specpool {vegan} | R Documentation

## 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).

### 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, a1 and a2 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:

Chao | S_P = S_0 + a1^2/(2*a2)
First order jackknife | S_P = S_0 + a1*(N-1)/N
Second order jackknife | S_P = S_0 + a1*(2*n-3)/n - a2*(n-2)^2/n/(n-1)
Bootstrap | S_P = S_0 + Sum (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 (unbiased variant) and ACE. In the Chao estimate a_i refers to number of species with abundance i instead of incidence:

Chao | S_P = S_0 + a1*(a1-1)/(2*(a2+1))
ACE | S_P = S_abund + S_rare/C_ace + a1/C_ace * gamma^2
where | C_{ace} = 1- a1/N_{rare}
| gamma^2 = max( S_rare/C_ace (sum[i=1..10] i*(i-1)*a_i) / N_rare/(N_rare-1) -1 , 0)

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 R source 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).

### 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.

### Note

The functions are based on assumption that there is a species pool: The community is closed so that there is a fixed pool size S_P. Such cases may exist, although I have not seen them yet. All indices are biased for open communities.

See http://viceroy.eeb.uconn.edu/EstimateS for a more complete (and positive) discussion and alternative software for some platforms.

### Author(s)

Bob O'Hara (`estimateR`) and Jari Oksanen (`specpool`).

### 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,])

[Package vegan version 1.8-8 Index]