1. 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

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

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

4. 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

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

6. 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

7. Phylogenetic diversityLj
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

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

9. 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

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

11. 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

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

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

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

15. 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.

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