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

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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

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## 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).

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