alakazam (version 1.3.0)

calcDiversity: Calculate the diversity index

Description

calcDiversity calculates the clonal diversity index for a vector of diversity orders.

Usage

calcDiversity(p, q)

Value

A vector of diversity scores \(D\) for each \(q\).

Arguments

p

numeric vector of clone (species) counts or proportions.

q

numeric vector of diversity orders.

Details

This method, proposed by Hill (Hill, 1973), quantifies diversity as a smooth function (\(D\)) of a single parameter \(q\). Special cases of the generalized diversity index correspond to the most popular diversity measures in ecology: species richness (\(q = 0\)), the exponential of the Shannon-Weiner index (\(q\) approaches \(1\)), the inverse of the Simpson index (\(q = 2\)), and the reciprocal abundance of the largest clone (\(q\) approaches \(+\infty\)). At \(q = 0\) different clones weight equally, regardless of their size. As the parameter \(q\) increase from \(0\) to \(+\infty\) the diversity index (\(D\)) depends less on rare clones and more on common (abundant) ones, thus encompassing a range of definitions that can be visualized as a single curve.

Values of \(q < 0\) are valid, but are generally not meaningful. The value of \(D\) at \(q=1\) is estimated by \(D\) at \(q=0.9999\).

References

1. Hill M. Diversity and evenness: a unifying notation and its consequences. Ecology. 1973 54(2):427-32.

See Also

Used by alphaDiversity.

Examples

# May define p as clonal member counts
p <- c(1, 1, 3, 10)
q <- c(0, 1, 2)
calcDiversity(p, q)

# Or proportional abundance
p <- c(1/15, 1/15, 1/5, 2/3)
calcDiversity(p, q)