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