Using codispersion analysis to characterize spatial patterns in species co-occurrences

Visualizing and quantifying spatial patterns of co-occurrence (i.e., of two or more species, or of species and underlying environmental variables) can suggest hypotheses about processes that structure species assemblages and their relevant spatial scales. Statistical models of spatial co-occurrence generally assume that underlying spatial processes are isotropic and stationary, but many ecologically realistic spatial processes are anisotropic and non-stationary. Here, we introduce codispersion analysis to ecologists and use it to detect and quantify anisotropic and nonstationary patterns and their relevant spatial scales in bivariate co-occurrence data. Simulated data illustrated that codispersion analysis can accurately characterize complex spatial patterns. Analysis of co-occurrence of common tree species growing in a 35-ha plot revealed both positive and negative codispersion between different species; positive codispersion values reflected positive correlation in species abundance (aggregation), whereas negative codispersion values reflected negative correlation in species abundance (segregation). Comparisons of observed patterns with those simulated using two different null models showed that the codispersion of most species pairs differed significantly from random expectation. We conclude that codispersion analysis can be a useful exploratory tool to guide ecologists interested in modeling spatial processes.