Untangling direct species associations from mediator species effects with graphical models

Ecologists often investigate co-occurrence patterns in multi-species data in order to gain insight into the ecological causes of observed co-occurrences. Apart from direct associations between two species, two species may co-occur because they both respond in similar ways to environmental variables, or due to the presence of other (mediator) species. A wide variety of methods are now available for modelling how environmental filtering drives species distributions. In contrast, methods for studying other causes of co-occurence are much more limited. 9Graphical9 methods, which can be used to study how mediator species impact co-occurrence patterns, have recently been proposed for use in ecology. However, available methods are limited to presence/absence data and methods assuming multivariate normality, which is problematic when analysing abundances. We propose Gaussian copula graphical models (GCGMs) for studying the effect of mediator species on co-occurence patterns. GCGMs are a flexible type of graphical model which naturally accommodates all data types -- binary (presence/absence), counts, as well as ordinal data and biomass, in a unified framework. Simulations for count data demonstrate that GCGMs are better able to distinguish effects of mediator species from direct associations than using existing methods designed for multivariate normal data. We apply GCGMs to counts of hunting spiders, in order to visualise associations between species. We then analyze abundance data of New Zealand native forest cover (on an ordinal scale) to show how GCGMs can be used analyze large and complex datasets. In these data, we were able to reproduce known species relationships as well as generate new ecological hypotheses about species associations.