Reducing over-reporting of deterministic co-occurrence patterns in biotic communities

Null models of species co-occurrence are widely used to infer the existence of various ecological processes. Here we investigate the susceptibility of the most commonly used of these models (the C-score in conjunction with the sequential swap algorithm) to type 1 and type 2 errors. To do this we use simulated datasets with a range of numbers of sites, species and coefficients of variation (CV) in species abundance. We find that this model is particularly susceptible to type 1 errors when applied to large matrices and those with low CV in species abundance. As expected, type 2 error rates decrease with increasing numbers of sites and species, although they increase with increasing CV in species abundance. Despite this, power remains acceptable over a wide range of parameter combinations. The susceptibility of this analytical method to type 1 errors indicates that many previous studies may have incorrectly reported the existence of deterministic patterns of species co-occurrence. We demonstrate that in order to overcome the problem of high type 1 error rates, the number of swaps used to generate null distributions for smaller matrices needs to be increased to over 50,000 swaps (well beyond the 5000 commonly used in published analyses and the 30,000 suggested by Lehsten and Harmand, 2006). We also show that this approach reduces type 1 error rates in real datasets. However, even using this solution, larger datasets still suffer from high type 1 error rates. Such datasets therefore require the use of very large numbers of swaps, which calls for improvements in the most commonly used software. In general, users of this powerful analytical method must be aware that they need surprisingly large numbers of swaps to obtain unbiased estimates of structuring in biotic communities.