# Simpson: Simpson entropy of a community In entropart: Entropy Partitioning to Measure Diversity

## Description

Calculates the Simpson entropy of a probability vector.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```Simpson(NorP, ...) bcSimpson(Ns, Correction = "Lande", CheckArguments = TRUE) ## S3 method for class 'ProbaVector' Simpson(NorP, ..., CheckArguments = TRUE, Ps = NULL) ## S3 method for class 'AbdVector' Simpson(NorP, Correction="Lande", ..., CheckArguments = TRUE, Ns = NULL) ## S3 method for class 'integer' Simpson(NorP, Correction="Lande", ..., CheckArguments = TRUE, Ns = NULL) ## S3 method for class 'numeric' Simpson(NorP, Correction="Lande", ..., 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. `Correction` A string containing one of the possible corrections accepted by `bcTsallis` or `"Lande"`, the default value (equivalent to `"Best"`). `...` 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

Lande's correction has been derived (Lande, 1996; Good, 1953) especially for Simpson entropy, while other corrections are for generalized Tsallis entropy. It is identical to the unbiased estimator proposed by Simpson, although arguments were different. It equals the plug-in etimator multiplied by n/(n-1) where n is the total number of individuals.

Bias correction requires the number of individuals to estimate sample `Coverage`. Use `bcSimpson` and choose the `Correction`.

The functions are designed to be used as simply as possible. `Simpson` 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 `bcSimpson` is called. Explicit calls to `bcSimpson` (with bias correction) or to `Simpson.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 entropy. The name is that of the bias correction used.

## Author(s)

Eric Marcon <[email protected]>

## References

Good, I. J. (1953). On the Population Frequency of Species and the Estimation of Population Parameters. Biometrika 40(3/4): 237-264.

Lande, R. (1996). Statistics and partitioning of species diversity, and similarity among multiple communities. Oikos 76: 5-13.

Simpson, E. H. (1949). Measurement of diversity. Nature 163(4148): 688.

`Tsallis`, `bcSimpson`
 ```1 2 3 4 5 6 7 8 9``` ```# 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) # Whittaker plot plot(Ns) # Calculate an unbiased estimator of Simpson's index of diversity Simpson(Ns) ```