vegan (version 1.8-1)

specpool: Extrapolated Species Richness in a Species Pool

Description

The functions estimate the extrapolated species richness in a species pool, or the number of unobserved species. Function specpool is based on incidences in sample sites, and gives a single estimate for a collection of sample sites (matrix). Function estimateR is based on abundances (counts) on single sample site.

Usage

specpool(x, pool)
specpool2vect(X, index = c("Jack.1","Jack.2", "Chao", "Boot","Species"))
estimateR(x, ...)

Arguments

x

Data frame or matrix with species data.

pool

A vector giving a classification for pooling the sites in the species data. If missing, all sites are pooled together.

X

A specpool result object.

index

The selected index of extrapolated richness.

...

Other parameters (not used).

Value

• Function specpool returns a data frame with entries for observed richness and each of the indices for each class in pool vector. The utility function specpool2vect maps the pooled values into a vector giving the value of selected index for each original site. Function estimateR returns the estimates and their standard errors for each site.

Details

Many species will always remain unseen or undetected in a collection of sample plots. The function uses some popular ways of estimating the number of these unseen species and adding them to the observed species richness (Palmer 1990, Colwell & Coddington 1994).

The incidence-based estimates in specpool use the frequencies of species in a collection of sites. In the following, $S_P$ is the extrapolated richness in a pool, $S_0$ is the observed number of species in the collection, $a_1$ and $a_2$ are the number of species occurring only in one or only in two sites in the collection, $p_i$ is the frequency of species $i$, and $N$ is the number of sites in the collection. The variants of extrapolated richness in specpool are: ll{ Chao $S_P = S_0 + a1^2/(2*a2)$ First order jackknife $S_P = S_0 + a_1 \frac{N-1}{N}$ Second order jackknife $S_P = S_0 + a_1 \frac{2N - 3}{N} - a_2 \frac{(N-2)^2}{N (N-1)}$ Bootstrap $S_P = S_0 + \sum_{i=1}^{S_0} (1 - p_i)^N$ }

The abundance-based estimates in estimateR use counts (frequencies) of species in a single site. If called for a matrix or data frame, the function will give separate estimates for each site. The two variants of extrapolated richness in estimateR are Chao and ACE. In the Chao estimate $a_i$ refers to number of species with abundance $i$ instead of incidence: ll{ Chao $S_P = S_0 + \frac{a_1^2}{ (a_2 + 1)} + \frac{a_1 a_2}{2(a_2+1)^2}$ ACE $S_P = S_{abund} + \frac{S_{rare}}{C_{ace}}+ \frac{a_1}{C_{ace}} \gamma^2_{ace}$ where $C_{ace} = 1 - \frac{a_1}{N_{rare}}$ $\gamma^2_{ace} = \max \left[ \frac{S_{rare} \sum_{i=1}^{10} i(i-1)a_i}{C_{ace} N_{rare} (N_{rare} - 1)}-1, 0 \right]$ } Here $a_i$ refers to number of species with abundance $i$ and $S_{rare}$ is the number of rare species, $S_{abund}$ is the number of abundant species, with an arbitrary threshold of abundance 10 for rare species, and $N_{rare}$ is the number of individuals in rare species.

Functions estimate the the standard errors of the estimates. These only concern the number of added species, and assume that there is no variance in the observed richness. The equations of standard errors are too complicated to be reproduced in this help page, but they can be studied in the Rsource code of the function. The standard error are based on the following sources: Chao (1987) for the Chao estimate and Smith and van Belle (1984) for the first-order Jackknife and the bootstrap (second-order jackknife is still missing). The variance estimator of $S_{ace}$ was developed by Bob O'Hara (unpublished).

References

Chao, A. (1987). Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43, 783--791. Colwell, R.K. & Coddington, J.A. (1994). Estimating terrestrial biodiversity through extrapolation. Phil. Trans. Roy. Soc. London B 345, 101--118.

Palmer, M.W. (1990). The estimation of species richness by extrapolation. Ecology 71, 1195--1198.

Smith, E.P & van Belle, G. (1984). Nonparametric estimation of species richness. Biometrics 40, 119--129.

See Also

veiledspec, diversity, beals.

Examples

data(dune)
data(dune.env)
attach(dune.env)
pool <- specpool(dune, Management)
pool
op <- par(mfrow=c(1,2))
boxplot(specnumber(dune) ~ Management, col="hotpink", border="cyan3",
 notch=TRUE)
boxplot(specnumber(dune)/specpool2vect(pool) ~ Management, col="hotpink",
 border="cyan3", notch=TRUE)
par(op)
data(BCI)
estimateR(BCI[1:5,])