diversity {vegan}R Documentation

Ecological Diversity Indices and Rarefaction Species Richness


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.

See Also

Function renyi for generalized Rényi diversity and Hill numbers.


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]