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.
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"), ...)

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). 
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
.
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 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.
Bob O'Hara (estimateR
) and Jari Oksanen.
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.
veiledspec
, diversity
, beals
,
specaccum
.
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,])

Loading required package: permute
Loading required package: lattice
This is vegan 2.44
Species chao chao.se jack1 jack1.se jack2 boot boot.se n
BF 16 17.19048 1.5895675 19.33333 2.211083 19.83333 17.74074 1.646379 3
HF 21 21.51429 0.9511693 23.40000 1.876166 22.05000 22.56864 1.821518 5
NM 21 22.87500 2.1582871 26.00000 3.291403 25.73333 23.77696 2.300982 6
SF 21 29.88889 8.6447967 27.66667 3.496029 31.40000 23.99496 1.850288 6
Warning message:
In bxp(list(stats = c(9, 9.5, 10, 11, 12, 11, 12, 13, 13, 14, 7, :
some notches went outside hinges ('box'): maybe set notch=FALSE
Warning message:
In bxp(list(stats = c(0.46551724137931, 0.491379310344828, 0.517241379310345, :
some notches went outside hinges ('box'): maybe set notch=FALSE
$chao
N Chao 2.5% 97.5% Std.Dev
[1,] 3 160.9476 142.0383 182.0807 11.270752
[2,] 4 173.5997 155.0614 202.1125 13.016805
[3,] 5 182.3512 164.8505 208.4667 11.409904
[4,] 6 188.3330 169.3107 211.0327 10.063760
[5,] 7 192.8775 175.3101 215.0049 10.345351
[6,] 8 197.7657 180.7702 220.0356 11.606898
[7,] 9 202.0651 184.7691 225.2545 11.598800
[8,] 10 203.3710 187.1018 227.0786 10.966502
[9,] 11 206.0874 186.7094 233.1239 11.528109
[10,] 12 208.6004 188.7337 231.6850 11.420835
[11,] 13 210.7562 192.0813 236.3161 11.861617
[12,] 14 213.8876 195.3327 245.4074 12.298981
[13,] 15 215.7278 198.3186 239.6563 11.504247
[14,] 16 218.4506 199.4048 248.1400 12.265903
[15,] 17 221.0832 201.5884 254.7577 13.824780
[16,] 18 222.9217 201.9699 256.3023 14.334215
[17,] 19 225.1057 204.9474 256.0500 14.449905
[18,] 20 226.9952 208.2056 265.5257 15.119429
[19,] 21 227.6770 207.9935 261.8546 14.309450
[20,] 22 228.1346 208.2300 265.9113 13.971391
[21,] 23 230.1290 209.9850 266.3476 13.917138
[22,] 24 231.3234 213.8082 262.0459 13.396352
[23,] 25 232.1365 213.4903 259.8252 12.905823
[24,] 26 232.8493 214.1666 264.2261 12.825957
[25,] 27 234.1063 217.1782 271.1798 13.596850
[26,] 28 234.7637 217.8379 267.7316 13.211930
[27,] 29 234.8600 218.1544 264.6304 12.116936
[28,] 30 235.1382 218.2368 260.7124 11.772531
[29,] 31 235.3100 220.6380 256.7887 10.369256
[30,] 32 235.3122 219.0983 256.0958 10.273185
[31,] 33 236.4081 221.9618 257.5468 10.528231
[32,] 34 237.0107 223.0025 253.8334 9.460398
[33,] 35 236.8786 222.2530 253.4946 9.262633
[34,] 36 236.6233 223.0696 254.2793 8.496782
[35,] 37 236.0124 223.9263 251.8931 8.121713
[36,] 38 236.1250 223.4082 252.0643 7.908177
[37,] 39 236.5839 224.1061 250.7979 7.249351
[38,] 40 237.0263 224.9062 250.3125 6.911123
[39,] 41 237.0698 225.6535 250.3881 6.799898
[40,] 42 236.9790 226.3669 249.2162 6.261920
[41,] 43 237.2999 228.3545 249.7360 5.873442
[42,] 44 236.7386 227.0561 248.7453 5.385509
[43,] 45 237.0167 227.7468 250.5073 5.304374
[44,] 46 236.9397 228.3009 248.5687 4.997460
[45,] 47 237.0969 229.4334 249.1601 4.777494
[46,] 48 236.8836 232.0803 249.3689 3.883288
[47,] 49 236.7236 233.3115 240.2413 2.406077
[48,] 50 236.3732 236.3732 236.3732 0.000000
attr(,"class")
[1] "summary.poolaccum"
1 2 3 4 5
S.obs 93.000000 84.000000 90.000000 94.000000 101.000000
S.chao1 117.473684 117.214286 141.230769 111.550000 136.000000
se.chao1 11.583785 15.918953 23.001405 8.919663 15.467344
S.ACE 122.848959 117.317307 134.669844 118.729941 137.114088
se.ACE 5.736054 5.571998 6.191618 5.367571 5.848474
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