R: Evaluate Statistics with Null Models of Biological...

oecosimu {vegan} | R Documentation

## Evaluate Statistics with Null Models of Biological Communities

### Description

Function evaluates a statistic or a vector of statistics in community and evaluates its significance in a series of simulated random communities. The approach has been used traditionally for the analysis of nestedness, but the function is more general and can be used with any statistics evaluated with simulated communities. Function `oecosimu` collects and evaluates the statistics. The Null model communities are described in `make.commsim` and `permatfull`/ `permatswap`, the definition of Null models in `nullmodel`, and nestedness statistics in `nestednodf` (which describes several alternative statistics, including nestedness temperature, N0, checker board units, nestedness discrepancy and NODF).

### Usage

    oecosimu(comm, nestfun, method, nsimul = 99, burnin = 0, thin = 1,
       statistic = "statistic", alternative = c("two.sided", "less", "greater"),
       batchsize = NA, parallel = getOption("mc.cores"), ...)
    ## S3 method for class 'oecosimu'
    as.ts(x, ...)
    ## S3 method for class 'oecosimu'
    as.mcmc(x)

### Arguments

`comm` | Community data, or a Null model object generated by `nullmodel` or an object of class `simmat` (array of permuted matrices from `simulate.nullmodel`). If `comm` is a community data, null model simulation `method` must be specified. If `comm` is a `nullmodel`, the simulation `method` is ignored, and if `comm` is a `simmat` object, all other arguments are ignored except `nestfun`, `statistic` and `alternative`.
`nestfun` | Function analysed. Some nestedness functions are provided in vegan (see `nestedtemp`), but any function can be used if it accepts the community as the first argument, and returns either a plain number or a vector or the result in list item with the name defined in argument `statistic`. See Examples for defining your own functions.
`method` | Null model method: either a name (character string) of a method defined in `make.commsim` or a `commsim` function. This argument is ignored if `comm` is a `nullmodel` or a `simmat` object. See Details and Examples.
`nsimul` | Number of simulated null communities (ignored if `comm` is a `simmat` object).
`burnin` | Number of null communities discarded before proper analysis in sequential methods (such as `"tswap"`) (ignored with non-sequential methods or when `comm` is a `simmat` object).
`thin` | Number of discarded null communities between two evaluations of nestedness statistic in sequential methods (ignored with non-sequential methods or when `comm` is a `simmat` object).
`statistic` | The name of the statistic returned by `nestfun`.
`alternative` | a character string specifying the alternative hypothesis, must be one of `"two.sided"` (default), `"greater"` or `"less"`. Please note that the p-value of two-sided test is approximately two times higher than in the corresponding one-sided test (`"greater"` or `"less"` depending on the sign of the difference).
`batchsize` | Size in Megabytes of largest simulation object. If a larger structure would be produced, the analysis is broken internally into batches. With default `NA` the analysis is not broken into batches. See Details.
`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. If you define a `nestfun` in Windows that needs other R packages than vegan or permute, you must set up a socket cluster before the call.
`x` | An `oecosimu` result object.
`...` | Other arguments to functions.

### Details

Function `oecosimu` is a wrapper that evaluates a statistic using function given by `nestfun`, and then simulates a series of null models based on `nullmodel`, and evaluates the statistic on these null models. The vegan packages contains some nestedness functions that are described separately (`nestedchecker`, `nesteddisc`, `nestedn0`, `nestedtemp`, `nestednodf`), but many other functions can be used as long as they are meaningful with simulated communities. An applicable function must return either the statistic as a plain number or a vector, or as a list element `"statistic"` (like `chisq.test`), or in an item whose name is given in the argument `statistic`. The statistic can be a single number (like typical for a nestedness index), or it can be a vector. The vector indices can be used to analyse site (row) or species (column) properties, see `treedive` for an example. Raup-Crick index (`raupcrick`) gives an example of using a dissimilarities.

The Null model type can be given as a name (quoted character string) that is used to define a Null model in `make.commsim`. These include all binary models described by Wright et al. (1998), Jonsson (2001), Gotelli & Entsminger (2003), Miklós & Podani (2004), and some others. There are several quantitative Null models, such those discussed by Hardy (2008), and several that are unpublished (see `make.commsim`, `permatfull`, `permatswap` for discussion). The user can also define her own `commsim` function (see Examples).

Function works by first defining a `nullmodel` with given `commsim`, and then generating a series of simulated communities with `simulate.nullmodel`. A shortcut can be used for any of these stages and the input can be

1. Community data (`comm`), Null model function (`nestfun`) and the number of simulations (`nsimul`).

2. A `nullmodel` object and the number of simulations, and argument `method` is ignored.

3. A three-dimensional array of simulated communities generated with `simulate.nullmodel`, and arguments `method` and `nsimul` are ignored.

The last case allows analysing several statistics with the same simulations.

The function first generates simulations with given `nullmodel` and then analyses these using the `nestfun`. With large data sets and/or large number of simulations, the generated objects can be very large, and if the memory is exhausted, the analysis can become very slow and the system can become unresponsive. The simulation will be broken into several smaller batches if the simulated `nullmodel` objective will be above the set `batchsize` to avoid memory problems (see `object.size` for estimating the size of the current data set). The parallel processing still increases the memory needs. The parallel processing is only used for evaluating `nestfun`. The main load may be in simulation of the `nullmodel`, and `parallel` argument does not help there.

Function `as.ts` transforms the simulated results of sequential methods into a time series or a `ts` object. This allows using analytic tools for time series in studying the sequences (see examples). Function `as.mcmc` transforms the simulated results of sequential methods into an `mcmc` object of the coda package. The coda package provides functions for the analysis of stationarity, adequacy of sample size, autocorrelation, need of burn-in and much more for sequential methods, and summary of the results. Please consult the documentation of the coda package.

Function `permustats` provides support to the standard `density`, `densityplot`, `qqnorm` and `qqmath` functions for the simulated values.

### Value

Function `oecosimu` returns an object of class `"oecosimu"`. The result object has items `statistic` and `oecosimu`. The `statistic` contains the complete object returned by `nestfun` for the original data. The `oecosimu` component contains the following items:

`statistic` | Observed values of the statistic.
`simulated` | Simulated values of the statistic.
`means` | Mean values of the statistic from simulations.
`z` | Standardized effect sizes (SES, a.k.a. the z-values) of the observed statistic based on simulations.
`pval` | The P-values of the statistic based on simulations.
`alternative` | The type of testing as given in argument `alternative`.
`method` | The `method` used in `nullmodel`.
`isSeq` | `TRUE` if `method` was sequential.

### Note

If you wonder about the name of `oecosimu`, look at journal names in the References (and more in `nestedtemp`).

The internal structure of the function was radically changed in vegan 2.2-0 with introduction of `commsim` and `nullmodel` and deprecation of `commsimulator`. However, the results and the basic user interface remain the same (except that `method = "r0_old"` must be used to reproduce the old results of `"method = r0"`).

### Author(s)

Jari Oksanen and Peter Solymos

### References

Hardy, O. J. (2008) Testing the spatial phylogenetic structure of local communities: statistical performances of different null models and test statistics on a locally neutral community. Journal of Ecology 96, 914–926.

Gotelli, N.J. & Entsminger, N.J. (2003). Swap algorithms in null model analysis. Ecology 84, 532–535.

Jonsson, B.G. (2001) A null model for randomization tests of nestedness in species assemblages. Oecologia 127, 309–313.

Miklós, I. & Podani, J. (2004). Randomization of presence-absence matrices: comments and new algorithms. Ecology 85, 86–92.

Wright, D.H., Patterson, B.D., Mikkelson, G.M., Cutler, A. & Atmar, W. (1998). A comparative analysis of nested subset patterns of species composition. Oecologia 113, 1–20.

### See Also

Function `oecosimu` currently defines null models with `commsim` and generates the simulated null model communities with `nullmodel` and `simulate.nullmodel`. For other applications of `oecosimu`, see `treedive` and `raupcrick`.

Function `rndtaxa` (labdsv package) randomizes a community table. See also `nestedtemp` (that also discusses other nestedness functions) and `treedive` for another application.

### Examples

    ## Use the first eigenvalue of correspondence analysis as an index
    ## of structure: a model for making your own functions.
    data(sipoo)
    ## Traditional nestedness statistics (number of checkerboard units)
    oecosimu(sipoo, nestedchecker, "r0")
    ## sequential model, one-sided test, a vector statistic
    out <- oecosimu(sipoo, decorana, "swap", burnin=100, thin=10,
       statistic="evals", alt = "greater")
    out
    ## Inspect the swap sequence as a time series object
    plot(as.ts(out))
    lag.plot(as.ts(out))
    acf(as.ts(out))
    ## Density plot
    densityplot(permustats(out), as.table = TRUE, layout = c(1,4))
    ## Use quantitative null models to compare
    ## mean Bray-Curtis dissimilarities
    data(dune)
    meandist <- function(x) mean(vegdist(x, "bray"))
    mbc1 <- oecosimu(dune, meandist, "r2dtable")
    mbc1

    ## Define your own null model as a 'commsim' function: shuffle cells
    ## in each row
    foo <- function(x, n, nr, nc, ...) {
       out <- array(0, c(nr, nc, n))
       for (k in seq_len(n))
          out[,,k] <- apply(x, 2, function(z) sample(z, length(z)))
       out
    }
    cf <- commsim("myshuffle", foo, isSeq = FALSE, binary = FALSE,
       mode = "double")
    oecosimu(dune, meandist, cf)

    ## Use pre-built null model
    nm <- simulate(nullmodel(sipoo, "curveball"), 99)
    oecosimu(nm, nestedchecker)
    ## Several chains of a sequential model -- this can be generalized
    ## for parallel processing (see ?smbind)
    nm <- replicate(5, simulate(nullmodel(sipoo, "swap"), 99,
       thin=10, burnin=100), simplify = FALSE)
    ## nm is now a list of nullmodels: use smbind to combine these into one
    ## nullmodel with several chains
    nm <- smbind(nm, MARGIN = 3)
    nm
    oecosimu(nm, nestedchecker)
    ## After this you can use as.mcmc() and tools in the coda package to
    ## analyse the chains (these will show that thin, burnin and nsimul are
    ## all too low for real analysis).

[Package vegan version 2.4-3 Index]