Dynamical phase transitions in eco-evolutionary systems

In large ecosystems, multiple phenotypically relevant mutants can emerge and compete, creating eco-evolutionary feedback loops involving mutation, selection, and ecological interactions. We demonstrate that, owing to this feedback, the details of the underlying mutational process can qualitatively impact the long-term eco-evolutionary dynamics, challenging the classical assumption that mutational processes are equivalent up to rescaling. Utilizing a modified MacArthur consumer-resource model, we compare systems with fixed mutation rates (e.g. those exposed to an environmental mutagen) to systems with replication-coupled mutations. We show that, at long times, externally supplied mutations result in a homogeneous distribution in phenotype space while, remarkably, replication-coupled mutations can induce a phenotypically patterned phase, specifically when the ecological relaxation rate is sufficiently fast. A mean-field analysis reveals that these patterns stem from a Turing-like mechanism driven by the non-reciprocal and nonlinear nature of replication-linked mutations. We incorporate demographic noise, revealing additional 'quasi-patterned' regimes, and we quantify the large deviations of the mutation current to characterize rare events over long timescales. Finally, we discuss how this phenomenology may be relevant to particular biological systems.