Samuel M. Scheiner National Science Foundation sscheine@nsf.gov A metric of biodiversity that integrates abundance, phylogeny, and function Samuel M. Scheiner National Science Foundation sscheine@nsf.gov

The components of diversity Abundance: numbers of individuals Phylogeny: divergence of individuals Function: distinctiveness of individuals

Central question How do these components compare within and co-vary across communities? Answer requires that the components be measured in similar units

Measuring diversity Hill index pi = the relative abundance of species i Units = effective number of species q = 0 Species richness q = 1 Exponential Shannon-Weiner q = 2 Inverse Simpson

Partitioning diversity qD(A) = R × qE(A) Diversity = Richness X Evenness Evenness is the distribution of relative abundances

Partitioning diversity 2D(A) = 4.0 2E(A) = 1.0 N = 12 2D(A) = 2.1 2E(A) = 0.5 N = 12 2D(A) = 4.0 2E(A) = 1.0 N = 8

Phylogenetic diversity Lj branch Lj : length (divergence) of the jth branch sj : number of species that share the jth branch Lij = Lj/sj Li = ΣLij : divergence the ith species L = Σ Li : total divergence of all species li = Li/L : proportional divergence of the ith species L1 = 2/1 + 2/2 + 2/3 + 2/4 = 4.17

Phylogenetic diversity li = the relative divergence of species i L = Total divergence Fauth’s Phylogenetic Diversity Index

Phylogenetic diversity 2D(P) = 3.87 2D(P) = 3.86 2D(P) = 3.92 2D(P) = 4.00 2D(P) = R if and only if the cladogram is perfectly symmetric

Functional diversity Two perspectives Function of: organismal traits and community role Function for: effects on ecosystem processes

Functional diversity sik : value of the kth trait of the ith species di : smallest distance between the ith species and all other species vi = Cm dim : functional volume of the ith species V = Σvi : total functional volume of all species fi = vi /V : proportional functional volume of the ith species Trait 1 Trait 2

V = Total distinctiveness Functional diversity qD(F) fi = the relative distinctiveness of species i V = Total distinctiveness

Functional diversity 2D(F) = 6.8 2E(F) = 0.97 V = 8.1 2D(F) = 6.2 Trait 1 Trait 2

An integrated diversity index Separate and integrated measures qD(A) qD(P) qD(F) qD(AP) qD(AF) qD(PF)

What is it good for? These measures separate total abundance, divergence, and distinctiveness from relative variation. All measures of diversity are in the same units, the effective number of species. All measures of diversity can be decomposed into evenness and richness (also α and β). Variation of diversity components among communities can be compared.

Questions? Scheiner, S. M. 2012. A metric of biodiversity that integrates abundance, phylogeny, and function. Oikos 121:1191-1202.