commsim {vegan}R Documentation

Create an Object for Null Model Algorithms

Description

The commsim function can be used to feed Null Model algorithms into nullmodel analysis. The make.commsim function returns various predefined algorithm types (see Details). These functions represent low level interface for community null model infrastructure in vegan with the intent of extensibility, and less emphasis on direct use by users.

Usage

commsim(method, fun, binary, isSeq, mode)
make.commsim(method)
## S3 method for class 'commsim'
print(x, ...)

Arguments

method

Character, name of the algorithm.

fun

A function. For possible formal arguments of this function see Details.

binary

Logical, if the algorithm applies to presence-absence or count matrices.

isSeq

Logical, if the algorithm is sequential (needs burnin and thinning) or not.

mode

Character, storage mode of the community matrix, either "integer" or "double".

x

An object of class commsim.

...

Additional arguments.

Details

The function fun must return an array of dim(nr, nc, n), and must take some of the following arguments:

You can define your own null model, but several null model algorithm are pre-defined and can be called by their name. The predefined algorithms are described in detail in the following chapters. The binary null models produce matrices of zeros (absences) and ones (presences) also when input matrix is quantitative. There are two types of quantitative data: Counts are integers with a natural unit so that individuals can be shuffled, but abundances can have real (floating point) values and do not have a natural subunit for shuffling. All quantitative models can handle counts, but only some are able to handle real values. Some of the null models are sequential so that the next matrix is derived from the current one. This makes models dependent from previous models, and usually you must thin these matrices and study the sequences for stability: see oecosimu for details and instructions.

See Examples for structural constraints imposed by each algorithm and defining your own null model.

Value

An object of class commsim with elements corresponding to the arguments (method, binary, isSeq, mode, fun).

If the input of make.comsimm is a commsim object, it is returned without further evaluation. If this is not the case, the character method argument is matched against predefined algorithm names. An error message is issued if none such is found. If the method argument is missing, the function returns names of all currently available null model algorithms as a character vector.

Binary null models

All binary null models preserve fill: number of presences or conversely the number of absences. The classic models may also preserve column (species) frequencies (c0) or row frequencies or species richness of each site (r0) and take into account commonness and rarity of species (r1, r2). Algorithms swap, tswap, curveball, quasiswap and backtracking preserve both row and column frequencies. Three first ones are sequential but the two latter are non-sequential and produce independent matrices. Basic algorithms are reviewed by Wright et al. (1998).

Quantitative Models for Counts with Fixed Marginal Sums

These models shuffle individuals of counts and keep marginal sums fixed, but marginal frequencies are not preserved. Algorithm r2dtable uses standard R function r2dtable also used for simulated P-values in chisq.test. Algorithm quasiswap_count uses the same, but preserves the original fill. Typically this means increasing numbers of zero cells and the result is zero-inflated with respect to r2dtable.

Quantitative Swap Models

Quantitative swap models are similar to binary swap, but they swap the largest permissible value. The models in this section all maintain the fill and perform a quantitative swap only if this can be done without changing the fill. Single step of swap often changes the matrix very little. In particular, if cell counts are variable, high values change very slowly. Checking the chain stability and independence is even more crucial than in binary swap, and very strong thinning is often needed. These models should never be used without inspecting their properties for the current data. These null models can also be defined using permatswap function.

Quantitative Swap and Shuffle Models

Quantitative Swap and Shuffle methods (swsh methods) preserve fill and column and row frequencies, and also either row or column sums. The methods first perform a binary quasiswap and then shuffle original quantitative data to non-zero cells. The samp methods shuffle original non-zero cell values and can be used also with non-integer data. The both methods redistribute individuals randomly among non-zero cells and can only be used with integer data. The shuffling is either free over the whole matrix, or within rows (r methods) or within columns (c methods). Shuffling within a row preserves row sums, and shuffling within a column preserves column sums. These models can also be defined with permatswap.

Quantitative Shuffle Methods

Quantitative shuffle methods are generalizations of binary models r00, r0 and c0. The _ind methods shuffle individuals so that the grand sum, row sum or column sums are preserved. These methods are similar as r2dtable but with still slacker constraints on marginal sums. The _samp and _both methods first apply the corresponding binary model with similar restriction on marginal frequencies and then distribute quantitative values over non-zero cells. The _samp models shuffle original cell values and can therefore handle also non-count real values. The _both models shuffle individuals among non-zero values. The shuffling is over the whole matrix in r00_, and within row in r0_ and within column in c0_ in all cases.

Author(s)

Jari Oksanen and Peter Solymos

References

Gotelli, N.J. & Entsminger, N.J. (2001). Swap and fill algorithms in null model analysis: rethinking the knight's tour. Oecologia 129, 281–291.

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

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.

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.

Patefield, W. M. (1981) Algorithm AS159. An efficient method of generating r x c tables with given row and column totals. Applied Statistics 30, 91–97.

Strona, G., Nappo, D., Boccacci, F., Fattorini, S. & San-Miguel-Ayanz, J. (2014). A fast and unbiased procedure to randomize ecological binary matrices with fixed row and column totals. Nature Communications 5:4114 doi:10.1038/ncomms5114.

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

See permatfull, permatswap for alternative specification of quantitative null models. Function oecosimu gives a higher-level interface for applying null models in hypothesis testing and analysis of models. Function nullmodel and simulate.nullmodel are used to generate arrays of simulated null model matrices.

Examples

## write the r00 algorithm
f <- function(x, n, ...)
    array(replicate(n, sample(x)), c(dim(x), n))
(cs <- commsim("r00", fun=f, binary=TRUE,
    isSeq=FALSE, mode="integer"))

## retrieving the sequential swap algorithm
(cs <- make.commsim("swap"))

## feeding a commsim object as argument
make.commsim(cs)

## making the missing c1 model using r1 as a template
##   non-sequential algorithm for binary matrices
##   that preserves the species (column) frequencies,
##   but uses row marginal frequencies
##   as probabilities of selecting sites
f <- function (x, n, nr, nc, rs, cs, ...) {
    out <- array(0L, c(nr, nc, n))
    J <- seq_len(nc)
    storage.mode(rs) <- "double"
    for (k in seq_len(n))
        for (j in J)
            out[sample.int(nr, cs[j], prob = rs), j, k] <- 1L
    out
}
cs <- make.commsim("r1")
cs$method <- "c1"
cs$fun <- f

## structural constraints
diagfun <- function(x, y) {
    c(sum = sum(y) == sum(x),
        fill = sum(y > 0) == sum(x > 0),
        rowSums = all(rowSums(y) == rowSums(x)),
        colSums = all(colSums(y) == colSums(x)),
        rowFreq = all(rowSums(y > 0) == rowSums(x > 0)),
        colFreq = all(colSums(y > 0) == colSums(x > 0)))
}
evalfun <- function(meth, x, n) {
    m <- nullmodel(x, meth)
    y <- simulate(m, nsim=n)
    out <- rowMeans(sapply(1:dim(y)[3],
        function(i) diagfun(attr(y, "data"), y[,,i])))
    z <- as.numeric(c(attr(y, "binary"), attr(y, "isSeq"),
        attr(y, "mode") == "double"))
    names(z) <- c("binary", "isSeq", "double")
    c(z, out)
}
x <- matrix(rbinom(10*12, 1, 0.5)*rpois(10*12, 3), 12, 10)
algos <- make.commsim()
a <- t(sapply(algos, evalfun, x=x, n=10))
print(as.table(ifelse(a==1,1,0)), zero.print = ".")
[Package vegan version 2.6-4 Index]