## Usage

sim3(speciesData)

## Arguments

- speciesData
- binary presence-absence matrix
(rows = species, columns = sites).

## Value

Returns a binary presence-absence matrix with the same
dimensions and colsums as the input matrix.

## Description

Randomizes a binary matrix speciesData by reshuffling elements
within each column equiprobably.

## Details

This algorithm assumes species are equiprobable, but preserves
differences among sites (= column sums).

## Note

This algorithm preserves differences in species richness among sites
(= colsums), but assumes that all species are equiprobable. This assumption
is usually unrealistic, and sim3 has a high frequency of Type I errors with
random matrices, so it is not recommended for co-occurrence analysis.

## References

Gotelli, N.J. 2000. Null model analysis of species co-occurrence
patterns. Ecology 81: 2606-2621.

## Examples

randomMatrix <- sim3(speciesData=matrix(rbinom(40,1,0.5),nrow=8))