Dynamical phase transitions in the eco-evolutionary dynamics of complex ecosystems

In complex ecosystems such as microbial communities, there is constant ecological and evolutionary feedback between the residing species and the environment occurring on concurrent timescales. Species respond and adapt to their surroundings by modifying their phenotypic traits, which in turn alters their environment and the resources available. To study this interplay between ecological and evolutionary mechanisms, we construct a consumer-resource model coupled with phenotypic mutations. Drawing from non-equilibrium statistical physics, we define time-integrated observables to characterize the effects of frequency-dependent selection and adaptation rate on the community structure in phenotype space and the temporal dynamics. Using these dynamical observables, we identify various phases that the ecosystem can exhibit and discuss the conditions for dynamical phase transitions and their ecological implications.