Finite Mixture of Regression Modeling for High-Dimensional Count and Biomass Data in Ecology

Understanding how species distributions respond as a function of environmental gradients is a key question in ecology, and will benefit from a multi-species approach. Multi-species data are often high dimensional, in that the number of species sampled is often large relative to the number of sites, and are commonly quantified as either presence-absence, counts of individuals, or biomass of each species. In this paper, we propose a novel approach to the analysis of multi-species data when the goal is to understand how each species responds to their environment. We use a finite mixture of regression models, grouping species into Archetypes according to their environmental response, thereby significantly reducing the dimension of the regression model. Previous research introduced such Species Archetype Models (SAMs), but only for binary assemblage data. Here, we extend this basic framework with three key innovations: (1) the method is expanded to handle count and biomass data, (2) we propose grouping on the slope coefficients only, whilst the intercept terms and nuisance parameters remain species-specific, and (3) we develop model diagnostic tools for SAMs. By grouping on environmental responses only, the model allows for inter-species variation in terms of overall prevalence and abundance. The application of our expanded SAM framework data is illustrated on marine survey data and through simulation. Supplementary materials accompanying this paper appear on-line.