Minimum dimensions required for co-occurrence and limiting similarity null models

Background/Question/Methods

The use of null models for species co-occurrence and limiting similarity analyses have become standard practice in community ecology; however, no detailed assessment has been made to determine the minimum number of species and plots needed for these analyses to yield reliable results. This is especially true for limiting similarity null models, which have not received the same level of critical analysis as species co-occurrence analyses. To determine the minimum matrix dimension (species x plots) at which these null models can be used, presence-absence matrices were generated; these ranged in size from 3 to 50 for both species and plots. Matrices were filled randomly with species abundances (number of plots occupied) drawn from a log-normal distribution and the number of species per plot drawn from a uniform distribution. Trait values for limiting similarity tests were drawn randomly from a uniform distribution. The C-Score and fixed-fixed algorithm were used for co-occurrence null models and the Nearest Trait Distance (NTD) and two randomization algorithms were used for the limiting similarity null models.

Results/Conclusions

The minimum matrix dimensions that resulted in acceptable type I error rates (p < 0.05) were 100 and 50 for co-occurrence and limiting similarity null models respectively. The use of inclusive P values (P >= 0.05) versus exclusive (P > 0.05) significantly influences the results of the type I error rates in smaller dimensioned matrices.  This is because the randomization of small matrices more frequently produces the same matrix, and because the resolution of the C-Score index decays with decreasing matrix dimension. Our analyses support the use of co-occurrence and limiting similarity null model analyses on small data sets provided minimum constraints of matrix dimension are met.