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) 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).
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)