Beyond resource selection: emergent spatio-temporal distributions from animal movements and stigmergent interactions

A principal concern of ecological research is to unveil the causes behind observed spatio-temporal distributions of species. A key tactic is to correlate observed locations with environmental features, in the form of resource selection functions or other correlative species distribution models. In reality, however, the distribution of any population both affects and is affected by those surrounding it, creating a complex network of feedbacks causing emergent spatio-temporal features that may not correlate with any particular aspect of the underlying environment. Here, we study the way in which the movements of populations in response to one another can affect the spatio-temporal distributions of ecosystems. We construct a stochastic individual-based modelling (IBM) framework, based on stigmergent interactions (i.e. organisms leave marks which cause others to alter their movements) between and within populations. We show how to gain insight into this IBM via mathematical analysis of a partial differential equation (PDE) system given by a continuum limit. We show how the combination of stochastic simulations of the IBM and mathematical analysis of PDEs can be used to categorise emergent patterns into homogeneous vs. heterogeneous, stationary vs. perpetually-fluctuating, and aggregation vs. segregation. In doing so, we develop techniques for understanding spatial bifurcations in stochastic IBMs, grounded in mathematical analysis. Finally, we demonstrate through a simple example how the interplay between environmental features and between-population stigmergent interactions can give rise to predicted spatial distributions that are quite different to those predicted purely by accounting for environmental covariates.