# diversity: Ecological Diversity Indices In vegan: Community Ecology Package

## Description

Shannon, Simpson, and Fisher diversity indices and species richness.

## Usage

 ```1 2 3``` ```diversity(x, index = "shannon", MARGIN = 1, base = exp(1)) fisher.alpha(x, MARGIN = 1, ...) specnumber(x, groups, MARGIN = 1) ```

## Arguments

 `x` Community data, a matrix-like object or a vector. `index` Diversity index, one of `"shannon"`, `"simpson"` or `"invsimpson"`. `MARGIN` Margin for which the index is computed. `base` The logarithm `base` used in `shannon`. `groups` A grouping factor: if given, finds the total number of species in each group. `...` Parameters passed to the function.

## Details

Shannon or Shannon–Weaver (or Shannon–Wiener) index is defined as H = -sum p_i log(b) p_i, where p_i is the proportional abundance of species i and b is the base of the logarithm. It is most popular to use natural logarithms, but some argue for base b = 2 (which makes sense, but no real difference).

Both variants of Simpson's index are based on D = sum p_i^2. Choice `simpson` returns 1-D and `invsimpson` returns 1/D.

`fisher.alpha` estimates the α parameter of Fisher's logarithmic series (see `fisherfit`). The estimation is possible only for genuine counts of individuals.

Function `specnumber` finds the number of species. With `MARGIN = 2`, it finds frequencies of species. If `groups` is given, finds the total number of species in each group (see example on finding one kind of beta diversity with this option).

Better stories can be told about Simpson's index than about Shannon's index, and still grander narratives about rarefaction (Hurlbert 1971). However, these indices are all very closely related (Hill 1973), and there is no reason to despise one more than others (but if you are a graduate student, don't drag me in, but obey your Professor's orders). In particular, the exponent of the Shannon index is linearly related to inverse Simpson (Hill 1973) although the former may be more sensitive to rare species. Moreover, inverse Simpson is asymptotically equal to rarefied species richness in sample of two individuals, and Fisher's α is very similar to inverse Simpson.

## Value

A vector of diversity indices or numbers of species.

## Author(s)

Jari Oksanen and Bob O'Hara (`fisher.alpha`).

## References

Fisher, R.A., Corbet, A.S. & Williams, C.B. (1943). The relation between the number of species and the number of individuals in a random sample of animal population. Journal of Animal Ecology 12, 42–58.

Hurlbert, S.H. (1971). The nonconcept of species diversity: a critique and alternative parameters. Ecology 52, 577–586.

These functions calculate only some basic indices, but many others can be derived with them (see Examples). Facilities related to diversity are discussed in a vegan vignette that can be read with `browseVignettes("vegan")`. Functions `renyi` and `tsallis` estimate a series of generalized diversity indices. Function `rarefy` finds estimated number of species for given sample size. Beta diversity can be estimated with `betadiver`. Diversities can be partitioned with `adipart` and `multipart`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```data(BCI) H <- diversity(BCI) simp <- diversity(BCI, "simpson") invsimp <- diversity(BCI, "inv") ## Unbiased Simpson (Hurlbert 1971, eq. 5) with rarefy: unbias.simp <- rarefy(BCI, 2) - 1 ## Fisher alpha alpha <- fisher.alpha(BCI) ## Plot all pairs(cbind(H, simp, invsimp, unbias.simp, alpha), pch="+", col="blue") ## Species richness (S) and Pielou's evenness (J): S <- specnumber(BCI) ## rowSums(BCI > 0) does the same... J <- H/log(S) ## beta diversity defined as gamma/alpha - 1: data(dune) data(dune.env) alpha <- with(dune.env, tapply(specnumber(dune), Management, mean)) gamma <- with(dune.env, specnumber(dune, Management)) gamma/alpha - 1 ```

### Example output ```Loading required package: permute