Effects of demographic stochasticity on eco-evolutionary dynamics and trait-space patterning of complex communities

In recent years, there have been mounting evidence that evolutionary and ecological processes can occur over concurrent timescales and can affect each other. To better understand how this eco-evolutionary feedback shapes the diversity of an ecosystem, we develop a phenotypic reaction-diffusion model of a community where consumers compete for resources and mutate. Within this model, we explore the factors that determine the evolutionary fate of the ecosystem. Depending on the competition kernel, competitive strength, and mutation rate, the community can exhibit competitive exclusion which manifests as a static periodic pattern in phenotype space, or Red Queen dynamics which appears as a traveling wave of persisting species participating in a coevolutionary arms race. Beyond these Turing patterns, we also investigate the role of demographic noise in driving phenotypic diversification and discuss new behaviors that may arise due to fluctuations.