simpson: Simpson's diversity index

Description Usage Arguments Details Author(s) References See Also Examples

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

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)

untb documentation built on March 19, 2018, 9:03 a.m.