diversity {vegan} | R Documentation |

Shannon, Simpson, and Fisher diversity indices and rarefied species richness for community ecologists.

diversity(x, index = "shannon", MARGIN = 1, base = exp(1)) rarefy(x, sample, se = FALSE, MARGIN = 1) rrarefy(x, sample) fisher.alpha(x, MARGIN = 1, se = FALSE, ...) specnumber(x, MARGIN = 1)

`x` |
Community data, a matrix-like object. |

`index` |
Diversity index, one of `"shannon"` ,
`"simpson"` or `"invsimpson"` . |

`MARGIN` |
Margin for which the index is computed. |

`base` |
The logarithm `base` used in `shannon` . |

`sample` |
Subsample size for rarefying community, either a single value or a vector. |

`se` |
Estimate standard errors. |

`...` |
Parameters passed to `nlm` |

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*.

Function `rarefy`

gives the expected species richness in random
subsamples of size `sample`

from the community. The size of
`sample`

should be smaller than total community size, but the
function will silently work for larger `sample`

as well and
return non-rarefied species richness (and standard error = 0). If
`sample`

is a vector, rarefaction is performed for each sample
size separately.
Rarefaction can be performed only with genuine counts of individuals.
The function `rarefy`

is based on Hurlbert's (1971) formulation,
and the standard errors on Heck et al. (1975).

Function `rrarefy`

generates one randomly rarefied community data
frame or vector of given `sample`

size. The `sample`

can be
a vector, and its values must be less or equal to observed number of
individuals. The random rarefaction is made without replacement so
that the variance of rarefied communities is rather related to
rarefaction proportion than to to the size of the `sample`

.

`fisher.alpha`

estimates the *α* parameter of
Fisher's logarithmic series (see `fisherfit`

).
The estimation is possible only for genuine
counts of individuals. The function can optionally return standard
errors of *α*. These should be regarded only as rough
indicators of the accuracy: the confidence limits of *α* are
strongly non-symmetric and the standard errors cannot be used in
Normal inference.

Function `specnumber`

finds the number of species. With
`MARGIN = 2`

, it finds frequencies of species. The function is
extremely simple, and shortcuts are easy in plain **R**.

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.

A vector of diversity indices or rarefied species richness values. With
a single `sample`

and `se = TRUE`

, function `rarefy`

returns a 2-row matrix
with rarefied richness (`S`

) and its standard error
(`se`

). If `sample`

is a vector in `rarefy`

, the
function returns a matrix with a column for each `sample`

size,
and if `se = TRUE`

, rarefied richness and its standard error are
on consecutive lines.
With option `se = TRUE`

, function `fisher.alpha`

returns a
data frame with items for *α* (`alpha`

), its approximate
standard errors (`se`

), residual degrees of freedom
(`df.residual`

), and the `code`

returned by
`nlm`

on the success of estimation.

Jari Oksanen and Bob O'Hara bob.ohara@helsinki.fi
(`fisher.alpha`

).

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.

Heck, K.L., van Belle, G. & Simberloff, D. (1975). Explicit
calculation of the rarefaction diversity measurement and the
determination of sufficient sample size. *Ecology* **56**,
1459–1461.

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

Function `renyi`

for generalized Rényi
diversity and Hill numbers.

data(BCI) H <- diversity(BCI) simp <- diversity(BCI, "simpson") invsimp <- diversity(BCI, "inv") r.2 <- rarefy(BCI, 2) alpha <- fisher.alpha(BCI) pairs(cbind(H, simp, invsimp, r.2, 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)

[Package *vegan* version 1.16-32 Index]