Advanced analytical approaches in ecological data analysis
description
Transcript of Advanced analytical approaches in ecological data analysis
Advanced analytical approaches in ecological data analysis
The world comes in fragments
Species abundance matrix MPhylogenetic distance matrix P
Species trait matrix T
Environmental variable matrix V
Interdepen-dence
matrix X
Species
Spec
ies
Spec
ies
Spec
ies
Sites
Sites
Varia
bles
Varia
bles
Traits
Traits
Multivariate approaches to biodiversity
Fourth corner statistics
Species abundance matrix MSpecies trait matrix T
Environmental variable matrix V
𝑻𝑚𝑘❑ 𝑇×𝑴𝑚𝑛×𝑽 𝑙𝑛❑
𝑇=𝑿𝑘𝑙
k
m
n
m
l
m species, n sites, k traits, l environmental variables
The matrix X is a kl matrix that contains information on the relationhips between traits and environmental variables mediated by species abundances or occurrences .
n
The Pearson coefficient of correlation
𝑟=𝜎𝑥𝑦
𝜎 𝑥𝜎 𝑦=
1𝑛−1∑ (𝑥 𝑖−𝑥)(𝑦 𝑖−𝑦 )
𝜎 𝑥𝜎 𝑦
𝑟= 1𝑛−1∑
(𝑥 𝑖−𝑥)𝜎 𝑥
(𝑦 𝑖− 𝑦)𝜎 𝑦
= 1𝑛−1∑ 𝑍 𝑥 ,𝑖𝑍 𝑦 , 𝑖
SpeciesLeaf mass [mg]
Leaf size [mm2]
Life span Light
Achillea_pannonica 82.33 567.84 5 7
Agrostis_capillaris 60.98 1147.93 5 7
Species Leaf mass [mg]
Leaf size
[mm2]Life span Light
Achillea_pannonica 0.79 -0.56 0.97 -0.02
Agrostis_capillaris 0.25 0.27 0.97 -0.02
Agrostis_stolonifera_agg.
=(C5-ŚREDNIA(C$3:C$125))/ODCH.STAND.POPUL(C$3:C$125)
Using Z-scores in fourth corner analysis leads to correlations between traits (phylogeny) and environmental (geographical) variables.
Output of the Ord software
S CaCO3 Sand pH Species AbundanceDNAcontent -0.347 0.534 -0.581 0.984 1.119Grazingtolerance -0.632 -0.621 0.275 0.343 0.161Leafmass[mg] 0.365 -0.488 -0.782 0.163 0.758Leafsize[mm2] 0.423 -0.780 -0.321 -0.649 0.053Lifespan -0.348 -2.006 0.567 1.935 2.495Light -0.055 1.170 -0.633 0.847 -0.283Meanseedweight 0.829 -0.233 -0.386 -0.217 -0.088Nitrogen -0.141 -0.889 -0.446 1.454 2.341Soilfertility -0.429 0.068 0.582 0.412 -0.624Specificleafareamm2 -0.278 1.606 0.554 -0.753 -0.543ln(Seedspershoot) 1.430 -1.201 0.686 -1.361 -0.248pH -1.366 1.558 -0.901 0.670 -1.919
The SES scores for traits of the proportional – proportional null model
We detect three significances.
Three significances is exactly the random expectation a the 5% error level.None of the relationships is really significant.
Use Bonferroni corrected significance levels!
Correlation coefficients and a neutral null model (AA)
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
DNAconte Grazingt Leafmass Leafsize Lifespan Light ln(Seeds Meanseed Nitrogen pH Soilfert Specific
r
CaCO3
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
DNAconte Grazingt Leafmass Leafsize Lifespan Light ln(Seeds Meanseed Nitrogen pH Soilfert Specific
r
pH
Clumped species co-occurrences
SES>0 0 35 89 90 89SES<0 123 88 34 33 34S CaCO3 Sand pH Species AbundanceAchillea_pannonica -0.47 -0.35 0.97 0.97 0.97Agrostis_capillaris -0.20 0.38 -0.72 -0.21 -0.30Agrostis_stolonifer -0.21 0.39 -0.72 -0.21 -0.30Agrostis_vinealis -0.21 0.39 -0.72 -0.21 -0.30Ajuga_genevensis -0.40 -0.21 0.43 0.97 0.80Apera_spica_venti -0.20 0.37 -0.74 -0.22 -0.30Arenaria_serpyllifo -0.64 -0.45 0.24 0.94 1.07Artemisia_vulgaris_ -0.49 -0.33 0.87 0.95 0.96Betula_pendula -0.59 -0.12 0.34 0.85 0.62Brachypodium_sylvat -0.21 0.38 -0.71 -0.19 -0.28Bromus_hordeaceus -0.21 0.37 -0.71 -0.21 -0.29Bromus_tectorum -0.22 0.36 -0.71 -0.21 -0.29Calamagrostis_epige -0.21 0.40 -0.73 -0.20 -0.30Carex_arenaria_agg. -0.28 0.31 -0.52 -0.05 -0.16
• Phylogenetic distance was negatively related to soil carbon content and sand.
• Phylogenetic distance was positively related to soil pH.
• Phylogenetic distance was positively related to soil species richness and abundance.
The SES scores for phylogeny of the proportional – proportional null model
Phylogenetic species co-occurrences
1 2 3 4 5 6 7 8V1 1 1.4 2.5 2.1 1.1 6.5 1.2 2.1 1.1V2 2 0.4 0.2 0.8 1.2 1.3 2.1 2.6 2.7
1 2 3 4 5 6 7 1 2 3 4 5 6 7 8
1 0 0.1 0.4 0.3 0.6 0.6 0.7 1 1 1 1 1 1 1 1 1
2 0.1 0 0.5 1 0.8 0.7 0.7 2 1 0 1 1 1 0 1 0
3 0.4 0.5 0 0.7 0.8 0.9 0.9 3 1 1 0 1 1 1 1 1
4 0.3 1 0.7 0 0.4 0.9 0.8 4 0 1 1 1 0 1 1 0
5 0.6 0.8 0.8 0.4 0 0.8 0.9 5 1 1 1 1 0 0 1 0
6 0.6 0.7 0.9 0.9 0.8 0 0.9 6 1 1 0 0 1 1 1 1
7 0.7 0.7 0.9 0.8 0.9 0.9 0 7 1 0 1 1 0 1 1 1
Niche conservatism
Sites
Spec
ies
Species
Spec
ies
Sites
Environmental variables
Phylogenetic assortment
Checkerboard
Togetherness
Clumping
Habitat filtering
Count for all checkerboard, clumped and togethernerss pairs the average phylogenetic and variable distances.
Compare these average with the random distribution after randomisation of the species occurrence matrix.
a b c dA 1 0 0 1B 0 1 0 1C 1 1 1 0D 1 1 0 1E 0 1 1 0F 1 1 1 0
Togethernessa b c d
A 1 0 0 1B 0 1 0 1C 1 1 1 0D 1 1 0 1E 0 1 1 0F 1 1 1 0
Checkerboarda b c d
A 1 0 0 1B 0 1 0 1C 1 1 1 0D 1 1 0 1E 0 1 1 0F 1 1 1 0
Clumping
Effec
t
RDphylDenv DphylDenv RDphylDenv DphylDenv RDphylDenv DphylDenv
RDphylDenv DphylDenv RDphylDenv DphylDenv RDphylDenv DphylDenv
EO
EU
PO
PU
EU
EO
PU
PO
NC
ND
ND
NC
EO
EU
DN
CN
PO
PU
+
-
Each effect is linked to an ecological pattern that can be related to an ecological process.
-60-40-20
020406080
100
2004 2006 2008 2010 2012
SES
scor
e
Study year
Phylogenetic relatedness during succession
: Clumping: Togetherness: Checkerboard
• Phylogenetic distances of co-occurring species increased during early succession.
• Phylogenetic distances of segregated species decreased.
• At the onset of succession phylogenetic community structure was random.
• 2008 marks a tipping point from a random to a structured pattern.
-10-505
1015202530
2004 2006 2008 2010 2012
SES
scor
e
Study year
A
-15-10
-505
101520
2004 2006 2008 2010 2012Study year
B
-5
0
5
10
15
20
2004 2006 2008 2010 2012Study year
C
: Clumping: Togetherness: Checkerboard
CaCO3 Sand
pH Co-occurrences in dependence on soil variables
• At the beginning of succession SES score were negative. Species co-occurred on similar soils (habitat filtering).
• At the end of the succession species co-occurred on different soils and co-occurred less often on soils osf similar structure. This points to competitive effects.
-0.4
-0.2
0
0.2
0.4
0.6
0.8
-0.5 -0.3 -0.1 0.1 0.3 0.5
Axis
2
Axis 1CaCO3
Sand
pH
C. vulgare
Ulmus sp
E. repens
E. arvense
PCA, PCoA multiplots
Eigenvector multiplots serve as a graphical representation of species associations with trait or soil variables.
Chicken Creek 2011 data
-0.6-0.4-0.2
00.20.40.60.8
-0.5 -0.3 -0.1 0.1 0.3 0.5 0.7
Axis
2
Axis 1
Sp. leaf area
Leaf size
C. vulgare
Ulmus sp
E. repens
E. arvense
Leaf mass
Seed weight
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
-0.5 -0.3 -0.1 0.1 0.3 0.5Axis
2
Axis 1
CaCO3
Sand
pH
Leaf massSp. leaf area
Seed weight
Principal coordinates analysis (Bray Curtis metric of distance) links the eigenvectors of species, trait, and environmental variable eigenvectors
• Leaf features are linked to the pH gradient.
• Seed weight is connected to the sand gradient