# simpson: Simpson's diversity index In RobinHankin/untb: Ecological Drift under the UNTB

## Description

Simpson's diversity index

## Usage

 1 simpson(x, with.replacement=FALSE) 

## Arguments

 x Ecosystem vector; coerced to class count with.replacement Boolean, with default FALSE meaning to sample without replacement; see details section

## Details

Returns the Simpson index D: the probability that two randomly sampled individuals belong to different species.

There is some confusion as to the precise definition: some authors specify that the two individuals are necessarily distinct (ie sampling without replacement), and some do not.

Simpson (1949) assumed sampling without replacement and gave

1-\frac{∑_{i=1}^Sn_i≤ft(n_i-1\right)}{J(J-1)}

in our notation.

He and Hu (2005) assumed sampling with replacement:

1-\frac{∑_{i=1}^Sn_i^2}{J^2}.

The difference is largely academic but is most pronounced when many species occur with low counts (ie close to 1).

## Author(s)

Robin K. S. Hankin

## 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

## See Also

preston

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 data(butterflies) D <- simpson(butterflies) theta <- optimal.prob(butterflies)*2*no.of.ind(butterflies) # compare theta with D/(1-D) (should be roughly equal; see He & Hu 2005): theta D/(1-D) # Second argument pedantic in practice. # Mostly, the difference is small: simpson(butterflies,FALSE) - simpson(butterflies,TRUE) # Most extreme example: x <- count(c(1,1)) simpson(x,TRUE) simpson(x,FALSE) 

RobinHankin/untb documentation built on June 7, 2019, 5:07 a.m.