Extrapolated Species Richness in a Species Pool
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 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 |
pool |
A vector giving a classification for pooling the sites in the species data. If missing, all sites are pooled together. |
smallsample |
Use small sample correction (N-1)/N, where
N is the number of sites within the |
X, object |
A |
index |
The selected index of extrapolated richness. |
permutations |
Usually an integer giving the number
permutations, but can also be a list of control values for the
permutations as returned by the function |
minsize |
Smallest number of sampling units reported. |
parallel |
Number of parallel processes or a predefined socket
cluster. With |
display |
Indices to be displayed. |
alpha |
Level of quantiles shown. This proportion will be left outside symmetric limits. |
type |
Type of graph produced in |
... |
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/(2*a2) * (N-1)/N |
| Chao bias-corrected | S_P = S_0 + a1*(a1-1)/(2*(a2+1)) * (N-1)/N |
| 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 |
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 + (N-1)/N * a1*(a1-1)/2.
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 + 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 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.
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. In general, the functions give only the lower limit of species richness: the real richness is S >= S_P, and there is a consistent bias in the estimates. Even the bias-correction in Chao only reduces the bias, but does not remove it completely (Chiu et al. 2014).
Optional small sample correction was added to specpool in
vegan 2.2-0. It was not used in the older literature (Chao
1987), but it is recommended recently (Chiu et al. 2014).
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.
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.
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,])Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.