specpool: Extrapolated Species Richness in a Species Pool

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

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

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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 plot function.

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 pool.

X, object

A specpool result object.

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 how, or a permutation matrix where each row gives the permuted indices.

minsize

Smallest number of sampling units reported.

parallel

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.

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).

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 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.

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 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.

Author(s)

Bob O'Hara (estimateR) and Jari Oksanen.

References

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.

See Also

veiledspec, diversity, beals, specaccum.

Examples

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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,])

Example output

Loading required package: permute
Loading required package: lattice
This is vegan 2.5-3
   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
$chao
       N     Chao     2.5%    97.5%   Std.Dev
 [1,]  3 162.7241 142.5322 183.6736 11.651118
 [2,]  4 176.2009 156.1655 199.9116 11.587640
 [3,]  5 184.1692 165.1728 204.3974 10.572525
 [4,]  6 189.9015 170.6893 207.6844 10.679309
 [5,]  7 195.3128 176.7054 222.5317 12.153506
 [6,]  8 199.1173 179.3531 232.5146 12.334124
 [7,]  9 202.6525 185.4892 230.5816 11.900323
 [8,] 10 206.4116 188.0714 238.0211 13.627590
 [9,] 11 208.9733 189.2598 239.5983 12.941334
[10,] 12 211.5900 192.9008 234.9307 12.008859
[11,] 13 213.7654 196.2798 243.1699 11.801855
[12,] 14 215.2463 197.0846 236.3511 10.902035
[13,] 15 217.7370 199.4119 242.0829 11.034536
[14,] 16 219.3586 201.2357 249.5701 11.554454
[15,] 17 221.4246 203.8008 251.7525 12.297785
[16,] 18 223.0332 205.3705 249.7936 11.754250
[17,] 19 224.5470 203.7904 255.6319 12.276005
[18,] 20 226.8565 205.6520 256.8238 13.129754
[19,] 21 228.2457 209.3398 259.3378 12.998032
[20,] 22 228.8011 210.8672 251.4756 12.460021
[21,] 23 229.2964 211.2156 249.8291 11.554114
[22,] 24 230.4333 213.4491 249.5708 11.036627
[23,] 25 230.8785 213.9983 253.9430 11.573105
[24,] 26 231.2109 215.2054 255.1335 10.870283
[25,] 27 232.0514 217.0037 257.0534 10.830343
[26,] 28 232.9604 217.9487 256.9853 11.172310
[27,] 29 233.6913 218.1718 257.1372 11.018775
[28,] 30 234.4244 219.6731 261.0495 10.479159
[29,] 31 235.6404 219.7073 259.1641 10.568832
[30,] 32 235.8722 219.7743 258.3233  9.902565
[31,] 33 236.2183 219.7780 255.1799 10.001019
[32,] 34 235.9722 220.1973 253.2699  9.118676
[33,] 35 236.5980 221.1694 255.1560  9.459715
[34,] 36 236.3611 221.2374 254.6526  9.219195
[35,] 37 236.7252 222.3488 252.5011  9.014863
[36,] 38 237.1404 222.4974 255.7030  9.083415
[37,] 39 237.6652 224.0517 256.8970  9.323587
[38,] 40 237.5839 225.1164 257.3015  8.582248
[39,] 41 237.0829 225.0503 259.0916  8.215869
[40,] 42 236.9058 226.0312 252.9061  6.905528
[41,] 43 236.5191 226.5947 251.3228  6.561439
[42,] 44 236.7838 227.5307 249.0585  5.783453
[43,] 45 236.3387 227.4650 247.6280  4.901946
[44,] 46 236.2438 228.4386 250.4983  5.003033
[45,] 47 236.1155 229.9739 246.7012  3.962238
[46,] 48 236.1785 229.9633 243.6493  3.223082
[47,] 49 236.2047 233.3115 240.2413  2.195275
[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

vegan documentation built on Jan. 8, 2021, 2:12 a.m.