Untangling direct species associations from indirect 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 the two species of interest, they may co-occur because of indirect effects, where both species respond to another variable, whether environmental or biotic (e.g. a 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. Graphical 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 or 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, for example binary (presence/absence), counts, as well as ordinal data and biomass, in a unified framework. Simulations demonstrate that GCGMs can be applied to a much broader range of data types than the methods currently used in ecology, and perform as well as or better than existing methods in many settings. We apply GCGMs to counts of hunting spiders, in order to visualise associations between species. We also analyse abundance data of New Zealand native forest cover (on an ordinal scale) to show how GCGMs can be used analyse 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.