benthos (version 2.0-0)

hill: Hill's Diversity Numbers

Description

According to Hill (1973): "a diversity number is figuratively a measure of how many species are present if we examine the sample down to a certain depth among its rarities. If we examine superficially (e.g., by using \(N_2\)) we shall see only the more abundant species. If we look deeply (e.g., by using \(N_0\)) we shall see all the species present."

Usage

hill(taxon, count, a = 0)
hill0(taxon, count)
hill1(taxon, count)
hill2(taxon, count)

Value

numeric vector of Hill's numbers

Arguments

taxon

character vector containing taxa

count

numeric vector containing counts

a

exponent in Hill's diversity number (R, with special cases for a in {0, 1, 2} (see details))

Functions

• hill0(): \(N_0\)

• hill1(): \(N_1\)

• hill2(): \(N_2\)

Details

Hill's diversity numbers are given by: $$N_a=\sum{i=1}^S (p_i^a)^{1/(1-a)}$$

Special cases are:

\(N_{-\infty}\)

reciprocal of the proportional abundance of the rarest species;

\(N_0\)

total number of species present;

\(N_1\)

exp(H), where H: Shannon's index (see also shannon);

\(N_2\)

reciprocal of Simpson's index (see also simpson);

\(N_{\infty}\)

reciprocal of the proportional abundance of the commonest species.

References

Hill, M.O., 1973. Diversity and Evenness: A Unifying Notation and Its Consequences. Ecology 54:427-432

See Also

species_richness, shannon, simpson

Examples

     hill(
         taxon = c("Euspira pulchella", "Nephtys cirrosa"),
         count = c(6, 12),
         a = 0
     )
     hill0(
         taxon = c("Euspira pulchella", "Nephtys cirrosa"),
         count = c(6, 12)
     )