## Indices of Species Evenvess

### Description

The function `specieseve` calculates evenness indices that rely on relative or absolute species abundance.

### Usage

```specieseve(comm, method = "full", tol = 1e-8)
```

### Arguments

 `comm` a data frame or a matrix typically with communities as rows, species as columns and abundance as entry. `method` a string or a vector of strings: one or several of "GiniSimpson", "Simpson", "Shannon", "Heip", "McIntosh", "SmithWilson", "full". See details. `tol` a tolerance threshold (a value between -`tol` and `tol` is considered equal to zero)

### Details

Let S_i be the number of species in community i, n_ij be the absolute abundance of species j in community i, N_i the sum of all species abundance in community i (N_i=sum_j n_ij; the sum of row i in `comm`), p_ij the relative abundance of species j in community i (p_ij=n_ij/N_i). If `method="GiniSimpson"`, the evenness index is that associated with Gini (1912) and Simpson (1949) diversity index: (1-∑_j p_ij^2)*S_i/(S_i-1). If `method="Simpson"`, the evenness index is (Simpson 1949; Magurran 2004): (1/sum_j p_ij^2)/S_i. If `method="Shannon"`, the evenness index is that associated with Shannon (1948) diversity index with neperian logarithm: (-sum_j p_ij ln(p_ij))/ln(S_i). If `method="Heip"`, the evenness index is that of Heip (1974) (Magurran 2004): [exp(-sum_j p_ij log(p_ij)) - 1]/(S_i-1). If `method="McIntosh"`, the evenness index is that of Pielou (1975) associated with McIntosh (1967) index of diversity: (N_i-sqrt(sum_j n_ij^2)/(N_i-N_i/sqrt(S_i)). If `method="SmithWilson"`, the Smith and Wilson (1996) evenness index is calculated (Magurran 2004): 1-[2/pi*arctan(sum_j (log(n_ij) - sum_k log(n_ik)/S_i)^2/S_i)]. The function uses neperian logarithm for all indices. If one of the strings is "full", then all indices are calculated.

### Value

Function `specieseve` returns a matrix with communities as rows and the evenness indices as columns.

### Author(s)

Sandrine Pavoine sandrine.pavoine@mnhn.fr

### References

Gini, C. (1912) Variabilita e mutabilita. Studi economicoaguridici delle facoltta di giurizprudenza dell, Universite di Cagliari III, Parte II.

Heip, C. (1974) A new index measuring evenness. Journal of the Marine Biological Association UK, 54, 555–557.

Magurran, A.E. (2004) Measuring biological diversity. Oxford, UK: Blackwell Publishing.

McIntosh, R.P. (1967) An index of diversity and the relation of certain conepts to diversity. Ecology, 48, 392–404.

Pielou, E.C. (1975) Ecological diversity. New York: Wiley InterScience.

Shannon, C.E. (1948) A mathematical theory of communication. Bell System technical journal, 27, 379–423, 623–656.

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

Smith, B. and Wilson, J.B. (1996) A consumer's guide to evenness measures. Oikos, 76, 70–82.

### Examples

```data(batcomm)
ab <- batcomm\$ab
specieseve(ab)
```