Studying the effect of species dominance on diversity patterns using Hill numbers-based indices

Transcription

1 Studying the effect of species dominance on diversity patterns using Hill numbers-based indices Loïc Chalmandrier Loïc Chalmandrier Diversity pattern analysis November 8th / 14

2 Introduction Diversity & Filters Assembly theory - From patterns to processes Meta-community diversity is the result of ecological processes that can be identified by studying the structure of communities Loïc Chalmandrier Diversity pattern analysis November 8th / 14

3 Introduction Diversity & Filters Assembly theory - From patterns to processes Meta-community diversity is the result of ecological processes that can be identified by studying the structure of communities Loïc Chalmandrier Diversity pattern analysis November 8th / 14

4 Introduction Diversity & Filters Assembly theory - From patterns to processes Meta-community diversity is the result of ecological processes that can be identified by studying the structure of communities Loïc Chalmandrier Diversity pattern analysis November 8th / 14

5 Introduction Diversity & Filters Assembly theory - From patterns to processes Meta-community diversity is the result of ecological processes that can be identified by studying the structure of communities Use of proxies of species ecological niche: functional traits, phylogeny... Loïc Chalmandrier Diversity pattern analysis November 8th / 14

6 Introduction Statistical tools Methodological steps Loïc Chalmandrier Diversity pattern analysis November 8th / 14

7 Introduction Statistical tools Methodological steps Loïc Chalmandrier Diversity pattern analysis November 8th / 14

8 Introduction Statistical tools Methodological steps Loïc Chalmandrier Diversity pattern analysis November 8th / 14

9 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. Loïc Chalmandrier Diversity pattern analysis November 8th / 14

10 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. Loïc Chalmandrier Diversity pattern analysis November 8th / 14

11 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. Loïc Chalmandrier Diversity pattern analysis November 8th / 14

12 Why doing it? Diversity index assumptions Choosing Rao s QE QE = i d ij p i p j j Loïc Chalmandrier Diversity pattern analysis November 8th / 14

13 Why doing it? Diversity index assumptions Choosing Rao s QE QE = i d ij p i p j j Species contribution to diversity proportional to relative abundance. Choler et al Loïc Chalmandrier Diversity pattern analysis November 8th / 14

14 Why doing it? Diversity index assumptions Choosing Rao s QE QE = i d ij p i p j j Species contribution to diversity proportional to relative abundance. Linear relationship between ecological niche dissimilarity and trait/phy. species distances. Godoy et al Loïc Chalmandrier Diversity pattern analysis November 8th / 14

15 Why doing it? Diversity index assumptions Choosing Rao s QE QE = i d ij p i p j j Species contribution to diversity proportional to relative abundance. Linear relationship between ecological niche dissimilarity and trait/phy. species distances. Loïc Chalmandrier Diversity pattern analysis November 8th / 14

16 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 Loïc Chalmandrier Diversity pattern analysis November 8th / 14

17 How doing it? The dominance effect: Hill numbers Derives from information theory Parametric diversity metric that unified Richness, Shannon, Simpson... { D(q) = ( i pq i )1/(1 q) if q 1 D(1) = exp( i ln(p i)p i ) if q = 1 Loïc Chalmandrier Diversity pattern analysis November 8th / 14

18 How doing it? The dominance effect: Hill numbers Derives from information theory Parametric diversity metric that unified Richness, Shannon, Simpson... { D(q) = ( i pq i )1/(1 q) if q 1 D(1) = exp( i ln(p i)p i ) if q = 1 { D(0) = ( i p0 i ) = N Richesse Loïc Chalmandrier Diversity pattern analysis November 8th / 14

19 How doing it? The dominance effect: Hill numbers Derives from information theory Parametric diversity metric that unified Richness, Shannon, Simpson... { D(q) = ( i pq i )1/(1 q) if q 1 D(1) = exp( i ln(p i)p i ) if q = 1 { D(0) = ( i p0 i ) = N Richesse { D(1) = exp( i ln(p i)p i ) Exp. of Shannon entropy Loïc Chalmandrier Diversity pattern analysis November 8th / 14

20 How doing it? The dominance effect: Hill numbers Derives from information theory Parametric diversity metric that unified Richness, Shannon, Simpson... { D(q) = ( i pq i )1/(1 q) if q 1 D(1) = exp( i ln(p i)p i ) if q = 1 { D(0) = ( i p0 i ) = N Richesse { D(1) = exp( i ln(p i)p i ) Exp. of Shannon entropy { D(2) = ( i p2 i )1/(1 2) = 1 i p2 i Inverse of Simpson Loïc Chalmandrier Diversity pattern analysis November 8th / 14

21 How doing it? The dominance effect: Hill numbers Derives from information theory Parametric diversity metric that unified Richness, Shannon, Simpson... { D(q) = ( i pq i )1/(1 q) if q 1 D(1) = exp( i ln(p i)p i ) if q = 1 { D(0) = ( i p0 i ) = N Richesse { D(1) = exp( i ln(p i)p i ) Exp. of Shannon entropy { D(2) = ( i p2 i )1/(1 2) = 1 Inverse of Simpson i p2 i { D( ) = 1 max(p i ) Indice de Berger-Parker Loïc Chalmandrier Diversity pattern analysis November 8th / 14

22 How doing it? Properties Increase when the number of species increases and when species abundances are more even Loïc Chalmandrier Diversity pattern analysis November 8th / 14

23 How doing it? Properties Increase when the number of species increases and when species abundances are more even Concave metric of diversity Loïc Chalmandrier Diversity pattern analysis November 8th / 14

24 How doing it? Properties Increase when the number of species increases and when species abundances are more even Concave metric of diversity Quantify species effective number (Value between 1 and N). Example One community with 8 equally abundant species and another with 16 equally abundant species. With Shannon entropy : 2.07 vs. 2.77; Gini-Simpson : vs With D(1) : 8 vs. 16; D(2) : 8 vs. 16 Loïc Chalmandrier Diversity pattern analysis November 8th / 14

25 How doing it? Properties Increase when the number of species increases and when species abundances 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 Loïc Chalmandrier Diversity pattern analysis November 8th / 14

26 How doing it? Behavior with uneven abundance Example of a two species community Species richness Loïc Chalmandrier Diversity pattern analysis November 8th / 14

27 How doing it? Behavior with uneven abundance Example of a two species community Species richness Exp. of Shannon Loïc Chalmandrier Diversity pattern analysis November 8th / 14

28 How doing it? Behavior with uneven abundance Example of a two species community Species richness Exp. of Shannon Inverse of Simpson Loïc Chalmandrier Diversity pattern analysis November 8th / 14

29 How doing it? Behavior with uneven abundance Example of a two species community Species richness Exp. of Shannon Inverse of Simpson Berger-Parker Loïc Chalmandrier Diversity pattern analysis November 8th / 14

30 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 Loïc Chalmandrier Diversity pattern analysis November 8th / 14

31 How doing it? How to adapt Hill numbers to phylogenetic and functional distances? Leinster s generalization of Hill numbers (includes Rao...) { D(q, δ) = ( i p i( j Z ijp j ) q 1 ) 1/(1 q) if q 1 D(q, δ) = exp( i p ilog( j Z ijp j )) if q = 1 p i : rel. abun. of species i Z ij : similarity between species i and j. Chao s generalization of Hill numbers (includes Faith, Allen, Rao, ( MPD)...) { D(q, δ) = ( L b (δ) b T pq b )1/(1 q) if q 1 D(q, δ) = exp( L b (δ) b T ln(p b)p b ) if q = 1 p b : rel. abun. of branch b descendants L b : branch b length. T : Tree length. Loïc Chalmandrier Diversity pattern analysis November 8th / 14

32 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 Loïc Chalmandrier Diversity pattern analysis November 8th / 14

33 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 Ecology Loïc Chalmandrier Diversity pattern analysis November 8th / 14

34 Application Results: varying diversity pattern according to q and δ. Conclusions Abiotic filtering on plant functional traits. Abiotic filtering on lineage composition. Widespread dominant and recent lineages. Chalmandrier et al Ecology Loïc Chalmandrier Diversity pattern analysis November 8th / 14

35 Application Results: varying diversity pattern according to q and δ. Conclusions with Faith s index Abiotic filtering on plant functional traits. Abiotic filtering on lineage composition. Widespread dominant and recent lineages. Chalmandrier et al Ecology Loïc Chalmandrier Diversity pattern analysis November 8th / 14

36 Application Results: varying diversity pattern according to q and δ. Conclusions with Allen s index Abiotic filtering on plant functional traits. Abiotic filtering on lineage composition. Widespread dominant and recent lineages. Chalmandrier et al Ecology Loïc Chalmandrier Diversity pattern analysis November 8th / 14

37 Application Results: varying diversity pattern according to q and δ. Conclusions with Rao s index Abiotic filtering on plant functional traits. Abiotic filtering on lineage composition. Widespread dominant and recent lineages. Chalmandrier et al Ecology Loïc Chalmandrier Diversity pattern analysis November 8th / 14

38 Application Results: varying diversity pattern according to q and δ. Conclusions with a transformed tree Abiotic filtering on plant functional traits. Abiotic filtering on lineage composition. Widespread dominant and recent lineages. Chalmandrier et al Ecology Loïc Chalmandrier Diversity pattern analysis November 8th / 14