Mathematical Biology Seminar (Special Day)

Speaker: Trevor GrandPre (Washington University in St. Louis)

Title: Phase Transitions in eco-evolutionary systems

Abstract: In complex ecosystems, multiple phenotypic variants can arise and compete, creating feedback among mutation, selection, and ecological interactions. We show that this eco-evolutionary coupling allows the specific form of the mutational process to alter long-term dynamics in a qualitative way, challenging the classical view that different mutation mechanisms are equivalent up to a simple time rescaling. Using a modified MacArthur consumer resource model, we compare systems in which mutations occur at a constant external rate, such as under exposure to an environmental mutagen, with systems in which mutations are coupled to replication errors. Our analysis reveals that externally driven mutations lead to a uniform distribution in phenotype space, whereas replication-linked mutations can give rise to stable pattern formation when ecological relaxation is sufficiently rapid. A mean-field treatment identifies a Turing-like instability that emerges from the nonlinear and nonreciprocal effects of replication-coupled mutation. These results demonstrate that the timing and mechanism of mutation can shape ecosystem-level organization and may be relevant to systems such as microbial communities and cancers.