Using codispersion analysis to characterize spatial patterns in species co - occurrences 1

Visualizing and quantifying spatial patterns of co-occurrence (i.e., of two or more 12 species, or of species and underlying environmental variables) can suggest hypotheses about 13 processes that structure species assemblages and their relevant spatial scales. Statistical models 14 of spatial co-occurrence generally assume that underlying spatial processes are isotropic and 15 stationary but many ecologically realistic spatial processes are anisotropic and non-stationary. 16 Here, we introduce codispersion analysis to ecologists and use it to detect and quantify 17 anisotropic and nonstationary patterns and their relevant spatial scales in bivariate co-occurrence 18 data. Simulated data illustrated that codispersion analysis can accurately characterize complex 19 spatial patterns. Analysis of co-occurrence of common tree species growing in a 35-ha plot 20 revealed both positive and negative codispersion between different species; positive codispersion 21 values reflected positive correlation in species abundance (aggregation), whereas negative 22 codispersion values reflected negative correlation in species abundance (segregation). 23 Comparisons of observed patterns with those simulated using two different null models showed 24 that the codispersion of most species pairs differed significantly from random expectation. We 25 conclude that codispersion analysis can be a useful exploratory tool to guide ecologists interested 26 in modeling spatial processes. 27 28