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)
"shannon",
"simpson" or "invsimpson".base used in shannon.nlmsample 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 $\alpha$ (alpha), its approximate
standard errors (se), residual degrees of freedom
(df.residual), and the code returned by
nlm on the success of estimation. 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 $\alpha$ 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 $\alpha$. These should be regarded only as rough
indicators of the accuracy: the confidence limits of $\alpha$ 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 $\alpha$ is very
similar to inverse Simpson.
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.
renyi for generalized data(BCI)
H <- diversity(BCI)
simp <- diversity(BCI, "simpson")
invsimp <- diversity(BCI, "inv")
## Unbiased Simpson of Hurlbert 1971 (eq. 5):
unbias.simp <- rarefy(BCI, 2) - 1
alpha <- fisher.alpha(BCI)
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)Run the code above in your browser using DataLab