# GenSimpson: Generalized Simpson's Entropy and Diversity In entropart: Entropy Partitioning to Measure Diversity

## Description

Calculates the Generalized Simpson's entropy of order r of a probability or abundance vector, and its effective number of species.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28``` ```GenSimpson(NorP, r = 1, ...) bcGenSimpson(Ns, r = 1, CheckArguments = TRUE) ## S3 method for class 'ProbaVector' GenSimpson(NorP, r = 1, ..., CheckArguments = TRUE, Ps = NULL) ## S3 method for class 'AbdVector' GenSimpson(NorP, r = 1, ..., CheckArguments = TRUE, Ns = NULL) ## S3 method for class 'integer' GenSimpson(NorP, r = 1, ..., CheckArguments = TRUE, Ns = NULL) ## S3 method for class 'numeric' GenSimpson(NorP, r = 1, ..., CheckArguments = TRUE, Ps = NULL, Ns = NULL) GenSimpsonD(NorP, r = 1, ...) bcGenSimpsonD(Ns, r = 1, CheckArguments = TRUE) ## S3 method for class 'ProbaVector' GenSimpsonD(NorP, r = 1, ..., CheckArguments = TRUE, Ps = NULL) ## S3 method for class 'AbdVector' GenSimpsonD(NorP, r = 1, ..., CheckArguments = TRUE, Ns = NULL) ## S3 method for class 'integer' GenSimpsonD(NorP, r = 1, ..., CheckArguments = TRUE, Ns = NULL) ## S3 method for class 'numeric' GenSimpsonD(NorP, r = 1, ..., CheckArguments = TRUE, Ps = NULL, Ns = NULL) ```

## Arguments

 `Ps` A probability vector, summing to 1. `Ns` A numeric vector containing species abundances. `NorP` A numeric vector, an integer vector, an abundance vector (`AbdVector`) or a probability vector (`ProbaVector`). Contains either abundances or probabilities. `r` A number: the order of diversity. Default is 1 for Simpson's diversity. `...` Additional arguments. Unused. `CheckArguments` Logical; if `TRUE`, the function arguments are verified. Should be set to `FALSE` to save time when the arguments have been checked elsewhere.

## Details

The Generalized Simpson's Entropy (Zhang and Zhou, 2010) of order r is, in the species accumulation curve, the probability for the individual sampled in rank r+1 to belong to a new species. It is a measure of diversity so long as r is lower than the number of species (Grabchak et al., 2016).

Bias correction requires the number of individuals. Use `bcGenSimpson`. It is limited to orders r less than or equal to the number of individuals in the community.

The effective number of species `GenSimpsonD` (explicit diversity) has been derived by Grabchak et al. (2016).

The functions are designed to be used as simply as possible. `GenSimpson` is a generic method. If its first argument is an abundance vector, an integer vector or a numeric vector which does not sum to 1, the bias corrected function `bcGenSimpson` is called. Explicit calls to `bcGenSimpson` (with bias correction) or to `GenSimpson.ProbaVector` (without correction) are possible to avoid ambiguity. The `.integer` and `.numeric` methods accept `Ps` or `Ns` arguments instead of `NorP` for backward compatibility.

## Value

A named number equal to the calculated index or diversity. The name is either "Biased" or "Unbiased", depending on the estimator used.

## Note

The unbiased estimator is calculated by the `GenSimp.z` function of the `EntropyEstimation` package.

## Author(s)

Eric Marcon <[email protected]>

## References

Grabchak, M., Marcon, E., Lang, G., and Zhang, Z. (2017). The Generalized Simpson's Entropy is a Measure of Biodiversity. Plos One, 12(3): e0173305.

Zhang Z. and Zhou J. (2010). Re-parameterization of multinomial distributions and diversity indices. Journal of Statistical Planning and Inference 140(7): 1731-1738.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```# Load Paracou data (number of trees per species in two 1-ha plot of a tropical forest) data(Paracou618) # Ns is the total number of trees per species Ns <- as.AbdVector(Paracou618.MC\$Ns) # Species probabilities Ps <- as.ProbaVector(Paracou618.MC\$Ns) # Whittaker plot plot(Ns) # Calculate GenSimpson entropy of order 1, equal to Simpson's index of diversity GenSimpson(Ps, 1) # Calculate an unbiased estimator of GenSimpson diversity of order 100 GenSimpsonD(Ns, 100) ```

entropart documentation built on Feb. 6, 2018, 1:04 a.m.