simpson: Simpson's diversity index

Description

Simpson's diversity index

Usage

simpson(x)

Arguments

Ecosystem vector; coerced to class count

Details

Returns the Simpson index $D$: the probability that two randomly sampled individuals belong to different species. This is $$1-\sum_{i=1}^S\left(p_i\right)^2$$

where $p_i$ is the relative frequency of the $i^{\rm th}$ species

References

S. P. Hubbell 2001.The Unified Neutral Theory of Biodiversity. Princeton University Press.
F. He and X.-S. Hu 2005.Hubbell's Fundamental Biodiversity Parameter and the Simpson Diversity Index. Ecology Letters, volume 8, pp386-390. doi:10.1111/j.1461-0248.2005.00729.x
E. H. Simpson 1949.Measurement of diversity. Nature, volume 163, p688

Examples

Run this code

data(butterflies)

D <- simpson(butterflies)
theta <- optimal.prob(butterflies)*2*no.of.ind(butterflies)

#compare theta with D/(1-D) (should be roughly equal):

theta
D/(1-D)