hill: Hill numbers

In hallucigenia-sparsa/seqtime: Time Series Analysis of Sequencing Data

Hill numbers

Description

The Hill numbers quantify biodiversity. The importance of the abundance distribution increases with increasing Hill order. For q=0, the Hill number is the richness, for q=1, it is the (exponential) Shannon entropy and for q=2, it is the inverse Simpson index. Note that the Hill order can also be a fraction, e.g. 0.5.

Usage

hill(p = rep(1/10, 10), q = 0)

Arguments

p	relative abundance vector, should sum to one
q	the Hill order

Details

The Hill number is defined as D=(SUM p_i^q)^1/(1-q), for i from 1 to S, where S is the species number, p_i is the proportion of species i and q is the Hill order. Since the Hill number involves a division by zero for q=1, please choose a sufficiently close q, such as 0.99999, when computing the Hill number for 1.

Value

the Hill number

References

Hill (1973) "Diversity and evenness: a unifying notation and its consequences", Ecology 54: 427-432.

Examples

# even species distribution
hill(generateAbundances(N=1000,mode=6,k=0.001,probabs=TRUE),q=2)
# uneven species distribution
hill(generateAbundances(N=1000,mode=6,k=0.2,probabs=TRUE),q=2)

hallucigenia-sparsa/seqtime documentation built on Jan. 9, 2023, 11:53 p.m.