

The unequivocal result emerging from the analysis of shell shape is that small E. prox-

ima from the populations studied are bluffer than large ones. The most parsimonious

explanation is that individual snails change shape during ontogeny. Selective mortal-

ity or washing away of bluffer snails as they grow could drive the same observed trend.

However, in these cases, the size-adjusted variance in shell height should decrease with

shell or aperture length. Figure 2.6 demonstrates no change or an increase. (Future

work should clearly include tracking individuals as they grow.)

Such an ontogenetic shift would be consistent with adaptive expectations from

a hydrodynamic perspective. Reynolds number estimates reported here for small

and large specimens exposed to relatively rapid flows suggest that E. proxima grow

through stages in which rather different shapes would optimize hydrodynamic per-

formance (see [64]). Furthermore, the Re estimates are largely consistent with values

reported in the literature for other stream snails and benthic fauna of similar size range

28

[40, 67]. (High estimates in this study do extend higher, but are based on greater flow

speeds.) The present research may offer the first evidence of a predicted but appar-

ently heretofore unobserved pattern, namely that stream benthic macroinvertebrates

should progress from bluffer to more streamlined shapes through ontogeny.

Although this prediction was developed from hydrodynamic considerations, other

factors could drive the same allometric pattern. For instance, developmental con-

straints might require E. proxima to begin life in stubby shells. The variation in

shape observed for small (tenth percentile) shells among sites and according to U∗bk,

however, suggests developmental leeway and plastic or genetic responsiveness to en-

vironment. Another explanation for the pattern might be that bluff shells help small

snails resist crushing by crayfish, a common snail predator. In turn, crayfish abun-

dance or variety might plausibly vary with U∗bk, and drive variation in shell shape of

juvenile snails. Simple tank experiments, coupled with field surveys of crayfish, could

help test these hypotheses. Limited data suggest crayfish may feed little on proso-

branch gastropods, such as E. proxima—prosobranchs have protective opercula and

often thick and ridgy shells—but experimental tests did not include small juveniles

[6].

2.4.3 Variation in shell shape with environment

Like the allometric variation observed, the pattern of shell shape differences among

sites appears consistent with an adaptive response to hydraulic environment. Snails

in rougher environments were bluffer when small (e.g. tenth percentile, Table 2.4)

but trended toward more streamlined shapes when large (e.g. ninetieth percentile).

In other words, snails at higher U∗bk sites appear to make an exaggerated ontogenetic

shift, expressed here as lower height-vs.-length regression slopes, when compared to

conspecifics in gentler reaches (Table 2.4).

One consequence of this pattern is a zone of intermediate size where expected

29

1 1.5 2

−0.1

0

0.1

ln(aperture length)

Res

idua

ls

Figure 2.6: Height variation after accounting for size. For each site, I regressed log-transformed shell height on log-transformed aperture length and calculated residuals.This figure plots the aggregated residuals from all regressions, and shows that afteraccounting for size, variance in shell height stays constant or increases slightly withaperture length. A similar result obtains for shell length.

30

shell shapes from snails developing in a wide range of hydraulic environments should

overlap, rendering detection of intersite shape differences more difficult. In this study,

the artificial sampling cutoff of 5 mm long shells compounded this problem. Sampling

regimes in future work of this nature should clearly emphasize acquiring the fullest

possible range of specimen sizes. The fact that in this study the largest snails at

high-stress sites were relatively small also complicates analysis; size and shape com-

pensation for high-velocity flows may be working in concert, with the former obscuring

the latter. Ironically, this potential joint and parallel action suggests that hydraulics

may be a powerful selective force on snails, yet makes detection of shape effects more

difficult. Considering these challenges, this study seems to provide reasonable evi-

dence for the existence of hydraulic environment–induced phenotypic variation in E.

proxima shape and ontogeny.

The data gathered do not address whether genetic differentiation or phenotypic

plasticity might be driving variation. Different considerations favor the alternative ex-

planations. U∗bk did not form monotonic gradients within study streams. Such spatial

complexity can render local adaptation less likely by disrupting the development of

genetic clines. Furthermore, plastic responses of shell form to flow environment have

been demonstrated in marine gastropods through reciprocal transplant and common

garden studies [69]. However, sites in this study were well separated, and gene flow

can be quite restricted in stream-dwelling snails, even within the same watercourse

[12, 59]. These latter considerations offer at least the possibility of local genetic adap-

tation. (Differential growth rates, mortality or entrainment in floods as a function of

shell shape could also explain the trends here, but these phenomena would favor an

eventual selective response.)

Future work might employ common garden or reciprocal transplant approaches

to distinguish between genetic or plastic bases for variation. Direct measurements of

drag on varying shell shapes could add valuable information as well.

31

2.4.4 Variation in relative foot size

This study provides no evidence for environmentally driven variation in foot size,

relative to shell size. Other work has documented snails to have relatively larger feet

in more violent hydrodynamic regimes [69]. The lack of findings here may reflect a

lack of variation, or may stem from the challenges of measuring a soft part when

compared to a shell. The coefficient of variation for pooled foot area data in this

study, 0.489, fairly exceeded that for pooled shell frontal area, 0.392, suggesting that

increased measurement error on feet may have obscured any trend present.

2.4.5 Broader context

Subtle variations in the size and shape of shells may seem unimportant in mountain

stream environments, where uneven discharge, high turbulence, and jumbled cobbles,

pebbles, and debris create highly variable and complex flow at every spatial and tem-

poral scale. In this context, behavioral adaptations like microhabitat preference and

refuge-seeking may intuitively seem more important for population survival. Perhaps

they are.

Another perspective is possible. At any point in time, the stream bed surface

paints a mosaic of flow environments. For a given benthic organism, some patches

are hydrodynamically suitable, allowing theoretically indefinite occupation at low

energetic cost; other patches are marginal, allowing passage or maintenance of position

but at higher cost; and a third set of patches are inhospitable, barring transit due

to excessive hydrodynamic forces that would damage, immobilize, or dislodge the

organism. The mosaic changes as flow fluctuates hourly and seasonally, sometimes

bringing sudden floods. Mountain stream beds may be paradigmatic patchy and

dynamic environments.

In this context, subtle differences in morphology with hydrodynamic ramifications

could have important consequences for organisms. Slight variations could lead to

32

small shifts in the proportion of acceptable patches at most flow levels. In turn,

percolation theory (see, e.g., [19]) suggests that small shifts in proportion could have

dramatic effects on overall habitat connectivity, and therefore on dispersal and access

to food, refuge, mates and other essentials. Even without changes in connectivity,

more hydrodynamic individuals should experience lower energetic costs of locomotion

for a given travel path and lower risk of dislodgement during floods, and have access

to more area for foraging.

The subtlety of variation observed in this study itself suggests the importance of

slight differences in form as they pertain to the hydraulic environment. The study

also offers a new approach, the analysis of intraspecific variation in size and shape

across environments, for exploring the interplay between hydrodynamic forces and

morphology in stream benthic fauna. In light of the challenges of measuring near-

bed flow environments directly, perhaps biological forms will prove to be the most

sensitive instruments.

33

Chapter 3

Influences of hydraulic

environment and flooding on

dispersal

3.1 Introduction

Dispersal exerts a key influence on many population genetic and demographic pro-

cesses. At the same time, it is difficult to fully characterize, especially with respect

to relatively long distance transport events which, despite their general rarity, have

important consequences for the spread of genes and populations [8].

Streams offer promising systems for the study of dispersal, its influences and

its effects. Organisms confined within their banks occupy a landscape of reduced

dimensionality where movement can be tracked and characterized along a single up-

stream/downstream axis. While branching tributaries increase spatial complexity in

the upstream direction to a degree, downstream dispersal is essentially confined to be

linear.

In a widely shared view, the flow of water dominates the biology of stream organ-

34

isms (see, e.g., [1, 33, 65]). It shapes and constrains morphology [72], behavior [40],

and distribution and abundance at small and large scales [1, 75]. It also introduces

a basic asymmetry to movement and dispersal because of its grossly unidirectional

nature.

Some benthic invertebrates appear to voluntarily enter the water column in order

to initiate downstream drift [54]. Both these and other organisms may also be en-

trained accidentally by floods [1, 63], likely an important mechanism for long distance

dispersal in stream biota. Because drifting individuals and any flood entrainment

survivors must be deposited along a one-dimensional path downstream from their

origin, detecting long moves should be easier than in other systems. Furthermore,

flow gauges (or, where they are absent, rainfall history) provide a record of events

capable of precipitating flood-driven dislocations.

A rich account of dispersal must include description of long distance movement

patterns. It must also detail the major relationships between environment and disper-

sal. Environmental variation affects movement at many spatial scales. Local features

may physically inhibit or facilitate locomotion or provide cues [48]. Larger scale

habitat patchiness may shape patterns of dispersal across landscapes [35, 36].

Streams offer ample variation for the study of such influences. Stream beds present

highly heterogeneous flow environments that strongly influence the paths and costs

of travel available to benthic fauna [48, 65]. At the same time, the gross features of

streams, including substrate composition, slope, and discharge levels, shift dramat-

ically as they descend from headwaters toward alluvial plains [18]. These features

have direct consequences for the near-bed hydraulic environment [56] which, in turn,

bears directly on dispersal.

This study investigates dispersal in Elimia proxima, a stream-dwelling proso-

branch snail common in the southern Appalachian Mountains of the United States.

Prosobranchs are not known to voluntarily enter stream drift, so long distance down-

35

stream displacements are likely caused by floods. I conducted mark-release-resurvey

experiments at sites spanning a range of hydraulic environments and flood histories,

and developed a series of nested models to fit my observations, in an attempt to

elucidate the importance of floods in shaping snail dispersal, and to register the influ-

ence of hydraulic environment on snail-driven and flood-driven dispersal alike. While

a number of studies document changes in site-specific species abundance and com-

position following spates (e.g. [53, 63]), and others anecdotally report long-distance

displacements [11, 55], I am unaware of previous attempts to isolate and quantify the

effect of natural floods on the dispersal of benthic stream macroinvertebrates.

Table 3.1: Experimental reaches by code name (see text). UTM-E and UTM-N giveUniversal Transverse Mercator coordinates (North American Datum 1983, Zone 17,in meters). Area indicates basin area drained (km2). Substrate lists the two mostcommon sedimentary grades on the Wentworth scale [76].

Reach UTM-E UTM-N Area SubstrateUB 262641 3884184 15.53 cobbles, bouldersLB 261223 3889745 38.79 pebbles, cobblesUT 266728 3877561 6.68 cobbles, bouldersLT 267896 3864791 99.64 pebbles, cobbles

3.2 Methods

3.2.1 Mark-release-resurvey experiments

From June 2003 to August 2004, I collected, marked, released and then returned to

search for over 4000 mature E. proxima at four hydraulically contrasting reaches di-

vided between Buck Creek and the Tallulah River, two watercourses in the mountains

of western North Carolina and northern Georgia (see Table 3.1; reaches coded UB,

LB, UT, and LT for upper and lower Buck and Tallulah, respectively). Within each

reach, I pseudorandomly selected multiple release points separated by mean distances

of 108 m, always leaving snails in a single pile near the stream bank in a sheltered

36

microsite. This practice allowed the snails to emerge from their shells and attach to

the stream bottom without first being swept away by currents. I marked subjects’

shells with tiny plastic tags following Freilich’s method [21]. Table 3.2 gives further

design details, as well as environmental and flood information associated with each

experimental release and resurvey.

To conduct surveys, I used a five-gallon bucket with the bottom cut out and

replaced by a clear acrylic panel. Placed on top of the water, this apparatus allowed

me to see clearly to the stream bottom (I used the unaided eye for shallow areas

and water surface interfaces). In each survey, I systematically and uniformly scanned

the entire width of stream moving away from the point of release in both upstream

and downstream directions until I could find no more marked snails for a consecutive

20 m. I then continued another 20 m, but searched only within 2 m of the release

bank. Any marked snails here triggered a continued full-width survey (after checking

the stream area already passed over), so that a consecutive 40 m without marked

snails on the release bank were required to terminate a search.

In one exception, I surveyed only within 6 m of the bank at the lower Tallulah

site for the “full-width” survey component because of the main current’s depth and

strength. This seemed acceptable because in the August 2003 surveys, >99 percent

of marked snails at other sites were found within 6 m of the release bank (n = 645),

and 100 percent of snails found at LT were within 4 m of the release bank (n = 202).

I measured the position of each snail located and assigned it a stream-wise dispersal

distance relative to its point of release.

3.2.2 Hydraulic environment and flow history reconstruction

Stream biologists widely view hydraulic forces as powerful influences on benthic biota

[1, 33]. Shear velocity U∗ is a metric of hydraulic environment especially likely to

bear on crawling dispersal of benthic organisms, including snails, because of its close

37

Table 3.2: Mark-release-resurvey experimental setup. Experiments are coded by two-letter reach code, followed by a number for subreach release site. Letters followingsite numbers differentiate multiple resurveys of the same cohort. Slopes were mea-sured over 62.6 m segments centered on release points (see Section 3.2.2). Intervalindicates days of dispersal until resurvey and n denotes the number of snails initiallyreleased. “Max flood” gives the estimated maximum flood increment during the dis-persal interval, as measured in multiples of reach-specific bankfull flow, and “Maxvel” is the corresponding mean peak current velocity (m s−1). Nos. 3-4 at LB and LTwere collocated but on opposite banks.

Experiment Slope U∗bk Release date Interval n Max flood Max velUB1 0.017 0.315 30 Jun 2003 56 468 0.62 1.46UB2a 0.044 0.505 30 Jun 2003 58 470 0.62 1.46UB2b 0.044 0.505 30 Jun 2003 483 470 2.29 1.46LB1a 0.009 0.258 30 Jun 2003 54 483 0.62 1.65LB1b 0.009 0.258 30 Jun 2003 384 483 1.06 1.93LB2 0.008 0.251 30 Jun 2003 389 483 1.06 1.93LB3 0.010 0.280 28 Feb 2004 137 150 0.33 1.37LB4 0.010 0.280 28 Feb 2004 137 150 0.33 1.37UT1a 0.051 0.474 17 Jul 2003 42 471 0.31 0.97UT1b 0.051 0.474 17 Jul 2003 383 471 2.20 1.84UT2a 0.043 0.435 29 Jun 2003 61 404 0.67 1.23UT2b 0.043 0.435 29 Jun 2003 401 404 2.20 1.84UT3 0.038 0.410 29 Feb 2004 153 150 0.33 0.96LT1a 0.002 0.143 17 Jul 2003 48 576 0.50 1.06LT1b 0.002 0.143 17 Jul 2003 385 576 2.20 1.59LT3 0.005 0.236 29 Feb 2004 161 150 0.33 0.94LT4 0.005 0.236 29 Feb 2004 161 150 0.33 0.94

38

relationship to near-bed water velocities and forces in turbulent flows [18]. Evidence

presented in Chapter 1 suggests a possible evolutionary effect of reach U∗ or corre-

lates on aspects of shell morphology relevant to the hydrodynamic forces E. proxima

experience. This possibility further suggests the significance of U∗ for dispersal.

Here, I employed estimates of shear velocity at standard bankfull discharge levels,

U∗bk, to compare hydraulic environments among sites. I computed U∗bk following the

methodology of Chapter 1, with the exception that I measured stream-wise streambed

slopes over shorter segments (one per subreach) and from channel reconstructions

based on detailed topographic surveys taken at three out of four reaches (see below).

Each segment centered on a snail release point and was 62.6 m long (two times the

standard deviation of all dispersal distances measured in the entire study, for all

releases). At UB, I used a digital clinometer, as in Chapter 1.

To explore the role of floods in snail dispersal, I reconstructed the flow history at

each location during the course of my experiments, and translated it into a record of

floods. I also employed the three-dimensional channel models already described, plus

a flow simulation software package, to estimate mean peak water velocity during each

flood event. Subsequent modeling and analysis of dispersal built on both the records

of floods and their peak velocities.

I reconstructed flow histories based on 15-minute discharge data from United

States Geological Survey (USGS) water flow gauges. The Tallulah reaches were both

upstream of USGS gauge 02178400, also on the Tallulah. The Buck Creek locations

were both upstream of gauge 03504000 on the Nantahala River, less than 500 m

downstream from where Buck Creek feeds into the river. The Buck Creek basin

accounts for 29 percent of the total watershed area drained through the gauge, so flow

through the Buck sites and Nantahala gauge should be reasonably well-correlated.

Standard levels of stream point discharge can be estimated using empirical power

laws acting upon the basin area drained [51]. Using published parameters for moun-

39

tain streams of western North Carolina at bankfull flow [31], I estimated each reach’s

discharge history during the experimental period based on downstream gauge flow

data. I obtained basin areas for each site and gauge following methods in Chapter 1,

and assumed the discharge ratio between sites and gauges, calculated for bankfull con-

ditions, remained constant across all flow levels (equivalent to assuming a constant

exponent of the power law across discharges).

I scaled flow records by bankfull discharge for each reach, and measured flood

magnitudes as the difference between peaks and their preceding troughs in the hy-

drograph (ignoring all events with changes under 10 percent of bankfull flow). Such

an incremental and scaled measure is comparable among sites and times with widely

varying baseline flows, and appropriate here because the chance of a snail becom-

ing dislodged by flow should depend more upon flow elevation than the exceeding of

absolute thresholds.

Finally, to generate flood current speed estimates, I conducted detailed topo-

graphic surveys at both Tallulah reaches and at lower Buck employing a Sokkia

Set 5W Total Station laser surveying unit. I used the software packages Surface-

Water Modeling System 8.1 to develop three-dimensional channel reconstructions

and Telemac 2D to model steady-state water velocity and depth on a 1 m grid for

a wide range of flow levels at each location. I computed mean water velocity as

depth-weighted average current speed, and developed power law functions of mean

velocity vs. discharge for each reach (R2 = 0.999, 1.000, 0.968, for LT, UT, and LB

respectively). I estimated power law parameters for upper Buck based on the rela-

tionship between area drained and power law coefficient (R2 = 0.939) and exponent

(R2 = 0.955) for the other three locations. Using these power law relationships,

I interpolated mean water velocities for all absolute peak flood discharges flowing

through each reach.

Fluid dynamic models were first calibrated using a tuneable roughness parameter

40

in Telemac 2D to optimize the match between predicted and observed water levels at

multiple locations for three different discharge levels at each modeled reach.

3.2.3 Models

To explore possible mechanisms of dispersal and relationships of those mechanisms

to hydraulic environment and flood history, I compared a series of hierarchically

nested models, using a simulated annealing algorithm to make maximum likelihood

estimates (MLEs) for parameter values in light of observations from the mark-release-

resurvey experiments. The fullest model included diffusion and advection processes

intended to capture snail-powered movement, and a separate module for flood-driven

dislodgement and drift. I further modeled the parameters governing each of these

processes as functions of subreach bankfull shear velocity, U∗bk.

The solution to a diffusion-advection process starting from a single point and

enduring for a time t is simply a shifted Gaussian distribution,

n(x, t) =1√

4πDte−

(x−Ct)2

4Dt , (3.1)

where x gives distance dispersed, D the coefficient of diffusion, and C the coefficient

of advection (with positive values corresponding to upstream movement). Equation

3.1 represents the first component of the full model. It can be understood as reflecting

the outcome from a biased random walk [57] on the part of the snails—the outcome

of their own active displacement. Diffusion and advection are commonly employed to

model animal movement under a wide range of circumstances [7].

The next model component incorporated flood processes by replaying the common

history of floods for each experimental cohort and modeling snail entrainment and

drift as functions of flood increment and peak mean water velocity, respectively. For

computational reasons, flood displacements were modeled sequentially after the com-

41

pletion of the diffusion-advection stage. This methodology relied on the assumption

that all parameters governing each cohort were constant in space—an imperfect but

reasonable assumption, largely because most individuals did not disperse far from

their point of release, and thus remained in similar environments.

To characterize entrainment, I used a simple model in which the odds ω of entrain-

ment in a given flood i varied linearly with the bankfull flow-scaled flood increment

magnitude mi, but were restricted to be positive, so

ωi = max{sωmi + hω, 0}. (3.2)

sω and hω give the slope and height (intercept), respectively, of the linear relation-

ship. Based on the basic relationship between odds and probability, the flood-specific

probability of entrainment pi can be expressed

pi = ωi/(1 + ωi). (3.3)

I used bankfull-scaled flood increment magnitude instead of mean flow velocity be-

cause only the former provides a standardized metric of flood severity comparable

across diverse sites.

With ample support from empirical findings on aquatic invertebrates [20, 2, 50], I

modeled the drift distance of entrained snails in a flood i as an exponential distribution

f(y) in which the expected distance βi increases linearly with flood peak mean flow

velocity vi and slope sβ, so βi = sβvi and

f(y) =1

βi

e− 1

βiy. (3.4)

Unlike the case for modeling dislodgement, flood velocity and not magnitude is the

appropriate independent variable, because of the mechanistic connection between cur-

42

rent speed and drift distance implied by the exponential distributions of invertebrate

drift distances observed in the literature. (Exponential distributions suggest that

drifting organisms settle out of flow with constant probability in time, making the

characteristic drift distance a function of water velocity.)

Assembling Equations 3.1, 3.3, and 3.4 together, then, the density of snails after

diffusion, advection, and the ith flood can be computed using the iterative model

ni(x, T ) = (1− pi)ni−1(x, T ) +∫ ∞

xpini−1(x

′, T )f(x′ − x) dx′ (3.5)

where n0(x, T ), the density of snails after diffusion and advection for a fixed period

T but prior to modeling any floods, is given by substituting t = T into Equation

3.1. Thus, following solution of 3.1, and given any history of k floods during the

dispersal interval, Equation 3.5 can be iterated k times, i = 1 . . . k, to solve for the

final expected distribution of snails. This distribution rests on the flood history,

dispersal interval, and five fundamental parameters, C, D, sω, hω, and sβ, for each

release-resurvey experiment.

In the final element of the full model, to help explore potential relationships be-

tween environment and dispersal, each of the fundamental model parameters itself

became a function of bankfull shear velocity U∗bk. This maneuver allowed all experi-

mental data to be considered simultaneously, instead of requiring separate parameter

fits for each release and resurvey of snails. For simplicity, and to focus the inquiry on

whether U∗bk had a positive, negative or neutral effect on each fundamental parameter,

I modeled the core parameters as linear functions of U∗bk at snail release locations j.

In two examples to illustrate symbology, Cj = sCU∗bkj+hC , and sωj

= ssωU∗bkj+hsω .

Values for sD and hD were restricted so that Dj > 0 for all j.

This arrangement allowed creation of nested models by imposing restrictions on

the parameters relating core parameters to shear velocity. For example, setting a

43

linear model slope to zero (e.g. sC = 0) forced the affected core parameter to some

constant value across all experiments (i.e. Cj = hC , as opposed to Cj = hC +sCU∗bkj);

setting both slope and intercept to zero eliminated the core parameter from the overall

model. I compared the complete unrestricted model against models with each core

parameter alternately held constant across environments; models with two of the

three flood-related parameters held constant; a model with all three flood parameters

constant; and a model with all flood parameters set to zero (no explicit flood-driven

dispersal component included at all). I did not experiment further with restricting C

or D because of the strong negative impacts of the restrictions already described on

overall model fit (see Results).

For each nested model and the full model, I determined maximum likelihood esti-

mates for all free parameters with a simulated annealing algorithm based on Goffe et

al. [24] and employing a Metropolis-Hastings rejection sampling algorithm. I accepted

a set of estimates when all parameter values were reproduced to within 5 percent of

each other in the top two trials as ranked by maximum likelihood (in all these cases,

the likelihoods themselves were essentially identical). I ran at least five trials per

model, starting with randomly generated initial parameter values each time.

I compared models using likelihood ratio tests. From among the best-performing

models undistinguishable through ratio tests, I selected the model with the lowest

Akaike information criterion (AIC) score as most parsimonious. I then ran five Monte

Carlo Markov chains with this model for 800,000 iterations using Metropolis-Hastings

rejection sampling, and computed upper and lower 95 percent confidence interval

limits around the MLE for each parameter in each chain. All five chain estimates for

each limit were within 5 percent of each other. I estimated each limit as the mean

from all five chains.

Finally, I used simulated annealing to determine MLEs for a full model in which

fundamental parameters were fit separately to data from each individual experiment,

44

Table 3.3: Nested models comparison. Model 0 is the full unrestricted model; restric-tions column entries denote parameters held constant in nested models, and NP liststhe number of free parameters for each model. pLRT gives p-values for likelihood ratiotests between the full model and each nested one; scores annotated with the letter “a”indicate nested models whose performance could not be statistically distinguished asinferior to the full model. Ln(L) lists computed log likelihoods, and AIC gives AkaikeInformation Criterion scores (best value boxed).

Model Restrictions NP pLRT Ln(L) AIC0 None 10 – −3451 69221 D 9 0.000 −3464 69462 C 9 0.002 −3456 69293 sω 9 0.192 a −3452 69224 hω 9 0.527 a −3451 69205 sβ 9 0.364 a −3451 69216 sω, hω 8 0.000 −3476 69687 sω, sβ 8 0.092 −3453 69238 hω, sβ 8 0.499 a −3452 69199 sω, hω, sβ 7 0.000 −3478 696910 sω, hω, sβ = 0 4 0.000 −3555 7119

instead of forcing the parameters to be functions of U∗bk. This exercise allowed assess-

ment and visualization of the best possible absolute performance of the core model

articulated in Equation 3.5.

Table 3.4: Parameter estimates with 95 percent confidence intervals for the mostparsimonious model, model 8.

Parameter MLE CI-2.5% CI-97.5%hD 3.33 2.74 4.02sD −5.20 −6.77 −3.74hC 0.11 0.08 0.15sC −0.19 −0.28 −0.09hsω

−0.82 −1.38 −0.77ssω

2.87 2.55 4.48hω −0.17 −0.37 −0.11shω – – –hsβ

24.47 19.98 30.04ssβ

– – –

3.3 Results

Likelihood ratio tests failed to distinguish four models with restrictive assumptions

as significantly different from the full model (see Table 3.3). Among these four, AIC

45

scores varied little; but the most parsimonious version made C, D, and sω functions of

U∗bk, while hω and sβ were constant across all locations. Table 3.4 gives MLEs with

95 percent confidence intervals for each free parameter in this most parsimonious

model, model 8. All estimates were significantly different than zero. Other models

(see Table 3.5) behaved similarly: coefficients of diffusion and advection generally

decreased with U∗bk, whereas the responsiveness of both entrainment odds and drift

distance to flood magnitude, sω and sβ respectively, generally increased. (Model 8

restricted sβ to be constant.)

Table 3.5: Parameter estimates for all models. Parameters converged for all mod-els (see text) except the full one, model 0. Twenty independent bouts of simulatedannealing produced generally consistent log likelihoods (best two simulations within0.003%), but not stable parameters. Here I present the maximum likelihood combi-nation. Parameter instability was likely due to model over-determination.

Model hD sD hC sC hsω ssω hhω shω hsβssβ

0 3.38 −5.31 0.11 −0.17 −1.16 3.56 0.17 −0.69 14.09 26.131 1.51 – 0.12 −0.23 −0.86 2.66 0.12 −0.52 18.50 19.592 3.72 −6.13 0.04 – −1.46 4.31 0.20 −0.79 7.94 37.953 3.53 −5.68 0.08 −0.12 0.39 – −0.93 1.74 105.63 −165.684 3.38 −5.30 0.11 −0.18 −0.79 2.79 −0.16 – 15.81 21.685 3.34 −5.22 0.11 −0.19 −1.42 4.18 0.20 −0.77 24.37 –6 3.18 −4.65 0.11 −0.19 0.34 – −0.12 – 7.80 43.667 3.55 −5.73 0.09 −0.12 0.42 – −0.83 1.52 27.27 –8 3.33 −5.20 0.11 −0.19 −0.82 2.87 −0.17 – 24.47 –9 3.00 −4.19 0.12 −0.22 0.32 – −0.12 – 27.39 –10 0.07 7.82 0.06 −0.19 – – – – – –

Figures 3.1-3.6 show the model 8 fit to data, and also the model fit in which funda-

mental parameters were estimated separately for each experiment, giving a reference

for the best possible fit given the underlying model.

A derivative result of interest is the flood size threshold mth for each release lo-

cation j: the minimum flow increment magnitude required to entrain at least some

snails. mthjcan be calculated by setting the unadjusted odds of entrainment, adapted

from Equation 3.2, equal to zero, or hωj+ sωj

mthj= 0. Through algebra and substi-

46

tution, we arrive at the more general expression

mthj=−hhω − shωU∗bkj

hsω + ssωU∗bkj

. (3.6)

In the most parsimonious model, model 8, hhω < 0 and shω = 0, making the numerator

always positive. Furthermore, hsω < 0 and ssω > 0, so at large U∗bk, the denominator

is large and mth is small. Flood size threshold increases with decreasing U∗bk until it

reaches infinity at U∗bkcrit= −hsω/ssω and all lesser values (due to the max operator

in Equation 3.2). In other words, no flood of any size causes entrainment at U∗bk ≤

U∗bkcrit. For model 8, U∗bkcrit

= 0.284, eliminating flood entrainment as a mechanism

for dispersal at half of the sites used.

Further derivative results include annual expected movements from flood entrain-

ment and advection, based upon MLE’s and likely patterns of discharge. I calcu-

lated these and related quantities from model 8 MLE’s and thirty years of discharge

data from USGS gauges downstream of experimental reaches (stations 02178400 and

03504000, October 1, 1975 to September 30, 2005). For each year, I predicted the

fraction of snails dislodged in each flood and their expected downstream drift dis-

tance, given entrainment. Using these values, I in turn estimated mean population

downstream movement from each flood and from flooding for the whole year. I also

estimated the expected fraction of snails entrained by floods at least once, the ex-

pected advection per snail, and the net expected stream-wise movement (the sum

of expected advection and flood-driven dispersal, since diffusive dispersal does not

affect mean position). I then averaged these quantities over the thirty-year record to

produce Table 3.6.

A model similar to model 8, but with flood size threshold constrained to be finite

(by forcing hsω ≥ 0; AIC= 6928; see Discussion section 3.4.1 and footnote), generated

Table 3.7.

47

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 92

42 days

UT1a

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 62

61 days

UT2a

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 18

378 days

UT1b

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 26

396 days

UT2b

Figure 3.1: Snail dispersal and model fits, upper Tallulah River. Dotted lines plotmodel 8 MLE fits; solid lines plot predictions from a model optimized for each survey.Vertical lines at distance = 0; bins are 10 m wide. Within subfigures, n indicates thenumber of snails found during the survey at the end of the specified “days” interval.Subplots in the same column depict distributions of snails from the same release, butat different times. Subplots in the same row depict distributions from releases atdifferent locations within the same site, at roughly the same time.

48

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 72

48 days

LT1a

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 26

385 days

LT1b

Figure 3.2: Snail dispersal and model fits, lower Tallulah River. Details as for Fig-ure 3.1.

49

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 115

56 days

UB1

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 196

58 days

UB2a

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 2

483 days

UB2b

Figure 3.3: Snail dispersal and model fits, upper Buck Creek. Lack of solid lineindicates insufficient data for per-site model fit. Other details as for Figure 3.1.

50

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 128

53 days

LB1a

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 4

383 days

LB1b

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 9

383 days

LB2

Figure 3.4: Snail dispersal and model fits, lower Buck Creek. Lack of solid lineindicates insufficient data for per-site model fit. Other details as for Figure 3.1.

51

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 9

153 days

UT3

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 14

161 days

LT3

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 2

161 days

LT4

Figure 3.5: Snail dispersal and model fits, intermediate dispersal interval for upperTallulah and lower Tallulah in the top and bottom rows, respectively (lower Tallulahreleases on opposite banks). Lack of solid line indicates insufficient data for per-sitemodel fit. Cut-off bin height for LT4 is 0.10. Other details as for Figure 3.1.

52

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 10

137 days

LB3

−125 0 125

0.02

0.04

0.06

Fre

quen

cy

Distance (m)

n = 22

137 days

LB4

Figure 3.6: Snail dispersal and model fits, intermediate dispersal interval for lowerBuck (releases on opposite banks). Other details as for Figure 3.1.

3.4 Discussion

A number of studies have anecdotally documented medium- to long-distance flood-

driven dispersal in stream invertebrates (e.g. [11, 55]). In the research described here,

I show that explicit inclusion of a flood dispersal mechanism can substantially improve

the overall account of dispersal in E. proxima. The only model not to incorporate

an explicit flood-driven mechanism, model 10, performed substantially worse than all

others considered (Table 3.3).

In another general finding, the results here imply that the hydraulic environment

widely influences mechanisms of dispersal. In all top-performing models, the MLE

coefficients of diffusion D and advection C both varied with U∗bk, as did at least one

core parameter involved in the flooding mechanism (Table 3.3).

3.4.1 Effects associated with shear velocity

Bankfull shear stress effects on C, D and sω exhibited a high degree of consistency

across models (Table 3.5). The other core parameters involved in flood-mediated

53

Table 3.6: Annual expected features of dispersal in the most parsimonious model,model 8. Pr(Entrain) gives the per capita probability of becoming entrained in aflood at least once. E(Drift), E(Advec) and E(Net) list expected population flooddisplacement, advection, and net stream-wise movement, respectively. All distancevalues are in meters; negative values indicate downstream displacement.

Group Pr(Entrain) E(Drift) E(Advec) E(Net)UB1 0.002 −0.1 19.9 19.8UB2 0.695 −46.1 6.7 −39.4LB1 0 0.0 23.8 23.8LB2 0 0.0 24.3 24.3LB3 0 0.0 22.3 22.3LB4 0 0.0 22.3 22.3UT1 0.544 −30.9 8.9 −22.0UT2 0.418 −22.1 11.6 −10.5UT3 0.326 −16.7 13.3 −3.4LT1 0 0.0 31.8 31.8LT3 0 0.0 25.3 25.3LT4 0 0.0 25.3 25.3

dispersal behaved more complexly. Because the most parsimonious overall model

incorporated variation only in C, D and sω, and because the consistency of results

among these parameters suggests robustness, I will focus discussion on the patterns

found amongst these three.

Advection

The coefficient of advection varied negatively with bankfull shear velocity in every

model (sC < 0). Furthermore, all estimates of C were positive, indicating upstream

movement, except for estimates at high-U∗bk sites under the lone model without an

explicit flooding mechanism. In this exception, model 10, advection (and diffusion)

had to account for the downstream tails that flood-driven dispersal explains in other

models, so negative values of C for experiments with heavy downstream tails—or

in environments highly affected by flooding—are not surprising. The other models

not only performed better overall, but were more consistent with a large body of

literature reporting positive rheotaxis in stream-dwelling snails (see Table 1 in [40]

for an extensive listing).

54

As for the variation of C with U∗bk, one potential explanation is that high shear

velocities make advancing upstream physically more difficult. This follows naturally

from the expectation that higher values of U∗ should correspond with faster near-bed

flows [18] and thus greater drag [72] exerted on snails moving in current. If upstream

mobility confers fitness, or if reduced mobility reflects environmental pressures that

diminish fitness, then the pattern observed here suggests environmental variation

in selective pressure consistent with the shell size and shape variation described in

Chapter 1.

In a related explanation, sites with higher U∗bk are likely to have smaller pro-

portions of stream bed suitable for snail locomotion at most flow levels. In these

less-connected matrices of potential habitat, snails may encounter barriers to up-

stream movement more frequently, and available upstream pathways may be more

tortuous.

In a study on four congeners to E. proxima, Huryn and Denny [40] found that

torque forces snails to face into currents above a critical threshold. The consequences

of this finding, if any, for the relationship between advection and hydraulic environ-

ment are not clear. Swifter near-bed flows at high-U∗bk sites might force more snails

to orient their locomotion by currents. Under the assumption that flows run predomi-

nantly downstream, this mechanism could lead to enhancement of upstream advection

at rougher sites (not observed). Alternatively, since substrate particle size generally

increases with U∗ [56], the complexity and variance of near-bed flow direction likely

does as well. If the fraction of near-bed current vectors facing downstream decreases

with U∗bk, then this trend could drive associated diminishing upstream movements,

aligning with observations here.

In one more possible explanation for bankfull shear velocity effects on C, high

U∗bk might drive increased entrainment by floods in such a way as to diminish model

estimates of advection. Upon closer examination, however, this possibility seems par-

55

ticularly unlikely, at least for snails. It would more or less require flood entrainment

to shift the modal dispersal distance downstream, suggesting that a majority of snails

became entrained in most experiments. Since most modes were close to release points,

drift distances following dislodgement would need to be short in a parsimonious model.

This suggested pattern of many small downstream jumps seems at odds with flood

parameter estimates. Estimates for sβ universally exceeded 20 s m−1, translating to

β ≥ 10 for any flood increment of ≥ 0.1 bankfull flow (mean peak water velocities ex-

ceeded 0.5 m s−1 at all sites for 0.1 bankfull events). A separate “advection-by-drift”

mechanism would imply a curious bimodal response to flow events: lots of tiny jumps

downstream from small and common flow increments, likely well under 0.1 bankfull,

combined with occasional major displacements from notable floods. Cased caddisflies

experienced frequent short-distance entrainments, with recovery, under elevated flow

in a laboratory flume [48]. However, this type of mechanism seems much more likely

for a fast-moving aquatic insect than for a snail, which would not be able to recover

its grip on the substrate quickly.

Diffusion

The coefficient of diffusion varied negatively with bankfull shear velocity in every

model (sD < 0) but model 10, which can be neglected. (Because model 10 lacks

an explicit mechanism of flood-driven dispersal, D increased with U∗bk in order to

account for the more substantial downstream tails also associated.) The decrease

in D with U∗bk may be driven by similar or the same factors influencing C. Near-

bed flows making upstream movement more costly may also complicate downstream

locomotion due to torque on snails’ shells (see [40]). More obviously, a diminished

proportion of patches suitable at all for locomotion should reduce D, especially as

matrix connectivity decreases.

Increased variance of flow orientation with U∗bk would seem to elevate D, but this

56

was not observed.

Increases in flood-driven entrainment with U∗bk cannot account for diminishing D.

They could have only the opposite effect (as illustrated by the exceptional behavior

of D with respect to U∗bk in model 10). This strand of evidence supplements the

case against frequent small flood-driven jumps as a mechanism of dispersal driving

the experimental observations in this study—which, in turn, further suggests that the

partitioning of advection and flooded dispersal in the models here corresponds well

to actual mechanism.

The trend in D with respect to U∗bk may also be influenced in part by apparently

flood-dispersed snails at LT (see Figure 3.2), where bankfull shear stress fell beneath

the threshold required to invoke the flood-dispersal mechanism in any of the models

including one, as fit here. This exception is unlikely to be an important driver,

however, because of its uniqueness and the small number of snails involved.

These various lines of inference suggest overall that trends in C and D were

not driven by floods and entrainment, but rather by environmental effects on snail-

powered movement. Plausible mechanisms implicate shear velocity or correlated hy-

draulic factors, although other possibilities cannot be dismissed. Regardless, the

apparent linkage of C and D to locomotion seems to represent a modeling success for

matching mechanism to intended representation.

Odds sensitivity

The responsiveness of entrainment odds to flood magnitude (sω, or “odds sensitivity”)

varied positively with bankfull shear stress in all models where it was free to vary

(ssω > 0). In other words, the probability of dislodgement increased more rapidly

with flood size at sites with higher U∗bk.1 When hω was fixed across sites, as was

1In the fitted models, sω became negative with low values of U∗bk, suggesting paradoxically thatentrainment odds should decrease with flood size under some conditions. In model 8, sω < 0 onlyat sites where no flood exceeded the minimum threshold required for dislodgement, rendering thevalue of sω meaningless. Furthermore, constraining model 8 further so that sω ≥ 0 (in practice, by

57

the case in model 8, this relationship translated into further responses: that the

minimum flood capable of initiating entrainment was smaller at higher U∗bk sites and,

more generally, that the probability of entrainment was always greater (if nonzero)

for a flood of any magnitude.

Table 3.7: Annual expected features of dispersal in constrained model 8. Key as forTable 3.6.

Group Pr(Entrain) E(Drift) E(Advec) E(Net)UB1 0.252 −13.9 16.8 2.9UB2 0.581 −38.0 8.0 −30.0LB1 0.143 −8.7 19.4 10.7LB2 0.132 −8.0 19.8 11.7LB3 0.183 −11.1 18.4 7.3LB4 0.183 −11.1 18.4 7.3UT1 0.513 −32.3 9.4 −22.8UT2 0.463 −28.3 11.2 −17.1UT3 0.428 −25.8 12.4 −13.4LT1 0.048 −2.4 24.8 22.4LT3 0.167 −8.1 20.5 12.3LT4 0.167 −8.1 20.5 12.3

Several factors could drive floods equivalent from a hydrological perspective to

pose different dangers at sites with different local environments. Sites that begin

with higher proportions of stressful near-bed flows should need smaller discharge

increments to elevate these to entraining flows. Additionally, high U∗bk sites may

offer fewer refugia. A body of research suggests that refuge availability mediates

the impact of floods on benthic invertebrates [49, 62, 23]. Furthermore, flume and

artificial stream experiments suggest that medium-grained substrates (e.g. pebbles

and gravels) afford snails superior high-flow refugia than larger-grained substrates

(e.g. cobbles) [38]. Because streambed particle size generally increases with U∗, high

U∗bk sites are likely to offer snails less refuge in floods. And if high U∗bk sites are

associated with greater variance in near-bed current direction, this complexity of flow

would likely reduce refuge availability further.

forcing hsω ≥ 0) did not qualitatively influence results. Models allowing variation in hω as well assω across sites produced more complex behavior.

58

3.4.2 Quantitative implications

Particular parameter estimates are less robust than the trends they portray. Here,

predictions of snail distribution from even the most parsimonious model relating dis-

persal to U∗bk matched observations crudely (see Figures). The worst correspondences

generally occurred with respect to experiments contributing relatively little data to

the overall model fit. Many sources of noise also certainly diminished matches. My

informal field observations suggest that rare major barriers to upstream dispersal at

stream margins—for example, large boulders extending from a bank into swift, deep

current—could have played an important role.

Despite mismatches between data and predictions, exploring the gross quantita-

tive implications of MLE’s could yield some additional insight. Tables 3.6 and 3.7

report assorted dispersal outcome metrics for each experimental release site, in light

of MLE’s for model 8 and a constrained version of model 8, respectively. Notably, at

high U∗bk sites under either scenario, snails’ chances of entrainment are appreciable,

and expected net displacement is downstream and substantial. Large expected drift

distances upon entrainment help drive the latter trend (>12 m for the smallest possi-

ble flood in model 8 at any site), but the high rates of dislodgement clearly contribute

as well. If caught in just one flood per year, a snail at UB or UT would be unlikely to

recover its former position. These numbers suggest strong challenges for population

persistence at sites with high U∗bk.

Underscoring the difficulty, the models here likely underestimate entrainment rates

because they do not account for the possibility of mortality instead of resettlement

following dislodgement. Floods commonly lead to high mortality in benthic inverte-

brates [38, 63], if not through direct physical damage, to which snails in their shells

might be somewhat resistant (e.g. see [38]), then through stranding organisms on

land as the floods recede [63].

Populations at high U∗bk sites likely require significant refuges or high levels of

59

immigration to persist.

3.4.3 Conclusion and consequences

In summary, the data and models presented here suggest that floods make a strong

imprint on patterns of dispersal for at least some benthic organisms in hydraulically

stressful stream environments. Furthermore, hydraulic environment appears to influ-

ence not only regular patterns of movement, but also the impact of high discharge

events.

Stereotypically, streams progress from relatively turbulent and hydrodynamically

forceful headwaters to ever smoother and gentler conditions as they descend. Actual

watercourses rarely present such monotonic gradients; tributaries, direct contribution

of sediment from hill slopes, and changes in bedrock geology, among other factors,

drive discontinuities in slope and, consequently, hydraulics [61]. Still, to the extent

that the gross pattern holds, such a hydraulic gradient could present a strong ob-

stacle to upstream colonization by benthic crawlers with dispersal biology similar to

E. proxima, with flow conditions potentially forcing an ultimate limit to upstream

distribution in some instances.

The same gradient, coupled with results presented here, also implies an asymmet-

ric pattern of gene flow within stream populations. Subpopulations in the stressful

upper reaches of streams should be relatively isolated, affording opportunity for local

adaptation as well as neutral genetic differentiation. At the same time, genes should

move downstream relatively rapidly with floods, so subpopulations occupying lower

reaches should be genetically better mixed; even low rates of immigration can have

important population genetic consequences. Consistent with this general prediction,

Dillon [16] found high rates of allozyme divergence among populations of E. proxima

sampled from headwater streams, even when taken from the same watershed.

60

Chapter 4

Relationships of hydrology and

hydraulics to distribution and

abundance

4.1 Introduction

The influence of flowing water on snail morphology and dispersal suggested in the

first two chapters begs the question of whether the effects of hydraulic environment

and discharge scale up to drive geographic patterns of snail density and occurrence.

The final components of my research program explored for relationships between

hydraulics, hydrology and the distribution and abundance of the snail Elimia proxima.

I conducted an extensive geographic survey of snail presence and absence, and an

intensive survey of snail density at a smaller set of focal sites. I estimated bankfull

shear stress U∗bk at each location following methods from earlier chapters, but required

new means for characterizing flooding hydrology because most watercourses were not

gauged. As a rough proxy, I employed publicly available weather data to estimate

precipitation parameters in the basin draining through each survey point. Finally, I

61

related bankfull shear stress and precipitation parameters to snail distribution and

abundance.

Several months after initial density surveys, Hurricanes Frances and Ivan dropped

25-75 cm of rain over most of the study region in a span of two weeks, causing century

floods in some area streams. A month later, I resurveyed most of my sites to assess

consequences and see whether they varied according to U∗bk.

4.2 Methods

The study region comprised eleven watersheds (hydrologic units codes 03050101-2,

03050105, 03060102, 06010105-6, 06010202-4, and 06020002-3) in the southern Ap-

palachian mountains, principally western North Carolina.

4.2.1 Snail surveys

I gathered data on the presence and absence of E. proxima from my own surveys and

outside sources. In my own work, I conducted timed visual searches to assess snail

presence or absence at over 350 sites between August 2002 and July 2004. E. proxima

are generally conspicuous; I scored the species as absent when I could not locate any

individuals within five minutes. (Mean time to detection, when snails were detected,

was 30.0 s, standard deviation 58.3 s, 95th percentile 184.5 s, n = 84.) When possi-

ble, I recorded site coordinates using a Global Positioning System device; otherwise,

I made detailed notes and map markings for later digital conversion. I focused my

surveys in mountainous areas and on public land where local and upstream anthro-

pogenic disturbance, including dams, were generally less prevalent than elsewhere.

I acquired additional survey data from the North Carolina Wildlife Resources

Commission Wildlife Diversity Program and from Dillon [15, 17]. I screened the

Wildlife Resources Commission (WRC) data to include only site visits including gas-

62

tropods among targeted or identified taxa, and counted absences only when at least

one collector present identified E. proxima on other trips. Other potential absences

were discarded. I accepted all absence data from Dillon, who searched explicitly for

E. proxima (pers. comm.). The WRC data included decimal degree site coordinates

and verbal location descriptions; Dillon shared detailed maps and stream names en-

abling placement on a digital map. These sources contributed 119 records after all

screening (see below), as compared to 291 from my own. Figure 4.1 shows records

from all surveys combined.

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North Carolina

Georgia

Tennessee

0 50

Kilometers

Figure 4.1: Snail survey locations. Black marks indicate presence, white marks indi-cate absence.

63

Between mid-June and early July 2004, I assessed snail density at the fifteen sites

on five streams detailed in Chapter 1. Depending upon the length of each study reach

(see Ch. 1), I selected between three and nine non-overlapping 10 m stream segments

at randomly determined locations, and conducted three-minute snail counts within

each. In the same manner, I also censused 10 m segments every 50 m from the

upstream edge of snail distribution in each stream down to the uppermost sampling

site (sites 1, Ch. 1), switching to 25 m intervals once counts exceeded 50 snails. Each

stream thus included a total of four census sites. I determined upstream edges in

summer 2003 as locations meeting three criteria: at least one snail found; no snails

found in a 100 m walk extending upstream, including a five-minute search in the

walk terminus area; and no snails found in a five-minute search at at least one site

500-1000 m farther upstream.

After Hurricanes Frances and Ivan, I re-censused a subset of sites as time allowed.

At each location, I counted snails in the same 10 m segments as previously.

4.2.2 Bankfull shear velocity

Using 28 m horizontal resolution digital elevation models (DEMs) from the United

States Geological Survey and the software packages TauDEM and ArcGIS, I generated

stream networks for the study area based on topography. Visual checks confirmed a

close match with watercourses downloaded from the Southern Appalachian Assess-

ment (SAA) Online Database [34]. I matched snail survey points to the nearest stream

links in the DEM-based network and checked each pairing against my map markings

and verbal descriptions of survey locations using the SAA database, which included

stream names, roads and other landmarks. Misaligned points were reassigned to the

nearest link on the correct stream (within 250 m). I retained only one datum in the

rare instances when more than one survey matched to the same link, except in the

rarer case of presence/absence disagreement, when I retained all survey findings for

64

the link.

Using TauDEM, I calculated the mean watershed area drained through each link

associated with a survey point, and the slope of the link. (I measured census site

slopes by digital clinometer in the field.) Together, these values allowed estimation

of bankfull shear stress U∗bk, as described in Chapter 1, for each point. All segments

with slope zero, and associated points, were screened from further analysis because of

uncertainty around calculation of U∗bk. I assumed that zero slope segments reflected

shortcomings of DEM data. Flat links were associated with a wide range of drainage

areas, suggesting a wide range of U∗bk values.

I also screened out links and points when dams blocked greater than 10 percent

of the basin area draining through them, because of the likely influence of dams on

flow regime and hydraulic environment. Data sources for dam locations comprised

the United States Army Corps of Engineers and the North Carolina Department of

Environment and Natural Resources Dam Safety Program. I used water bodies in

the USGS National Hydrography Dataset to infer the presence of additional dams;

few to no natural lakes or ponds exist in the study area. I associated all dams with

the nearest stream link within 250 m, and water bodies with outlet stream links.

I then matched each flow blockage to any downstream snail survey points when no

other blockage interceded (to avoid double counting), and finally compared the area

drained through all blockages associated with each survey point to the total area

drained through the survey point.

To develop a broader metapopulation perspective, I followed the branching stream

network upstream from each remaining survey point, and matched the point with

every link whose downstream terminus was within one kilometer of the upstream

terminus of the survey link. Inside these neighborhoods, which included survey links,

I calculated the minimum bankfull shear stress value U∗bk−nmin and associated it

with the survey point. Hydraulically gentle upstream sites could represent large-

65

scale refuges from floods and rapid recolonization sources for downstream areas more

strongly affected by high flows.

Finally, for wider landscape context, I estimated U∗bk for every link in the entire

study region, and computed differences between all adjacent pairs, excluding pairs

with one or more zero values.

4.2.3 Precipitation parameters

I obtained daily precipitation information recorded at National Weather Service Co-

operative weather stations in my study region, including a 58.5 km circumferential

buffer (15 percent of region major axis length), and covering the thirty-year period

October 1, 1975 to September 30, 2005. The State Climate Office of North Carolina

(NC CRONOS database) provided data. I screened out stations missing precipitation

values for more than 5 percent of period days, leaving a total of 125 stations.

For each remaining weather station, I calculated mean annual precipitation (MAP)

and the mean annual number of precipitation events (MAE). Events comprised un-

interrupted periods of precipitation bounded on both ends by at least one dry day,

and the total liquid accumulation during an event defined its size. I modeled event

sizes at each site with a gamma distribution. 95 percent confidence intervals around

maximum likelihood estimates of shape parameters did not include the value 1 in over

95 percent of cases, demonstrating the unsuitability of simpler exponential models.

I regressed MAP, MAE, and gamma size and shape parameters on station elevation

using ordinary least squares. MAP, MAE and the size parameter increased with

elevation (p < 10−5 in all cases), while the shape parameter decreased slightly (p <

.01). Simple kriging on residuals from each regression created four interpolated maps

over the study region. The combination of simple kriging with regression is a tested

method for estimating rainfall in mountainous regions [26].

To perform the kriging, I used the Geostatistical Analyst toolbox provided with

66

ArcMap 9.2. I tested spherical and exponential semivariogram models (the most

widely used [25]), assumptions of isotropy and anisotropy, and a variety of neighbor-

hood sizes to draw upon for point estimation. Across all parameters, an isotropic ex-

ponential model utilizing three neighbors (max) per quadrant minimized the absolute

mean standardized prediction error from cross-validation (0.010). My study region is

mountainous and likely to be highly heterogeneous in patterns of rainfall; therefore,

an exponential model, which gives relatively heavy weight to nearby neighbors, and a

small neighborhood of influence size, are consistent with expectations. Although the

Appalachian Mountains run NE to SW, most of my focal area was within the massif,

making isotropy at least as appropriate an assumption as anisotropy.

To estimate precipitation parameters for the basins draining through each survey

point, I added expected basin values from the kriged maps to local prediction com-

ponents based on the elevation models. I first extracted the mean elevation for each

basin from DEM data.

Finally, from the resulting estimates, I developed an integrative parameter de-

signed to reflect the size of the largest precipitation event in a typical year, because

such an index seems likely to be related to patterns of flooding. If n samples are

repeatedly and randomly drawn from any probability density function, the median

maximum percentile drawn will converge to 0.51/n. For each basin, I evaluated the

gamma distribution of precipitation event sizes at the percentile 0.51/MAE to compute

the estimated median annual maximum event size (MAMES).

4.2.4 Statistics

I used logistic regression to relate snail presence or absence to U∗bk, neighborhood

minimum U∗bk, and selected precipitation parameter estimates, singly and in pairs

matching U∗bk with one precipitation parameter, with and without interaction. I

chose parameters to represent both mass and extremes as parsimoniously as possible:

67

MAP and MAMES, respectively.

I employed the same parameters and combinations to analyze variation in snail

density. I fit linear models relating counts in each sub-site survey segment to the

random factor stream and to each focal parameter set, avoiding pseudoreplication by

comparing effects to variation at the level of individual sites, the experimental unit.

I repeated the same procedure to analyze paired differences in counts between post-

and pre-hurricane surveys, but using only stream and U∗bk as factors.

Table 4.1: Fitted parameters for logistic regressions on snail presence-absence data.Upper table portion gives coefficient estimates; the lower portion reports correspond-ing intercepts. Columns Est and Est2 give estimates for one- and two-factor models,respectively, for row label factors; column U∗bk-Est2 contains coefficient estimates forU∗bk in two-factor models. Addition of interaction terms to models (not shown) elimi-nated all significant effects of simple factors; among interaction terms, only U∗bk:MAPexerted a statistical effect (-0.08, p < .05). Among single-factor models, U∗bk−nmin

outperformed U∗bk (p = 10−6, AIC= 546, vs. p = .0004, AIC= 559). n = 410 for alltests.

Factor Est Est2 U∗bk-Est2U∗bk -2.53 ***U∗bk−nmin -3.61 ***MAP −0.03 *** −0.02 *** -1.79 *MAMES -0.19 *** -0.17 *** -2.24 **

InterceptsU∗bk 0.93 ***U∗bk−nmin 1.01 ***MAP 4.20 *** 4.45 ***MAMES 2.55 *** 3.07 ***

4.3 Results

All factors tested exerted negative effects on the probability of snail presence (see

Table ??). Mean annual precipitation predicted occupancy with the greatest certi-

tude, and minimum neighborhood bankfull shear stress U∗bk−min appeared to have a

stronger relationship than local U∗bk. Factors remained significant when paired with

U∗bk in two-factor models, but not when interactions were added. Analysis restricted

68

to my own survey data only produced the same results, except that flooding MAMES

exerted no statistical effects.

None of the same factors or combinations had any significant effect (p < .05)

on summer snail density (df = (4, 1, 14) for one-factor analyses). However, U∗bk

exerted a strong negative effect on change in snail density after hurricanes Frances

and Ivan (p < .01, df = (3, 1, 7)). Most sites lost snails, but some gained substantial

numbers, suggesting that even major floods transport many individuals intact. Table

4.2 summarizes the data.

This network transport potential and the apparent influence of U∗bk on snail dis-

persal (Chapter 2) and distribution (here) motivate an interest in characterizing the

spatial pattern of U∗bk in stream networks. Based on analysis of the entire study

region, U∗bk generally increased in the upstream direction (Student’s t-test on ad-

jacent link differences, p < .001, df = 92, 512), with a mean increment per stream

link (mean length, 507.4 m) of 0.025 m s−1 (s.d. = 0.127). Analysis of variation in

interlink differences with respect to basin area drained showed that U∗bk gradients

also steepen in the upstream direction (p < .001, df = 92, 511).

4.4 Discussion

Precipitation estimates bore strong relationships to snail occurrence, with high rainfall

totals and event sizes corresponding to lower probabilities of snail presence. Further-

more, precipitation appeared more tightly linked to snail distribution than elevation

(logistic regression Akaike Information Criterion (AIC) values 539 for MAP, 556 for

MAMES, and 559 for elevation; p < .001 in all cases). Elevation is an important

correlate to rainfall and to numerous other biologically significant factors, such as

temperature. The closer connection between snail occurrence and precipitation pa-

rameters thus weighs in favor of some causal link, although the influence of other

69

Table 4.2: Snail summer 2004 mean densities and change following Hurricanes Francesand Ivan. Standard errors of the mean (sem) given as well as average segment counts(Summer) and mean paired segment changes (Change). Number of sample segmentsn listed separately for change data in cases where only a predetermined subset ofsegments recensused.

Stream Site U∗bk Summer sem n Change sem nBuck edge 0.23 35.6 6.4 28 0.4 21.1 7

1 0.27 102.2 13.5 9 −76.6 15.32 0.20 123.1 12.4 9 −32.1 15.83 0.27 90.3 8.0 9 12.8 11.4

Curtis edge 0.59 80.8 31.5 41 0.49 143.8 26.1 62 0.57 385.9 26.4 93 0.40 37.6 4.8 9

Long edge 0.62 58.0 25.6 7 −10.1 7.91 0.48 116.7 8.4 3 42.3 24.42 0.36 389.8 39.6 53 0.26 174.0 61.8 6 250.2 46.9

Snow edge 0.34 32.9 12.4 14 −3.3 12.0 61 0.29 101.9 22.1 9 −29.1 23.02 0.38 132.0 21.3 93 0.34 72.1 12.5 9

Tal edge 0.57 53.6 13.9 9 −36.1 19.21 0.51 86.9 21.1 7 −40.4 29.02 0.22 303.7 19.4 93 0.21 31.1 9.1 9 71.6 22.9

70

correlates to elevation is far from ruled out.

The most obvious means through which a wet climate might inhibit E. proxima

site occupancy are the high flows and flooding likely to ensue. Chapter 1 suggests that

hydraulically challenging environments exert pervasive selective pressures on snails

throughout ontogeny; some environments might simply offer too little suitable habitat

under common flow conditions to sustain populations. The findings of Chapter 2

imply both that strong currents present obstacles to upstream advancement, and

that floods can entrain snails and sweep them downstream. These mechanisms could

shape snail distribution through blocking colonization or driving local extinction via

removal. In this study, the large losses and gains in snail density relative to baseline

levels likely driven by hurricanes Frances and Ivan (Table 4.2) emphasize the potential

importance of floods in dictating patterns of abundance, if not occurrence.

The same mechanisms all share potential to explain the relationship shown here

between bankfull shear stress and snail distribution. The possible implications from

Chapter 1 apply here, as for when considering climatic effects. Chapter 2 suggests

that elevated U∗bk inhibits upstream movement and enhances the probability of snail

entrainment in floods. In a consistent finding, U∗bk appeared to mediate effects of

Frances and Ivan.

In light of the evident mechanistic interaction between U∗bk and the effects of high

discharge, the breakdown of logistic regressions relating snail presence or absence to

U∗bk and a precipitation parameter when an interaction term was added to the model

is puzzling (see Table 4.1 and caption). However, weak but significant correlations

between U∗bk and MAP (correlation coefficient R = 0.231, p < .001) and precipitation

MAMES (R = 0.031, p < .05) for all snail survey points may explain this outcome.

Adding interaction terms to models already dependent on correlated predictors may

have obscured the contributions of all regression components.

Factors driving species presence or absence must also influence density. The lack

71

of relationship between summer snail counts and precipitation or U∗bk thus presents

another puzzle, considering the apparent influences of these factors on snail distri-

bution. However, analysis of post-hurricane snail abundance, when consequences of

hydrology and hydraulics should have been most evident, did suggest a negative effect

of U∗bk (ANOVA with random factor stream, p < .05, df = (3, 1, 7)); this analysis is

related to but separate from the analysis of density change from pre- to post-hurricane

censes, Table 4.2.) At times farther removed from major events, many factors unre-

lated to flow forces, including water chemistry, food supply, or natural enemies, must

affect snail abundance and potentially obscure hydrologic influences (see e.g. [52, 73]).

Although Frances and Ivan appeared to cut some populations in half or worse,

they did not come close to causing local extinctions at any of the sites examined.

These hurricanes constituted outlier rainfall events, suggesting that flooding does not

generally lead directly to population extinction on a reach scale. This inference is

consistent with a body of research showing that local flow refugia enable persistence

of benthic macroinvertebrates during floods [49, 62, 46].

Instead, the challenge of moving upstream may play a stronger role in limiting

snail distribution. Beyond the links already suggested, data here support an addi-

tional argument. Reanalysis of summer snail density data for only edge sites appears

to indicate a positive relationship between U∗bk and abundance (ANOVA, p < .1,

df = (1, 3)). One possible explanation for this seeming paradox is that snails con-

centrate downstream of barriers to upstream passage, and barriers define the upper

limits to snail distribution in some streams. The frequency of barriers or bottlenecks

is very likely to increase with U∗bk, so the findings here help implicate U∗bk or corre-

lates in governing snail distributional boundaries by inhibiting upstream movement.

Landscape gradients of U∗bk, increasing and steepening with elevation, lend further

weight to the likely importance of U∗bk in setting limits.

The apparently stronger relationship between minimum upstream neighborhood

72

bankfull shear stress U∗bk−nmin and snail presence and absence invites further consid-

eration. Although U∗bk increases with elevation on average, the standard deviation

of step changes between stream links far exceeds the mean. By sampling a larger

number of links, U∗bk−nmin likely provides a truer representation of general stream

habitat.

An upstream link with low U∗bk also represents a potential large-scale refuge dur-

ing floods, and may hold a source population capable of re-seeding downstream links

through flow-mediated dispersal. With this mechanism, segments barring upstream

passage under most flow conditions could still maintain small populations in pro-

tected pockets; and rare low-flow conditions might offer “jailbreak” opportunities for

colonization of upstream, low-U∗bk sites. This possibility brings back into focus the

strong relationship between precipitation levels and snail distribution. High rainfall

areas may present fewer opportunities for upstream passage across steep, hydraulically

stressful reaches. Paradoxically, this potential limitation on dispersal may represent a

more important mechanism relating precipitation to snail distribution than flooding.

To summarize, the assorted evidence presented here collectively suggests that

hydraulics and hydrology exert strong influences on the distribution and abundance

of the stream-dwelling snail E. proxima, consistent with smaller-scale mechanisms

pointed to by earlier chapters. The documentation of flood effects adds to a plentiful

existing literature, but studies concerning the inhibitive influence of flow and hydraulic

stress on upstream dispersal of benthic fauna appear rarer. In broader consequence,

together with Chapter 2, the results here suggest that upstream terminal populations

of E. proxima may experience little influx of genes from downstream populations,

making them potential loci for genetic differentiation, innovation and maintenance

of diversity. The same pattern may characterize other stream invertebrates as well,

especially those confined to water at all life stages.

73

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