specpool: Extrapolated Species Richness in a Species Pool
In pattakosn/Rworkshop: Community Ecology Package

Description Usage Arguments Details Value Note Author(s) References See Also Examples

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.

specpool(x, pool)
estimateR(x, ...)
specpool2vect(X, index = c("jack1","jack2", "chao", "boot","Species"))
poolaccum(x, permutations = 100, minsize = 3)
estaccumR(x, permutations = 100)
## S3 method for class 'poolaccum'
summary(object, display, alpha = 0.05, ...)
## S3 method for class 'poolaccum'
plot(x, alpha = 0.05, type = c("l","g"), ...)

`x`	Data frame or matrix with species data or the analysis result for `plot` function.
`pool`	A vector giving a classification for pooling the sites in the species data. If missing, all sites are pooled together.
`X, object`	A `specpool` result object.
`index`	The selected index of extrapolated richness.
`permutations`	Number of permutations of sampling order of sites.
`minsize`	Smallest number of sampling units reported.
`display`	Indices to be displayed.
`alpha`	Level of quantiles shown. This proportion will be left outside symmetric limits.
`type`	Type of graph produced in `xyplot`.
`...`	Other parameters (not used).

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/(2a2)*
First order jackknife	S_P = S_0 + a1(N-1)/N*
Second order jackknife	S_P = S_0 + a1(2n-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 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).

Functions poolaccum and estaccumR are similar to specaccum, but estimate extrapolated richness indices of specpool or estimateR in addition to number of species for random ordering of sampling units. Function specpool uses presence data and estaccumR count data. The functions share summary and plot methods. The summary returns quantile envelopes of permutations corresponding the given level of alpha and standard deviation of permutations for each sample size. The plot function shows the mean and envelope of permutations with given alpha for models. The selection of models can be restricted and order changes using the display argument in summary or plot. For configuration of plot command, see xyplot

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. Functions poolaccum and estimateR return matrices of permutation results for each richness estimator, the vector of sample sizes and a table of means of permutations for each estimator.

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.

Bob O'Hara (estimateR) and Jari Oksanen.

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.

veiledspec, diversity, beals, specaccum.

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)
## Accumulation model
pool <- poolaccum(BCI)
summary(pool, display = "chao")
plot(pool)
## Quantitative model
estimateR(BCI[1:5,])