The role of interspecific cooperative interactions on the spatial dynamics of species.

Understanding the mechanisms shaping the biogeography i.e. spatial distribution of species is a fundamental question in ecology. Recent research has begun to acknowledge the crucial role of interspecific (biotic) interactions in driving the joint spatial distributions of the interacting species. One such interaction is interspecific cooperation (or mutualism), a ubiquitous yet understudied mechanism that impacts the population dynamics of the species.

Here, we develop a coupled partial differential equation model of two-species mutualism to understand its long-term spreading behaviour and subsequent species spatial distributions. We incorporate both the dispersal (e.g. bacterial motility, wind dispersal of seeds) as well as population dynamics of the species that arise from intraspecific competition and interspecific cooperation. We find that mutualisms give rise to weak and strong Allee effects which in turn result in travelling waves of spreading species which transition from pulled to pushed under certain regimes of interspecific cooperativity. We further calculate the speed of these waves. We integrate the outcomes from this model with previous results from two-species models to propose a general framework of spatial dynamics for interactions along a spectrum of antagonistic to mutualistic. Ultimately our work proposes a new biological mechanism, namely mutualisms, by which pushed waves of species spread arise. Our work has implications for predicting and managing species invasions.