rarity: Compute Hill diversity: the mean species rarity

In mikeroswell/MeanRarity: Hill Diversity Estimation and Visualization

Compute Hill diversity: the mean species rarity

Description

Compute the empirical Hill diversity from abundances or relative abundances. Hill diversity is also the mean species rarity.

Usage

rarity(ab, l, q = NULL, na.rm = TRUE)

Arguments

ab	A numeric vector of species abundances or relative abundances.
l	Scaling exponent for the mean, can be any real number.
q	Scalar, traditional Hill number scaling exponent, q = 1-l where l is the scaling parameter for the generalized mean. Can be any real number.
na.rm	Logical, replace NA values with 0 abundance

Details

We parameterize Hill diversity D as a the frequency-weighted mean species rarity, with scaling exponent l

D = \sum{p_i * r_i^{\ell}}^{-\ell}

where rarity of species i r_1 = 1/p_i. When \ell = 0 this is defined base on the limit from the left and the right, which is the geometric mean

\exp(\frac{\sum{p_i * \ln(r_i)}}{\sum{p_i}})

This is equivalent to the q notation of Jost 2006

D=\sum{p_i^q}^{\frac{1}{1-q}}

where q=1-l.

This function can also be called with dfun()

Value

Generalized mean community rarity with scaling exponent "l".

When l = 1, arithmetic mean rarity (species richness).

When l = 0, geometric mean rarity (Hill-Shannon diversity), Shannon's entropy \insertCiteShannon1963MeanRarity exponentiated.

When l = -1, harmonic mean rarity (Hill-Simpson diversity), the inverse of the Simpson concentration \insertCiteSimpson1949MeanRarity.

References

\insertRef

Simpson1949MeanRarity \insertRefShannon1963MeanRarity

See Also

pfun, ipfun

Examples

rarity(c(20,8,5,4,2,1), 1) #species richness
rarity(c(20,8,5,4,2,1), 0) # Hill-Shannon diversity
rarity(c(20,8,5,4,2,1), -1) # Hill-Simpson diversity
rarity(c(20,8,5,4,2,1), q = 2) # The parameter `q` can be used instead for
# traditional Hill number parameterization

mikeroswell/MeanRarity documentation built on May 5, 2024, 4:50 p.m.