specaccum: Species Accumulation Curves

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

Description

Function specaccum finds species accumulation curves or the number of species for a certain number of sampled sites or individuals.

Usage

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specaccum(comm, method = "exact", permutations = 100,
          conditioned =TRUE, gamma = "jack1",  w = NULL, subset, ...)
## S3 method for class 'specaccum'
plot(x, add = FALSE, random = FALSE, ci = 2, 
    ci.type = c("bar", "line", "polygon"), col = par("fg"), ci.col = col, 
    ci.lty = 1, xlab, ylab = x$method, ylim, 
    xvar = c("sites", "individuals", "effort"), ...)
## S3 method for class 'specaccum'
boxplot(x, add = FALSE, ...)
fitspecaccum(object, model, method = "random", ...)
## S3 method for class 'fitspecaccum'
plot(x, col = par("fg"), lty = 1, xlab = "Sites", 
    ylab = x$method, ...) 
## S3 method for class 'specaccum'
predict(object, newdata, interpolation = c("linear", "spline"), ...)
## S3 method for class 'fitspecaccum'
predict(object, newdata, ...)
specslope(object, at)

Arguments

comm

Community data set.

method

Species accumulation method (partial match). Method "collector" adds sites in the order they happen to be in the data, "random" adds sites in random order, "exact" finds the expected (mean) species richness, "coleman" finds the expected richness following Coleman et al. 1982, and "rarefaction" finds the mean when accumulating individuals instead of sites.

permutations

Number of permutations with method = "random". 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.

conditioned

Estimation of standard deviation is conditional on the empirical dataset for the exact SAC

gamma

Method for estimating the total extrapolated number of species in the survey area by function specpool

w

Weights giving the sampling effort.

subset

logical expression indicating sites (rows) to keep: missing values are taken as FALSE.

x

A specaccum result object

add

Add to an existing graph.

random

Draw each random simulation separately instead of drawing their average and confidence intervals.

ci

Multiplier used to get confidence intervals from standard deviation (standard error of the estimate). Value ci = 0 suppresses drawing confidence intervals.

ci.type

Type of confidence intervals in the graph: "bar" draws vertical bars, "line" draws lines, and "polygon" draws a shaded area.

col

Colour for drawing lines.

ci.col

Colour for drawing lines or filling the "polygon".

ci.lty

Line type for confidence intervals or border of the "polygon".

xlab,ylab

Labels for x (defaults xvar) and y axis.

ylim

the y limits of the plot.

xvar

Variable used for the horizontal axis: "individuals" can be used only with method = "rarefaction".

object

Either a community data set or fitted specaccum model.

model

Nonlinear regression model (nls). See Details.

lty

line type code (see par.

newdata

Optional data used in prediction interpreted as number of sampling units (sites). If missing, fitted values are returned.

interpolation

Interpolation method used with newdata.

at

Number of plots where the slope is evaluated. Can be a real number.

...

Other parameters to functions.

Details

Species accumulation curves (SAC) are used to compare diversity properties of community data sets using different accumulator functions. The classic method is "random" which finds the mean SAC and its standard deviation from random permutations of the data, or subsampling without replacement (Gotelli & Colwell 2001). The "exact" method finds the expected SAC using sample-based rarefaction method that has been independently developed numerous times (Chiarucci et al. 2008) and it is often known as Mao Tau estimate (Colwell et al. 2012). The unconditional standard deviation for the exact SAC represents a moment-based estimation that is not conditioned on the empirical data set (sd for all samples > 0). The unconditional standard deviation is based on an estimation of the extrapolated number of species in the survey area (a.k.a. gamma diversity), as estimated by function specpool. The conditional standard deviation that was developed by Jari Oksanen (not published, sd=0 for all samples). Method "coleman" finds the expected SAC and its standard deviation following Coleman et al. (1982). All these methods are based on sampling sites without replacement. In contrast, the method = "rarefaction" finds the expected species richness and its standard deviation by sampling individuals instead of sites. It achieves this by applying function rarefy with number of individuals corresponding to average number of individuals per site.

Methods "random" and "collector" can take weights (w) that give the sampling effort for each site. The weights w do not influence the order the sites are accumulated, but only the value of the sampling effort so that not all sites are equal. The summary results are expressed against sites even when the accumulation uses weights (methods "random", "collector"), or is based on individuals ("rarefaction"). The actual sampling effort is given as item Effort or Individuals in the printed result. For weighted "random" method the effort refers to the average effort per site, or sum of weights per number of sites. With weighted method = "random", the averaged species richness is found from linear interpolation of single random permutations. Therefore at least the first value (and often several first) have NA richness, because these values cannot be interpolated in all cases but should be extrapolated. The plot function defaults to display the results as scaled to sites, but this can be changed selecting xvar = "effort" (weighted methods) or xvar = "individuals" (with method = "rarefaction").

The summary and boxplot methods are available for method = "random".

Function predict for specaccum can return the values corresponding to newdata. With method "exact", "rarefaction" and "coleman" the function uses analytic equations for interpolated non-integer values, and for other methods linear (approx) or spline (spline) interpolation. If newdata is not given, the function returns the values corresponding to the data. NB., the fitted values with method="rarefaction" are based on rounded integer counts, but predict can use fractional non-integer counts with newdata and give slightly different results.

Function fitspecaccum fits a nonlinear (nls) self-starting species accumulation model. The input object can be a result of specaccum or a community in data frame. In the latter case the function first fits a specaccum model and then proceeds with fitting the a nonlinear model. The function can apply a limited set of nonlinear regression models suggested for species-area relationship (Dengler 2009). All these are selfStart models. The permissible alternatives are "arrhenius" (SSarrhenius), "gleason" (SSgleason), "gitay" (SSgitay), "lomolino" (SSlomolino) of vegan package. In addition the following standard R models are available: "asymp" (SSasymp), "gompertz" (SSgompertz), "michaelis-menten") (SSmicmen), "logis" (SSlogis), "weibull" (SSweibull). See these functions for model specification and details.

When weights w were used the fit is based on accumulated effort and in model = "rarefaction" on accumulated number of individuals. The plot is still based on sites, unless other alternative is selected with xvar.

Function predict for fitspecaccum uses predict.nls, and you can pass all arguments to that function. In addition, fitted, residuals and coef, AIC and deviance work on the result object.

Function specslope evaluates the derivative of the species accumulation curve at given number of sample plots, and gives the rate of increase in the number of species. The function works with specaccum result object when this is based on analytic models "exact", "rarefaction" or "coleman", and with non-linear regression results of fitspecaccum.

Nonlinear regression may fail for any reason, and some of the fitspecaccum models are fragile and may not succeed.

Value

Function specaccum returns an object of class "specaccum", and fitspecaccum a model of class "fitspecaccum" that adds a few items to the "specaccum" (see the end of the list below):

call

Function call.

method

Accumulator method.

sites

Number of sites. For method = "rarefaction" this is the number of sites corresponding to a certain number of individuals and generally not an integer, and the average number of individuals is also returned in item individuals.

effort

Average sum of weights corresponding to the number of sites when model was fitted with argument w

richness

The number of species corresponding to number of sites. With method = "collector" this is the observed richness, for other methods the average or expected richness.

sd

The standard deviation of SAC (or its standard error). This is NULL in method = "collector", and it is estimated from permutations in method = "random", and from analytic equations in other methods.

perm

Permutation results with method = "random" and NULL in other cases. Each column in perm holds one permutation.

weights

Matrix of accumulated weights corresponding to the columns of the perm matrix when model was fitted with argument w.

fitted, residuals, coefficients

Only in fitspecacum: fitted values, residuals and nonlinear model coefficients. For method = "random" these are matrices with a column for each random accumulation.

models

Only in fitspecaccum: list of fitted nls models (see Examples on accessing these models).

Note

The SAC with method = "exact" was developed by Roeland Kindt, and its standard deviation by Jari Oksanen (both are unpublished). The method = "coleman" underestimates the SAC because it does not handle properly sampling without replacement. Further, its standard deviation does not take into account species correlations, and is generally too low.

Author(s)

Roeland Kindt r.kindt@cgiar.org and Jari Oksanen.

References

Chiarucci, A., Bacaro, G., Rocchini, D. & Fattorini, L. (2008). Discovering and rediscovering the sample-based rarefaction formula in the ecological literature. Commun. Ecol. 9: 121–123.

Coleman, B.D, Mares, M.A., Willis, M.R. & Hsieh, Y. (1982). Randomness, area and species richness. Ecology 63: 1121–1133.

Colwell, R.K., Chao, A., Gotelli, N.J., Lin, S.Y., Mao, C.X., Chazdon, R.L. & Longino, J.T. (2012). Models and estimators linking individual-based and sample-based rarefaction, extrapolation and comparison of assemblages. J. Plant Ecol. 5: 3–21.

Dengler, J. (2009). Which function describes the species-area relationship best? A review and empirical evaluation. Journal of Biogeography 36, 728–744.

Gotelli, N.J. & Colwell, R.K. (2001). Quantifying biodiversity: procedures and pitfalls in measurement and comparison of species richness. Ecol. Lett. 4, 379–391.

See Also

rarefy and rrarefy are related individual based models. Other accumulation models are poolaccum for extrapolated richness, and renyiaccum and tsallisaccum for diversity indices. Underlying graphical functions are boxplot, matlines, segments and polygon.

Examples

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data(BCI)
sp1 <- specaccum(BCI)
sp2 <- specaccum(BCI, "random")
sp2
summary(sp2)
plot(sp1, ci.type="poly", col="blue", lwd=2, ci.lty=0, ci.col="lightblue")
boxplot(sp2, col="yellow", add=TRUE, pch="+")
## Fit Lomolino model to the exact accumulation
mod1 <- fitspecaccum(sp1, "lomolino")
coef(mod1)
fitted(mod1)
plot(sp1)
## Add Lomolino model using argument 'add'
plot(mod1, add = TRUE, col=2, lwd=2)
## Fit Arrhenius models to all random accumulations
mods <- fitspecaccum(sp2, "arrh")
plot(mods, col="hotpink")
boxplot(sp2, col = "yellow", border = "blue", lty=1, cex=0.3, add= TRUE)
## Use nls() methods to the list of models
sapply(mods$models, AIC)

Example output

Loading required package: permute
Loading required package: lattice
This is vegan 2.4-3
Warning message:
In cor(x > 0) : the standard deviation is zero
Species Accumulation Curve
Accumulation method: random, with 100 permutations
Call: specaccum(comm = BCI, method = "random") 

                                                                            
Sites     1.00000   2.00000   3.00000   4.00000   5.0000   6.00000   7.00000
Richness 90.97000 122.01000 139.03000 150.89000 159.4300 165.85000 171.27000
sd        7.14561   7.87593   7.29252   7.01642   6.2833   5.65931   5.22205
                                                                              
Sites      8.00000   9.00000  10.00000  11.00000  12.00000  13.00000  14.00000
Richness 175.53000 179.05000 182.45000 185.59000 187.76000 190.17000 192.33000
sd         5.13151   4.99975   4.79978   4.64518   4.55964   4.52837   4.46548
                                                                             
Sites     15.0000  16.00000  17.00000  18.00000  19.00000  20.00000  21.00000
Richness 194.2800 196.05000 197.90000 199.38000 201.01000 202.22000 203.50000
sd         4.4132   4.34468   4.24383   4.04215   3.89896   3.93785   3.93508
                                                                            
Sites     22.00000  23.00000  24.00000  25.00000  26.0000  27.00000  28.0000
Richness 204.88000 206.15000 207.36000 208.45000 209.3000 210.29000 211.1600
sd         3.76126   3.82014   3.78866   3.73456   3.7457   3.59656   3.4516
                                                                              
Sites     29.00000  30.00000  31.00000  32.00000  33.00000  34.00000  35.00000
Richness 212.08000 212.94000 213.90000 214.65000 215.35000 216.06000 216.77000
sd         3.45733   3.27778   3.13179   3.04304   3.00294   2.96041   2.93999
                                                                             
Sites     36.0000  37.00000  38.00000  39.00000  40.00000  41.00000  42.00000
Richness 217.3900 218.02000 218.80000 219.52000 220.12000 220.65000 221.13000
sd         2.7776   2.82478   2.60148   2.52054   2.33671   2.21736   2.02337
                                                                              
Sites     43.00000  44.00000  45.00000  46.00000  47.00000  48.00000  49.00000
Richness 221.65000 222.07000 222.55000 223.08000 223.62000 224.08000 224.52000
sd         1.81673   1.78238   1.53987   1.45422   1.27747   1.09802   0.74508
            
Sites     50
Richness 225
sd         0
 1 sites          2 sites         3 sites       4 sites         5 sites        
 Min.   : 77.00   Min.   :103.0   Min.   :119   Min.   :132.0   Min.   :144.0  
 1st Qu.: 85.00   1st Qu.:117.0   1st Qu.:134   1st Qu.:146.0   1st Qu.:156.0  
 Median : 91.00   Median :122.5   Median :139   Median :151.0   Median :160.0  
 Mean   : 90.97   Mean   :122.0   Mean   :139   Mean   :150.9   Mean   :159.4  
 3rd Qu.: 97.25   3rd Qu.:127.0   3rd Qu.:145   3rd Qu.:156.2   3rd Qu.:164.0  
 Max.   :109.00   Max.   :144.0   Max.   :154   Max.   :164.0   Max.   :171.0  
 6 sites         7 sites         8 sites         9 sites        
 Min.   :150.0   Min.   :159.0   Min.   :162.0   Min.   :165.0  
 1st Qu.:163.0   1st Qu.:168.0   1st Qu.:173.0   1st Qu.:176.8  
 Median :166.0   Median :171.0   Median :175.5   Median :179.0  
 Mean   :165.8   Mean   :171.3   Mean   :175.5   Mean   :179.1  
 3rd Qu.:170.0   3rd Qu.:175.0   3rd Qu.:179.0   3rd Qu.:182.2  
 Max.   :178.0   Max.   :184.0   Max.   :186.0   Max.   :190.0  
 10 sites        11 sites        12 sites        13 sites       
 Min.   :168.0   Min.   :172.0   Min.   :175.0   Min.   :178.0  
 1st Qu.:179.0   1st Qu.:182.0   1st Qu.:185.0   1st Qu.:187.0  
 Median :183.0   Median :186.0   Median :188.0   Median :190.0  
 Mean   :182.4   Mean   :185.6   Mean   :187.8   Mean   :190.2  
 3rd Qu.:186.0   3rd Qu.:189.0   3rd Qu.:191.0   3rd Qu.:193.0  
 Max.   :192.0   Max.   :195.0   Max.   :197.0   Max.   :200.0  
 14 sites        15 sites        16 sites        17 sites       
 Min.   :180.0   Min.   :182.0   Min.   :184.0   Min.   :187.0  
 1st Qu.:189.8   1st Qu.:191.8   1st Qu.:193.0   1st Qu.:195.0  
 Median :193.0   Median :195.0   Median :197.0   Median :198.0  
 Mean   :192.3   Mean   :194.3   Mean   :196.1   Mean   :197.9  
 3rd Qu.:195.2   3rd Qu.:197.0   3rd Qu.:199.0   3rd Qu.:201.0  
 Max.   :204.0   Max.   :206.0   Max.   :208.0   Max.   :209.0  
 18 sites        19 sites      20 sites        21 sites        22 sites       
 Min.   :189.0   Min.   :190   Min.   :190.0   Min.   :191.0   Min.   :194.0  
 1st Qu.:197.0   1st Qu.:199   1st Qu.:200.0   1st Qu.:201.0   1st Qu.:202.8  
 Median :199.0   Median :201   Median :203.0   Median :204.0   Median :205.0  
 Mean   :199.4   Mean   :201   Mean   :202.2   Mean   :203.5   Mean   :204.9  
 3rd Qu.:202.0   3rd Qu.:204   3rd Qu.:205.0   3rd Qu.:206.0   3rd Qu.:207.2  
 Max.   :210.0   Max.   :211   Max.   :213.0   Max.   :215.0   Max.   :215.0  
 23 sites        24 sites        25 sites        26 sites       
 Min.   :196.0   Min.   :196.0   Min.   :197.0   Min.   :197.0  
 1st Qu.:204.0   1st Qu.:205.0   1st Qu.:207.0   1st Qu.:207.8  
 Median :207.0   Median :208.0   Median :209.0   Median :209.0  
 Mean   :206.2   Mean   :207.4   Mean   :208.4   Mean   :209.3  
 3rd Qu.:208.0   3rd Qu.:210.0   3rd Qu.:211.0   3rd Qu.:212.0  
 Max.   :215.0   Max.   :217.0   Max.   :217.0   Max.   :218.0  
 27 sites        28 sites        29 sites        30 sites       
 Min.   :200.0   Min.   :202.0   Min.   :202.0   Min.   :204.0  
 1st Qu.:208.0   1st Qu.:209.0   1st Qu.:210.0   1st Qu.:211.0  
 Median :210.0   Median :211.5   Median :212.5   Median :213.0  
 Mean   :210.3   Mean   :211.2   Mean   :212.1   Mean   :212.9  
 3rd Qu.:213.0   3rd Qu.:213.0   3rd Qu.:215.0   3rd Qu.:215.2  
 Max.   :219.0   Max.   :219.0   Max.   :220.0   Max.   :221.0  
 31 sites        32 sites        33 sites        34 sites       
 Min.   :205.0   Min.   :206.0   Min.   :207.0   Min.   :207.0  
 1st Qu.:212.0   1st Qu.:212.8   1st Qu.:213.0   1st Qu.:214.0  
 Median :214.0   Median :215.0   Median :215.0   Median :216.0  
 Mean   :213.9   Mean   :214.7   Mean   :215.3   Mean   :216.1  
 3rd Qu.:216.2   3rd Qu.:217.0   3rd Qu.:217.2   3rd Qu.:218.0  
 Max.   :222.0   Max.   :222.0   Max.   :222.0   Max.   :222.0  
 35 sites        36 sites        37 sites      38 sites        39 sites       
 Min.   :207.0   Min.   :208.0   Min.   :208   Min.   :209.0   Min.   :211.0  
 1st Qu.:215.0   1st Qu.:216.0   1st Qu.:216   1st Qu.:217.0   1st Qu.:218.0  
 Median :216.0   Median :218.0   Median :218   Median :219.0   Median :220.0  
 Mean   :216.8   Mean   :217.4   Mean   :218   Mean   :218.8   Mean   :219.5  
 3rd Qu.:219.0   3rd Qu.:219.0   3rd Qu.:220   3rd Qu.:221.0   3rd Qu.:221.0  
 Max.   :222.0   Max.   :222.0   Max.   :223   Max.   :223.0   Max.   :224.0  
 40 sites        41 sites        42 sites        43 sites       
 Min.   :214.0   Min.   :215.0   Min.   :216.0   Min.   :217.0  
 1st Qu.:219.0   1st Qu.:219.0   1st Qu.:220.0   1st Qu.:220.0  
 Median :220.0   Median :221.0   Median :221.0   Median :222.0  
 Mean   :220.1   Mean   :220.7   Mean   :221.1   Mean   :221.7  
 3rd Qu.:222.0   3rd Qu.:222.0   3rd Qu.:223.0   3rd Qu.:223.0  
 Max.   :224.0   Max.   :225.0   Max.   :225.0   Max.   :225.0  
 44 sites        45 sites        46 sites        47 sites       
 Min.   :217.0   Min.   :218.0   Min.   :220.0   Min.   :220.0  
 1st Qu.:221.0   1st Qu.:221.0   1st Qu.:222.0   1st Qu.:223.0  
 Median :222.0   Median :223.0   Median :223.0   Median :224.0  
 Mean   :222.1   Mean   :222.6   Mean   :223.1   Mean   :223.6  
 3rd Qu.:223.0   3rd Qu.:224.0   3rd Qu.:224.0   3rd Qu.:225.0  
 Max.   :225.0   Max.   :225.0   Max.   :225.0   Max.   :225.0  
 48 sites        49 sites        50 sites     
 Min.   :221.0   Min.   :222.0   Min.   :225  
 1st Qu.:223.8   1st Qu.:224.0   1st Qu.:225  
 Median :224.0   Median :225.0   Median :225  
 Mean   :224.1   Mean   :224.5   Mean   :225  
 3rd Qu.:225.0   3rd Qu.:225.0   3rd Qu.:225  
 Max.   :225.0   Max.   :225.0   Max.   :225  
      Asym       xmid      slope 
258.440682   2.442061   1.858694 
 [1]  94.34749 121.23271 137.45031 148.83053 157.45735 164.31866 169.95946
 [8] 174.71115 178.78954 182.34254 185.47566 188.26658 190.77402 193.04337
[15] 195.11033 197.00350 198.74606 200.35705 201.85227 203.24499 204.54643
[22] 205.76612 206.91229 207.99203 209.01150 209.97609 210.89054 211.75903
[29] 212.58527 213.37256 214.12386 214.84180 215.52877 216.18692 216.81820
[36] 217.42437 218.00703 218.56767 219.10762 219.62811 220.13027 220.61514
[43] 221.08369 221.53679 221.97528 222.39991 222.81138 223.21037 223.59747
[50] 223.97327
  [1] 323.0717 341.3868 332.6834 342.4211 358.0178 345.2216 315.1033 322.4612
  [9] 320.1974 317.3514 327.5915 316.9724 302.3015 281.7547 316.1479 348.1764
 [17] 352.4154 353.2717 317.7539 337.9884 344.3120 318.1150 360.9480 327.0056
 [25] 299.7821 342.1344 331.7578 363.4896 344.9060 329.9862 333.5556 339.5104
 [33] 307.6372 336.0589 346.2054 284.1864 263.3566 285.0028 358.1501 321.8131
 [41] 344.2241 338.7433 306.6802 354.2406 306.2675 348.1462 342.4255 315.5634
 [49] 323.2725 292.0440 339.8582 322.2898 371.9230 352.1725 306.2792 329.0107
 [57] 304.2660 361.3904 339.0634 354.6308 316.5934 298.0690 349.8517 312.0757
 [65] 341.8240 333.0405 343.8575 327.7161 340.0718 321.3245 329.4584 304.2948
 [73] 351.5482 351.9405 315.4029 319.0922 336.9580 337.4708 338.4089 332.1611
 [81] 344.7823 322.6134 362.8288 358.2178 323.7816 345.2883 324.0142 360.9966
 [89] 352.9998 332.9889 334.2561 323.0296 348.9373 349.7626 340.6058 321.9601
 [97] 321.3303 320.9482 342.7446 319.3514

vegan documentation built on May 31, 2017, 4:08 a.m.