alakazam (version 0.2.2)

calcDiversity: Calculate the diversity index

Description

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

Usage

calcDiversity(p, q)

Arguments

p

numeric vector of clone (species) counts or proportions.

q

numeric vector of diversity orders.

Value

• A vector of diversity scores $D$ for each $q$.

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 rarefyDiversity and testDiversity.

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)