Habitat Modelling, by Guillem Chust

Introduc)on to Sta)s)cal Modelling Tools for Habitat Models Development, 26-‐28th Oct 2011 EURO-‐BASIN, www.euro-‐basin.eu

2

• Introduction to species habitat and some concepts in community ecology

• Statistical methods dealing with communities

• Analysis of β-diversity: Similarity and distance matrices & Mantel and

partial Mantel test

� Practical session “Community Ecology with R”

• Direct Ordination Methods (CCA and RDA)

• Variation partitioning

� Practical session “Community Ecology with R”

• 4th corner method

Index

3

• Which are the main factors that determine the distribution (or the habitat) of species?

• Environmental factors (e.g. temperature, nutrients, …) → Adaptation processes versus• Dispersal limitation factors (reproduction and mortality rate, growth, migration,…) → Historical processes

• for a species, but species compete for resources (hence, for space)• for an assemblage (or community) of species, within a guild

A guild (or ecological guild) is any group of species that exploit the same resources: e.g. zooplankton, phytoplankton, trees

Hypothesis

4

A

B

C

DE

Site 1 Site 2

FG

AB

CD

EF

G

Site 1 Site 2

• Which are the main factors that determine the species composition of a community in a region?

• What are the factors that determine the maintenance of local and regional diversity?

Shared species↓ Shared species↑

Hypothesis

5

γ-diversity / Landscape

α-diversity /Within an homogeneous habitat

β-diversity / Environnemental

gradient

Whittaker (1960, 1977)

diversities…

6

Abundance a b c d e

Environmental Gradient

1. Environmental factors ⇔ Niche ⇔ « Environmental patchiness »

2. Geographic Distance ⇔ Dispersal limitation ⇔ « random walk »(Neutral theory, Hubbell 2001)

Distance between sites

Sharedspecies

Neutral community: all individuals have the same rates of reproduction and mortality

Habitat theories

7

Niche model

• The Hutchinsonian niche views niche as an multi-dimensional hypervolume, where the

dimensions are environmental conditions and the resources that define the requirements of

an individual or a species (E. Hutchinson, 1957).

• The full range of environmental conditions (physical and biological, i.e. the resources) under

which an organism can exist describes its fundamental niche.

Two dimensional nicheUnidimensional niche

Three dimensional niche

Ab

un

dan

ce

Variable

8

Dispersal-limited model

• Species composition fluctuates in a random, autocorrelated way.

A

B

C

DE

Site 1 Site 2

FG

AB

CD

EF

G

Site 1 Site 2

Geographical distance

Shared

species

β-diversity

Metacommunity A

Metacommunity B

Similarity ↓ : β-diversity↑ Similarity ↑: β-diversity ↓

Distance decay

Metacommunity: a set of local communities

that are linked by dispersal of multiple,

potentially interacting species

9

A metapopulation is a group of spatially separated populations of the same

species which interact at some level

A metacommunity is a set of local communities that are linked by dispersal of

multiple, potentially interacting species

n1

n2

m1

na1

ma1

nb1

nc1

na2

nb2

na3

mb1

Terminology

10

• The number of species found on an undisturbed island is determined by immigration and

extinction.

• Immigration and emigration are affected by the distance of an island from a source of colonists

(distance effect).

• Large islands => lower extinction

• Near islands to continents => higher immigration rate

The theory of island biogeography

(MacArthur and Wilson, 1967)

MacArthur, R. H. and Wilson, E. O. 1967. The Theory

of Island Biogeography. Princeton, N.J.: Princeton

University Press.

11

Condit et al. Science,January 25, 2002.

β-diversity

Duivenvoorden et al. Science,January 25, 2002.

Variance partitionning

Dispersal limited model

12

Geographic distance

Spatial Autocorrelation

Legendre, P. (1993) Spatial autocorrelation: trouble or new paradigm. Ecology, 74, 1659–1673.

Environmental Gradient

Sh

are

d

spe

cie

s

• Environmental variables and species distributions tend to be spatially autocorrelated:

• Species distributions are most often aggregated because of contagious biotic processes such as

local dispersal

• But also, environment is structured primarily by climate and geomorphological processes on

land that cause gradients and patchy structures.

• Therefore values of these variables are not stochastically independent from one another. This may

lead to misinterpretation of patterns using classical statistics when ecologists conclude that species–

habitat associations are statistically significant.

• To evaluate the relative importance of environmental segregation and limited dispersal in explaining

species distributions, spatial structure must be considered.

• Spatial autocorrelation can be a problem for explaining species ecological niche, however, it can

improve habitat modelling

13

Some statistical methods to analyse distribution

patterns of species communities

• Similarity and distance matrices &

Mantel and partial Mantel test

(Analysis of β-diversity)� Practical session “Community Ecology

with R”

• Direct Ordination Methods (CCA and

RDA)

• Variation partitioning

• Practical session “Community Ecology

with R”

• 4th corner method

14

Analysis of β-diversity: Similarity and distance matrices

&Mantel and partial Mantel test

15

=

1....

1...

1..

1.

1

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β-diversity

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AMBsim

Environmental similarity

Similarity Coefficient / Distance

=

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11211

Species Matrix: m sites x n species

Environmental Matrix: m sites x q variables

(Euclidean, …)

(Jaccard, …)

Similarity and distance matrices

e.g. n = 5 sites

16

(Dis)Similarity and distance indices

Similarity indices (for species data): 0 → 1• Jaccard index (for presence-absence data) is the

number of species shared between the two plots,

divided by the total number of species observed.

0 (no shared species) → 1 (all species shared)• Bray-Curtis index (for abundance data) is defined by

2W/(A+B), where W is the sum over all species of the

minimum abundances between the two stations of

each species, and A and B are the sums of the

abundances of all species at each of the two stations.

• Bray-Curtis is also known as Steinhaus dissimilarity,

Sørensen index, or Czekanowski

• …

Distance indices (for variables):

• Euclidean :

• …

sp1 sp2 min

St1 3 4 → 3

St2 5 2 → 2

W = 5

AB

CD

EF

Site 1 Site 2

Jaccard = 4 / 6

dvar1 var2

St1 32.3 0.2

St2 34.6 0.3

d1=2.32 d2=0.12

17

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β-diversity

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Similarity Coefficient / Distance Mantel Test

=

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Species Matrix

Environmental Matrix

(Euclidean, …)

(Jaccard, …)

18

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β-diversity

=

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0.

0

45

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d

dd

ddd

dddd

d

Geographic distance

Similarity Coefficient / Distance Mantel Test

Species Matrix

Site location: x,y

Euclidean

(Jaccard, …)

=

mm

xy

yx

x

yx

d

.

.

...2

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e.g. 5 sites

19

Floristic data:

708 tree species (> 10 cm dbh)

53 sites of ~1 ha

Case Study 1: Tree rainforest in Panama

PrecipitationGradient

FloristicComposition

Environmental Variables:

• Precipitation• Elevation• Slope• Water accumulation flow• Geology• Fragmentation

20

Condit et al. Science,January 25, 2002.

β-diversity


Jaccard Geographical Distance (GD) 0.637 ln(GD) 0.696 Dispersal-related factors Cross-plot forest fraction 0.323 Elevation 0.424 Slope 0.318 Runoff 0.078 Precipitation 0.572 Dry season 0.461

Environmental factors

Geologic types 0.126 Band 1 0.305 Band 2 0.117 Band 3 0.127 Band 4 0.258 Band 5 0.148

Spectral data

Band 7 0.160

Distance (km)

Fra

ctio

n s

pec

ies

shar

ed

21

Identification of complementary areas of diversity

A

B

C

DE

Site 1 Site 2

FG

AC

DE

F

Site 1 Site 2

• Problem of the minimal areaMinimise the total surface while preserving all species

• Problem of the maximal coverageMaximise the number of species within a fixed surface

Optimisingγ-diversity

22

8%

20%

Similarity0%

Cluster 3.1 3.2 3.3 3.4 3.5 2.1 2.2 1.1 1.2

Plots 34 40 41 36 35 371,3,4,21,22,29,23,27,24,28,30,C1, C4,C2,C3

2,S0,S1,S3,S2,S4,SH,25,26,5,17,13, 10,11,18,14,P1, P2,6,7,12,15,16,8,9, 20,19,G1,G2

31,3233

Cluster 3.1 3.2 3.3 3.4 3.5 2.1 2.2 1.1 1.2

Plots 34 40 41 36 35 371,3,4,21,22,29,23,27,24,28,30,C1, C4,C2,C3

2,S0,S1,S3,S2,S4,SH,25,26,5,17,13, 10,11,18,14,P1, P2,6,7,12,15,16,8,9, 20,19,G1,G2

31,3233

Step 1. Hierarchical agglomerative clustering

Step 2. Multiple Regression Model between distance matrices

Identification of complementary areas

23

8%

20%

Similarity0%

Cluster 3.1 3.2 3.3 3.4 3.5 2.1 2.2 1.1 1.2

Plots 34 40 41 36 35 371,3,4,21,22,29,23,27,24,28,30,C1, C4,C2,C3

2,S0,S1,S3,S2,S4,SH,25,26,5,17,13, 10,11,18,14,P1, P2,6,7,12,15,16,8,9, 20,19,G1,G2

31,3233

Cluster 3.1 3.2 3.3 3.4 3.5 2.1 2.2 1.1 1.2

Plots 34 40 41 36 35 371,3,4,21,22,29,23,27,24,28,30,C1, C4,C2,C3

2,S0,S1,S3,S2,S4,SH,25,26,5,17,13, 10,11,18,14,P1, P2,6,7,12,15,16,8,9, 20,19,G1,G2

31,3233

Step 1. Hierarchical agglomerative clustering

Predicted

0.2 0.4 0.6 0.8 1.0

Jacc

ard

sim

ilarit

y

0.2

0.4

0.6

0.8

1.0

R2 = 0.57 (p < 0.001)

Step 2. Multiple Regression Model between distance matrices

Step 3. Extrapolation of the model and cluster assignation

Ŝ(pixel i, site 1)Ŝ(pixel i, site 2):Ŝ(pixel i, site 53)

• Log(GD)• Elevation• Bands 1-4

Identification of complementary areas

24

Non-rain forest Water surfaces Cluster 1.1 Cluster 1.2 Cluster 2.1 Cluster 2.2 Cluster 3.1 Cluster 3.2 Cluster 3.3 Cluster 3.4 Cluster 3.5

Predicted floristic types: identification of complementary areas

Chust, G., J. Chave, R. Condit, S. Aguilar, S. Lao, & R. Pérez (2006)Determinants and spatial modelingof beta-diversity in a tropical forest landscape in Panama. Journal of Vegetation Science 17: 83-92.

25

Case Study 2: zooplankton in the Bay of Biscay

-7 -6 -5 -4 -3 -2 -1 043

44

45

46

47200 m

100 m

Gironde EstuaryBay of Biscay

Arcachon Bay

Adour river

Cap Breton Canyon

Cap Ferret Canyon

267 Zooplankton samples collected from May 2-16, 2004

Irigoien, X., G.Chust, J.A. Fernandes, A. Albaina, L. Zarauz (2011) Factors determiningmesozooplankton species distribution and community structure in shelf and coastal waters. Journal of Plankton Research33: 1182-1192.

CopepodCalanus helgolandicus

24 most abundantcopepods

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Distance (km)

0 50 100 150 200 250 300 350

Sp

ecie

s si

mila

rity

(B

ray-

curt

is)

0.0

0.2

0.4

0.6

0.8

1.0

Distance (km)

0 50 100 150 200 250 300 350

Sp

ecie

s si

mila

rity

(Ja

ccar

d)

0.0

0.2

0.4

0.6

0.8

Species similarity indices against geographic distance


Sp

ecie

s si

mila

rity

Distance (km)

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Species similarity indices against environment:

• 15 environmental variables (bottom depth, temperature, salinity and density at surface and bottom, difference in density between surface and bottom, Frequency of Brunt-Vaisala, integrated fluorescence, depth of the maximum fluorescence, fluorescence at the maximum, abundance of chaetognath, jellyfish and fish eggs)

• 32767 possible subsets were compared

• ∑�!

�� !�!

�� , where n: number of var., k: combinations

• The best subset of environmental variables selected so that explain the maximum variation of the species similarity were 4: Frequency of Brunt-Vaisala, salinity at surface, density at bottom and jellyfish abundance (for Bray-Curtis index)


28

Aim: to select the best subset of environmental variables, so that distances of (scaled) environmental variables have the maximum correlation with community dissimilarities

Model Selection

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Environmental Matrix

(Euclidean, …)

=

.

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mx

x

xx

AMB

n combinations of q variables → n Environmental similarity matrices

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Mantel r p-value Terms selected for Environmental variablesBray-Curtis × Environment 0.54 0.001 Frequency of Brunt-Vaisala, Salinity at surface,

Density at bottom, Jellyfish abundanceBray-Curtis × Distance 0.43 0.001Bray-Curtis × Environment (Distance partially out) 0.50 0.001

Jaccard × Environment 0.44 0.001 Temperature at bottom, Density at surface and at bottom, Fish abundance

Jaccard × Distance 0.47 0.001Jaccard × Environ selec (Distance partially out) 0.34 0.001


ENV

DIS

Conclusion: mesozooplankton communities in the Bay of Biscay are subjected to balanced degree of dispersal limitation and niche segregation.

30

Case Study 2: a comparison of estuarine intertidal communities

rM = 0.625Slope = -0.0021

rM = 0.316Slope = -0.0020

rM = 0.064Slope = -0.0003

Saltmarsh and seagrass plants Macroalgae Macroinvertebrates

31

• R: veganpackage (Oksanen et al. 2011, see Docs)

• PRIMER (Clarke & Gorley 2006; http://www.primer-e.com/)

• …

Software for Similarity/distance indices and Mantel tests

32

Practical session 1 “Community Ecology with R: vegan package”

33

ANALYZING BETA DIVERSITY: PARTITIONING THE SPATIAL VARIATION OF COMMUNITY COMPOSITION

DATA (Legendre et al. 2005, Ecological Monographs)

• The variance of a dissimilarity matrix among sites (rM2) is not the variance of the

community composition,• hence, partitioning on distance matrices should not be used to study the variation in

community composition among sites.• Partitioning on distance matrices underestimated the amount of variation in

community composition explained by the raw-data approach.

• The proper statistical procedure for partitioning the spatial variation of communitycomposition data among environmental and spatial components, and for testinghypotheses about the origin and maintenance of variation in community compositionamong sites, is canonical partitioning.

• The Mantel approach is appropriate for testing other hypotheses, such as the variationin beta diversity among groups of sites. Regression on distance matrices is alsoappropriate for fitting models to similarity decay plots.

34

Direct (constrained) Ordination Methods

&Variation partitionning

35

Constrained (Canonical) Ordination Methods

• Univariate: e.g. (multiple) regression model

• Multivariate response data: e.g. Canonical Ordination

• Residual variation of multivariate response data: e.g. Partial ordination

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× ×

=

mm

xy

yx

x

yx

d

.

.

...2

11

One species (Occurrence, abundance)

q environ. var.

Species composition data. q environ. var.

Species composition data. q environ. var. Spatial terms

36

Response models Indirect Direct Multivariate

Linear PCA Constrained Ordination: RDA

Unimodal Constrained Ordination: CCA

• Ordination methods such as principal component analysis (PCA) are used to reduce the variation in community composition in an ordination diagram.(PCA uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of uncorrelated variables called principal components)

• Constrained (Canonical) Ordination: is a combination of ordination and multiple regression. It extracts continuous axes of variation from species abundance data in order to explain which portion of this variation is directly explained by environmental variables. The axes are constrained to be linear combinations of environmental variables. The orthogonal directions in PCA is particular and other directions may well be better related to env. var. Canonical Ordination is a solution for this.

=

mnm

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×→

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PCA


37

Redundancy Analysis (RDA): species are assumed to have linear response surfaces with respect to compound environmental gradients. Thus, RDA is a direct extension of multiple regression to the modelling of multivariate response data. It is related to PCA and it is based on Euclidean Distances.

a b c

Environnemental Gradient

Abundance

Abundance

Environnemental Gradient

ab

c

Canonical Correspondence Analysis (CCA): species are assumed to have unimodalresponse surfaces with respect to compound environmental gradient. It is related to Correspondence Analysis and it is based on Chi-squared distance.


38

0

5

10

15

20

25

30

1

2

3

4

5

1

23

4

Z D

ata

X Dat

a

Y Data

-150

-100

-50

0

50

100

1

2

3

4

5

1

23

4

Z D

ata

X Dat

a

Y Data

Linearx, y

Cubicx, y, xy, x2, y2, x2y, y2x, x3, y3

Trend surface model

d

x y. .. .. .

Geographic distancefor Mantel approaches

Spatial terms for Canonical Ordination Methods: trend surface

39

© AZTI-Tecnalia

Variation Partitionning

Chust, G., et al. (2003).Conservation Biology17 (6): 1712-1723.

UNA

ENV ANT

DIS

a b

c

d

e fg

UNA: Not explained

ENV

DIS

a

b

c

Steps (just algebra):1. Canonical Ordination (CO) between Species and ENV → a+c2. pCO between Species and ENV, partially out SPA→ a; → c = (a+c)-a 3. CO between Species and (ENV & Distance) → a+b+c; i.e. 1-UNA

Thus, b = (a+b+c) – a – cOr 3bis. CO between Species and DIS → b+c→

Thus b = (b+c) – c ; UNA = 1 – [a + b + c]

UNA = 50%

ENV

DIS

30%

10%

10%

2 variable types Example 3 variable types

e.g. Environment, Distance, Anthropogenic ANTe.g. Environment ENV, Distance DIS, UNA: unaccounted (not explained)

40

• R: veganpackage (Oksanen et al. 2011, see Docs)

• CANOCO (ter Braak and Smilauer 1998; http://www.pri.wur.nl/uk/products/canoco/)

• …

Software for Canonical and Redundancy analysis, and Variation Partitioning:

41

*Chust, G., J. Chave, R. Condit, S. Aguilar, S. Lao, & R. Pérez (2006) Determinants and spatial modelingof beta-diversity in a tropical forest landscape in Panama. Journal of Vegetation Science 17: 83-92.

Conclusion: The distribution of Panamanian tree species appears to be primarily determined by dispersal limitation, then by environmental heterogeneity


Duivenvoorden et al. Science,2002.

Based on Mantel test

Chust et al. 2006. JVS*

25% 10%

17%

46%

Shared

Spatial terms

Environment

Not explained

Based on Canonical Correspondence Analysis

42

Practical session 2 “Community Ecology with R: vegan package”

43

4th Corner Method

44

A B C

Presence/Absence × Traits × Environment

245 sp× 78 sites 3 life form Fragmentation

4 types of dispersion

D = C * A’ * B

××××

)(var)(var

)()(

traitDsitesC

traitspBsitesspA

• test F (global)• Correlation r

Legendre, P., Galzin, R. & Harmelin-Vivien, L. (1997) Relating behavior to habitat: solutions to the fourth-corner problem. Ecology, 78, 547–562.

4th Corner Method (Legendre et al. 1997)

• The fourth-corner tests for the association between biological traits to habitat at locations where the corresponding species are found.• How do the biological and behavioral characteristics of species determine their relative locataions in an ecosystem?• e.g. are the modes of dispersion related to habitat fragmentation?

45

Case study 1: Coral reef fish data

• Biological and behavioural traits

• Environmental variables:Bottom typeDepth…

Legendre et al. 1997

46

Case study 2: Plant traits

3 life forms

4 types of dispersion

Habitat fragmentation

47

Test F

Case study: Plant traits

Correlation

Interpretation: The effects of fragmentation of scrubland on scrub species community are related to the dispersal type

Fragmentation

Interpretation: Wind-dispersed species are positively related to the defragmentation

48

Chust, G., A. Pérez-Haase, J. Chave, & J. Ll. Pretus. (2006) Linking floristic patterns and plant traits of Mediterranean communities in fragmented habitats. Journal of Biogeography 33: 1235–1245.

Case study: Plant traits

Fragmentation

Num

ber

of s

peci

es

in s

crub

land

s Woody plantsAnnual herbs

Animal-dispersedWind-dispersed

Fraction of scrubland (%)

0-33 34-66 67-100

Interpretation: Wind-dispersed and annual species are positively related to the defragmentation of scrublands

Introduc)on to Sta)s)cal Modelling Tools for Habitat Models Development, 26-‐28th Oct 2011 EURO-‐BASIN, www.euro-‐basin.eu

Technology

Habitat Modelling, by Guillem Chust