R: Species Accumulation Curves

specaccum {vegan} | R Documentation

## Species Accumulation Curves

### Description

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

### Usage

    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"), lty = 1,
        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.
`lty` | line type (see `par`).
`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.
`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

    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)

[Package vegan version 2.4-3 Index]