Measuring functional diversity from multiple traits

Etienne Laliberté, PhD candidateRural Ecology Research Group (RERG)School of Forestry, University of Canterbury, Christchurch, New Zealand

Functional diversity (FD)

• Functional composition: the value of species traits

• Functional dispersion: the spread, or variability, of species traits

• How to measure FD from multiple traits?

Sébastien Villéger et al 2008 EcologyAugust issue

Figure taken from Villéger et al 2008 Ecology

Species 1

Species 2

etc…

9 species in functional trait space (2 traits)

Size of black circle = relative abundance

Functional trait space

Trait 1

Trai

t 2

Figure taken from Villéger et al 2008 Ecology

Functional richnessFRic

Functional richness (FRic):

Volume of the minimum convex hull that includes all species

Amount of functional space filled by a community

Figure taken from Villéger et al 2008 Ecology

Functional divergenceFDiv Functional divergence (FDiv):

The divergence of species from the center of gravity of the convex hull

Functional dispersion:

… the spread, or variability, in the locations of the S species in the T-dimensional space

This concept is termed dispersion in statistics (e.g. SS, variance, SD, range, etc)

Back to the basics

Figures taken from Villéger et al 2008 Ecology

FRic FDiv

• Sensitive to outliers• Strongly positively correlatedwith species richness

• Does not consider abundances• Need at least 3 species• Need more species than traits

Problems with FRic and FDiv

• Sensitive to outliers• Not sensitive to the sizeof the convex hull

• Need more species than traits• Need at least 3 species

0 1 2 3 40

1

2

3

4

Trait 1

Trai

t 2FDiv = 0.808

FDiv = 0.808

FDiv does not measure relative differencesin functional dispersion

Laliberté and Legendre submitted

0 1 2 3 40

1

2

3

4

Trait 1

Trai

t 2

Centroid

Distance of species A to group centroid

A

FDis = average distance to centroid

Functional dispersion (FDis)

0 1 2 3 40

1

2

3

4

Trait 1

Trai

t 2

Centroid

FDis and relative abundances

Centroid shifts towards the more abundant species

Laliberté and Legendre submitted

0 1 2 3 40

1

2

3

4

Trait 1

Trai

t 2FDis = 1.395FDiv = 0.808

FDis = 0.697FDiv = 0.808

FDis measures relative differences infunctional dispersion

Laliberté and Legendre submitted

Figure taken from Villéger et al 2008 Ecology

Simulations of Villéger et al

FRic is positively relatedto species richness

FDis is not influenced by

species richness

5 15 25 35 45

0.5

1.0

1.5

2.0

2.5

3.0

3.5

a

Species richnessFD

is

r = 0.061

0.0 0.2 0.4 0.6

0.5

1.0

1.5

2.0

2.5

3.0

3.5

FRic

FDis

b r = 0.313

0.2 0.4 0.6 0.80.5

1.0

1.5

2.0

2.5

3.0

3.5

c

FEve

FDis

r = -0.007

0.4 0.6 0.8 1.00.5

1.0

1.5

2.0

2.5

3.0

3.5

FDivFD

is

d r = 0.166Positively

related to FRic and to a lesser

degree FDiv

Laliberté and Legendre submitted

Desirable properties of FDis

1) Intuitive2) Can use multiple traits (any number or type)3) Less sensitive to outliers4) Direct comparison of functional dispersion5) Min. 2 species (3 for FRic and FDiv)6) Independent of species richness7) Can integrate relative abundances

dbFD: R function to measure FD

• www.elaliberte.info• Any type of traits (continuous, categorical, ordinal)• Tolerates missing trait values• 3 indices of Villéger et al, plus FDis• Community-weighted trait means (CWM):

functional composition• Functional group richness (FGri)

Acknowledgements

for fundingto come here

for generousscholarships

Talk at ESA

Global patterns of plant response diversity with land use intensification

Thursday, after morning tea