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Varying richness need not imply non-random species co-occurrence: implications for specifying null models

Background Non-random species co-occurrence is of fundamental interest to ecologists. One approach to analysing non-random patterns is null modelling. This involves calculation of a metric for the observed dataset, and comparison to a distribution obtained by repeatedly randomising the data. Choice of randomisation algorithm, specifically whether null model species richness is fixed at that of the observed dataset, is likely to affect model results. This is particularly important in cases when there is high variation in species richness between sampling units in the observed data. Methods Here I demonstrate the effects of accounting for variation in species richness. I use the C-score, a metric measuring species segregation as “checkerboard units”, applied to 289 datasets. First, I run null models in which sites are equally likely to be occupied (fixed-equiprobable algorithm). I do this both for the original datasets, and for the same datasets where occurrences are randomised with the species richness distribution fixed (pre-randomised datasets). Second, I run null models that fix site species richness to that observed (fixed-fixed algorithm). Results For real datasets, using the fixed-equiprobable algorithm (sites are equally likely to be colonised), C-score standardised effect size (SES) was positively related to variability in species richness between sites within a dataset. This effect was also found for pre-randomised datasets, indicating that variability in species richness can be exclusively responsible for detection of non-random species co-occurrence. When using the fixed-fixed algorithm (richness is constrained to that of real sites), there was no relationship between SES and variability in species richness. There was also a reverse in the effect direction, with 94% of significant tests indicating a lower C-score than expected for the fixed-equiprobable algorithm, but 98% of significant tests indicating a higher C-score than expected for the fixed-fixed algorithm. Discussion I speculate that when variation in species richness is high, fewer checkerboard units are possible, regardless of segregation between species. Therefore, use of fixed-equiprobable algorithms in situations where real species richness is highly variable between sites within a dataset will yield significant results, even if species co-occur randomly within the constraints of the species richness distribution. Consequently, use of such tests makes the a priori assumption that high within-dataset variation in species richness indicates non-random species co-occurrence. I recommend using algorithms that explicitly take into account species richness distributions when one wants to eliminate the effect of richness variation in terms of producing significant but spurious positive co-occurrence results. Alternatively, non-null mechanistic models can be created, in which hypothesised species assembly processes must be explicitly stated and tested.