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
1 2 3 4 5 6 7 8 9  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"), ...)

Arguments
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 (N1)/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). 
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 incidencebased 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) * (N1)/N 
Chao biascorrected  S_P = S_0 + a1*(a11)/(2*(a2+1)) * (N1)/N 
First order jackknife  S_P = S_0 + a1*(N1)/N 
Second order jackknife  S_P = S_0 + a1*(2*N3)/N  a2*(N2)^2/N/(N1) 
Bootstrap  S_P = S_0 + Sum (1p_i)^N 
specpool
normally uses basic Chao equation, but when there
are no doubletons (a2=0) it switches to biascorrected
version. In that case the Chao equation simplifies to
S_0 + (N1)/N * a1*(a11)/2.
The abundancebased 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 biascorrected 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 smallsample
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*(i1)*a_i) / N_rare/(N_rare1) 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 firstorder Jackknife and the
bootstrap (secondorder 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
.
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. 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.
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. 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 biascorrection 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 2.20. 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.
Author(s)
Bob O'Hara (estimateR
) and Jari Oksanen.
References
Chao, A. (1987). Estimating the population size for capturerecapture 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 GoodTuring 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.
See Also
veiledspec
, diversity
, beals
,
specaccum
.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  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,])

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