Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
Studying the effect of species dominance on diversitypatterns using Hill numbers-based indices
Loıc Chalmandrier
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 1 / 14
Introduction Diversity & Filters
Assembly theory - From patterns to processes
� Meta-community diversity is the result of ecological processes thatcan be identified by studying the structure of communities
� Use of proxies of species ecological niche: functional traits,phylogeny...
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 2 / 14
Introduction Diversity & Filters
Assembly theory - From patterns to processes
� Meta-community diversity is the result of ecological processes thatcan be identified by studying the structure of communities
� Use of proxies of species ecological niche: functional traits,phylogeny...
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 2 / 14
Introduction Diversity & Filters
Assembly theory - From patterns to processes
� Meta-community diversity is the result of ecological processes thatcan be identified by studying the structure of communities
� Use of proxies of species ecological niche: functional traits,phylogeny...
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 2 / 14
Introduction Diversity & Filters
Assembly theory - From patterns to processes
� Meta-community diversity is the result of ecological processes thatcan be identified by studying the structure of communities
� Use of proxies of species ecological niche: functional traits,phylogeny...
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 2 / 14
Introduction Statistical tools
Methodological steps
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 3 / 14
Introduction Statistical tools
Methodological steps
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 3 / 14
Introduction Statistical tools
Methodological steps
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 3 / 14
Introduction Statistical tools
To test a functional/phylo diversity pattern, you need:
A diversity index
� for a given facet, α, β, γ, σ...
� Richesse, Shannon, Rao, MPD, MNTD...
� Function of species relative abundances.
A species ecological similarity matrix
� Different traits, phylogeny.
� Link function between data and species ecological similarity metric.
A null model
� Null hypothesis.
� A species pool.
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 4 / 14
Introduction Statistical tools
To test a functional/phylo diversity pattern, you need:
A diversity index
� for a given facet, α, β, γ, σ...
� Richesse, Shannon, Rao, MPD, MNTD...
� Function of species relative abundances.
A species ecological similarity matrix
� Different traits, phylogeny.
� Link function between data and species ecological similarity metric.
A null model
� Null hypothesis.
� A species pool.
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 4 / 14
Introduction Statistical tools
To test a functional/phylo diversity pattern, you need:
A diversity index
� for a given facet, α, β, γ, σ...
� Richesse, Shannon, Rao, MPD, MNTD...
� Function of species relative abundances.
A species ecological similarity matrix
� Different traits, phylogeny.
� Link function between data and species ecological similarity metric.
A null model
� Null hypothesis.
� A species pool.
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 4 / 14
Testing across diversity indices Why doing it?
Diversity index assumptions
Choosing Rao’s QE
QE =∑i
∑j
dijpipj
� Species contribution to diversity proportional to relativeabundance.
� Linear relationship between ecological niche dissimilarity andtrait/phy. species distances.
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 5 / 14
Testing across diversity indices Why doing it?
Diversity index assumptions
Choosing Rao’s QE
QE =∑i
∑j
dijpipj
� Species contribution to diversity proportional to relativeabundance.
� Linear relationship between ecological niche dissimilarity andtrait/phy. species distances.
Choler et al. 2001
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 5 / 14
Testing across diversity indices Why doing it?
Diversity index assumptions
Choosing Rao’s QE
QE =∑i
∑j
dijpipj
� Species contribution to diversity proportional to relativeabundance.
� Linear relationship between ecological niche dissimilarity andtrait/phy. species distances.
Godoy et al. 2014
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 5 / 14
Testing across diversity indices Why doing it?
Diversity index assumptions
Choosing Rao’s QE
QE =∑i
∑j
dijpipj
� Species contribution to diversity proportional to relativeabundance.
� Linear relationship between ecological niche dissimilarity andtrait/phy. species distances.
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 5 / 14
Testing across diversity indices Why doing it?
Diversity index assumptions
� Dominance effect: how species abundance are taken into account
� Similarity effect: how species similarities (functional, phylogenetic)are taken into account
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 6 / 14
Testing across diversity indices How doing it?
The dominance effect: Hill numbers
� Derives from information theory� Parametric diversity metric that unified Richness, Shannon,
Simpson... {D(q) = (
∑i p
qi )1/(1−q) if q 6= 1
D(1) = exp(−∑
i ×ln(pi )pi ) if q = 1
{D(0) = (
∑i p
0i ) = N Richesse{
D(1) = exp(−∑
i ×ln(pi )pi ) Exp. of Shannon entropy{D(2) = (
∑i p
2i )1/(1−2) = 1∑
i p2i
Inverse of Simpson{D(∞) = 1
max(pi )Indice de Berger-Parker
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 7 / 14
Testing across diversity indices How doing it?
The dominance effect: Hill numbers
� Derives from information theory� Parametric diversity metric that unified Richness, Shannon,
Simpson... {D(q) = (
∑i p
qi )1/(1−q) if q 6= 1
D(1) = exp(−∑
i ×ln(pi )pi ) if q = 1{D(0) = (
∑i p
0i ) = N Richesse
{D(1) = exp(−
∑i ×ln(pi )pi ) Exp. of Shannon entropy{
D(2) = (∑
i p2i )1/(1−2) = 1∑
i p2i
Inverse of Simpson{D(∞) = 1
max(pi )Indice de Berger-Parker
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 7 / 14
Testing across diversity indices How doing it?
The dominance effect: Hill numbers
� Derives from information theory� Parametric diversity metric that unified Richness, Shannon,
Simpson... {D(q) = (
∑i p
qi )1/(1−q) if q 6= 1
D(1) = exp(−∑
i ×ln(pi )pi ) if q = 1{D(0) = (
∑i p
0i ) = N Richesse{
D(1) = exp(−∑
i ×ln(pi )pi ) Exp. of Shannon entropy
{D(2) = (
∑i p
2i )1/(1−2) = 1∑
i p2i
Inverse of Simpson{D(∞) = 1
max(pi )Indice de Berger-Parker
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 7 / 14
Testing across diversity indices How doing it?
The dominance effect: Hill numbers
� Derives from information theory� Parametric diversity metric that unified Richness, Shannon,
Simpson... {D(q) = (
∑i p
qi )1/(1−q) if q 6= 1
D(1) = exp(−∑
i ×ln(pi )pi ) if q = 1{D(0) = (
∑i p
0i ) = N Richesse{
D(1) = exp(−∑
i ×ln(pi )pi ) Exp. of Shannon entropy{D(2) = (
∑i p
2i )1/(1−2) = 1∑
i p2i
Inverse of Simpson
{D(∞) = 1
max(pi )Indice de Berger-Parker
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 7 / 14
Testing across diversity indices How doing it?
The dominance effect: Hill numbers
� Derives from information theory� Parametric diversity metric that unified Richness, Shannon,
Simpson... {D(q) = (
∑i p
qi )1/(1−q) if q 6= 1
D(1) = exp(−∑
i ×ln(pi )pi ) if q = 1{D(0) = (
∑i p
0i ) = N Richesse{
D(1) = exp(−∑
i ×ln(pi )pi ) Exp. of Shannon entropy{D(2) = (
∑i p
2i )1/(1−2) = 1∑
i p2i
Inverse of Simpson{D(∞) = 1
max(pi )Indice de Berger-Parker
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 7 / 14
Testing across diversity indices How doing it?
Properties
� Increase when the number of species increases and when speciesabundances are more even
� Concave metric of diversity
� Quantify species “effective number” (Value between 1 and N).
� Return “true” estimates of β-diversity (Jost 2007, Tuomisto 2011)
Example
� One community with 8 equally abundant species and another with16 equally abundant species.
� With Shannon entropy : 2.07 vs. 2.77; Gini-Simpson : 0.875 vs.0.9375
� With D(1) : 8 vs. 16; D(2) : 8 vs. 16
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 8 / 14
Testing across diversity indices How doing it?
Properties
� Increase when the number of species increases and when speciesabundances are more even
� Concave metric of diversity
� Quantify species “effective number” (Value between 1 and N).
� Return “true” estimates of β-diversity (Jost 2007, Tuomisto 2011)
Example
� One community with 8 equally abundant species and another with16 equally abundant species.
� With Shannon entropy : 2.07 vs. 2.77; Gini-Simpson : 0.875 vs.0.9375
� With D(1) : 8 vs. 16; D(2) : 8 vs. 16
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 8 / 14
Testing across diversity indices How doing it?
Properties
� Increase when the number of species increases and when speciesabundances are more even
� Concave metric of diversity
� Quantify species “effective number” (Value between 1 and N).
� Return “true” estimates of β-diversity (Jost 2007, Tuomisto 2011)
Example
� One community with 8 equally abundant species and another with16 equally abundant species.
� With Shannon entropy : 2.07 vs. 2.77; Gini-Simpson : 0.875 vs.0.9375
� With D(1) : 8 vs. 16; D(2) : 8 vs. 16
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 8 / 14
Testing across diversity indices How doing it?
Properties
� Increase when the number of species increases and when speciesabundances are more even
� Concave metric of diversity
� Quantify species “effective number” (Value between 1 and N).
� Return “true” estimates of β-diversity (Jost 2007, Tuomisto 2011)
beta-diversity
� γ/α
� Quantifies the “effective number” of site in a meta-community
� set between 1 and the number of site
� “independent” from the α-diversity
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 8 / 14
Testing across diversity indices How doing it?
Behavior with uneven abundance
Example of a two species community
� Species richness
� Exp. of Shannon
� Inverse of Simpson
� Berger-Parker
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 9 / 14
Testing across diversity indices How doing it?
Behavior with uneven abundance
Example of a two species community
� Species richness
� Exp. of Shannon
� Inverse of Simpson
� Berger-Parker
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 9 / 14
Testing across diversity indices How doing it?
Behavior with uneven abundance
Example of a two species community
� Species richness
� Exp. of Shannon
� Inverse of Simpson
� Berger-Parker
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 9 / 14
Testing across diversity indices How doing it?
Behavior with uneven abundance
Example of a two species community
� Species richness
� Exp. of Shannon
� Inverse of Simpson
� Berger-Parker
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 9 / 14
Testing across diversity indices How doing it?
Parametrization of the dominance effect
� When ’q’ is low, all species are taken into account
� When ’q’ is high, only dominant species are taken into account
Example : Change of community ranking with q
Leinster & Cobbold 2012
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 10 / 14
Testing across diversity indices How doing it?
How to adapt Hill numbers to phylogenetic and functionaldistances?
Leinster’s generalization of Hill numbers (includes Rao...)
{D(q, δ) = (
∑i pi (
∑j Zijpj)
q−1)1/(1−q) if q 6= 1
D(q, δ) = exp(−∑
i pi log(∑
j Zijpj)) if q = 1
pi: rel. abun. of species iZij: similarity betweenspecies i and j.
Chao’s generalization of Hill numbers (includes Faith, Allen, Rao,( MPD)...)
{D(q, δ) = (
∑b
Lb(δ)T × pqb )1/(1−q) if q 6= 1
D(q, δ) = exp(−∑
bLb(δ)T × ln(pb)pb) if q = 1
pb: rel. abun. of branchb descendantsLb: branch b length.T : Tree length.
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 11 / 14
Testing across diversity indices How doing it?
The similarity effect
� Idea : Varying the link between ecological similarity and phylo.distance
� Link to niche evolution theory through Pagel’s tree transformations
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 12 / 14
Testing across diversity indices Application
Varying plant meta-community phylogenetic β-diversity
120 communities across the gradients of the Guisane valley (Alps)Genus-level phylogeny as species ecological similarity.
Chalmandrier et al. 2015 Ecology
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 13 / 14
Testing across diversity indices Application
Results: varying diversity pattern according to q and δ.
Conclusions
� Abiotic filtering on plantfunctional traits.
� Abiotic filtering on lineagecomposition.
� Widespread dominant and recentlineages.
Chalmandrier et al. 2015 Ecology
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 14 / 14
Testing across diversity indices Application
Results: varying diversity pattern according to q and δ.
Conclusions with Faith’s index
� Abiotic filtering on plantfunctional traits.
� Abiotic filtering on lineagecomposition.
� Widespread dominant and recentlineages.
Chalmandrier et al. 2015 Ecology
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 14 / 14
Testing across diversity indices Application
Results: varying diversity pattern according to q and δ.
Conclusions with Allen’s index
� Abiotic filtering on plantfunctional traits.
� Abiotic filtering on lineagecomposition.
� Widespread dominant andrecent lineages.
Chalmandrier et al. 2015 Ecology
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 14 / 14
Testing across diversity indices Application
Results: varying diversity pattern according to q and δ.
Conclusions with Rao’s index
� Abiotic filtering on plantfunctional traits.
� Abiotic filtering on lineagecomposition.
� Widespread dominant and recentlineages.
Chalmandrier et al. 2015 Ecology
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 14 / 14
Testing across diversity indices Application
Results: varying diversity pattern according to q and δ.
Conclusions with a transformedtree
� Abiotic filtering on plantfunctional traits.
� Abiotic filtering on lineagecomposition.
� Widespread dominant and recentlineages.
Chalmandrier et al. 2015 Ecology
Loıc Chalmandrier Diversity pattern analysis November 8th 2017 14 / 14