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, smallsample = TRUE)
estimateR(x, ...)
specpool2vect(X, index = c("jack1","jack2", "chao", "boot","Species"))
poolaccum(x, permutations = 100, minsize = 3)
estaccumR(x, permutations = 100, parallel = getOption("mc.cores"))
# S3 method for poolaccum
summary(object, display, alpha = 0.05, ...)
# S3 method for poolaccum
plot(x, alpha = 0.05, type = c("l","g"), ...)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.
Data frame or matrix with species data or the analysis result
for plot function.
A vector giving a classification for pooling the sites in the species data. If missing, all sites are pooled together.
Use small sample correction \((N-1)/N\), where
\(N\) is the number of sites within the pool.
A specpool result object.
The selected index of extrapolated richness.
Usually an integer giving the number
permutations, but can also be a list of control values for the
permutations as returned by the function how,
or a permutation matrix where each row gives the permuted indices.
Smallest number of sampling units reported.
Number of parallel processes or a predefined socket
cluster. With parallel = 1 uses ordinary, non-parallel
processing. The parallel processing is done with parallel
package.
Indices to be displayed.
Level of quantiles shown. This proportion will be left outside symmetric limits.
Type of graph produced in xyplot.
Other parameters (not used).
Bob O'Hara (estimateR) and Jari Oksanen.
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:
| Chao | \(S_P = S_0 + \frac{a_1^2}{2 a_2}\frac{N-1}{N}\) |
| Chao bias-corrected | \(S_P = S_0 + \frac{a_1(a_1-1)}{2(a_2+1)} \frac{N-1}{N}\) |
| 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 | \(S_P = S_0 + \sum_{i=1}^{S_0} (1 - p_i)^N\) |
specpool normally uses basic Chao equation, but when there
are no doubletons (\(a2=0\)) it switches to bias-corrected
version. In that case the Chao equation simplifies to
\(S_0 + \frac{1}{2} a_1 (a_1-1) \frac{N-1}{N}\).
The abundance-based estimates in estimateR use counts
(numbers of individuals) 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 bias-corrected Chao and ACE (O'Hara 2005, Chiu
et al. 2014). The Chao estimate is similar as the bias corrected
one above, but \(a_i\) refers to the number of species with
abundance \(i\) instead of number of sites, and the small-sample
correction is not used. The ACE estimate is defined as:
| 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 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 and are discussed
in the vignette that can be read with the
browseVignettes("vegan"). The standard error are based on the
following sources: Chiu et al. (2014) for the Chao estimates and
Smith and van Belle (1984) for the first-order Jackknife and the
bootstrap (second-order jackknife is still missing). For the
variance estimator of \(S_{ace}\) see O'Hara (2005).
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. NB., these
are not based on standard deviations estimated within specpool
or estimateR, but they are based on permutations. 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.
Chao, A. (1987). Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43, 783--791.
Chiu, C.H., Wang, Y.T., Walther, B.A. & Chao, A. (2014). Improved nonparametric lower bound of species richness via a modified Good-Turing frequency formula. Biometrics 70, 671--682.
Colwell, R.K. & Coddington, J.A. (1994). Estimating terrestrial biodiversity through extrapolation. Phil. Trans. Roy. Soc. London B 345, 101--118.
O'Hara, R.B. (2005). Species richness estimators: how many species can dance on the head of a pin? J. Anim. Ecol. 74, 375--386.
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)
pool <- with(dune.env, specpool(dune, Management))
pool
op <- par(mfrow=c(1,2))
boxplot(specnumber(dune) ~ Management, data = dune.env,
col = "hotpink", border = "cyan3")
boxplot(specnumber(dune)/specpool2vect(pool) ~ Management,
data = dune.env, col = "hotpink", border = "cyan3")
par(op)
data(BCI)
## Accumulation model
pool <- poolaccum(BCI)
summary(pool, display = "chao")
plot(pool)
## Quantitative model
estimateR(BCI[1:5,])
Run the code above in your browser using DataLab