A theory of ecological invasions and its implications for short-term eco-evolutionary dynamics

Over the last few years, there has been growing interest in developing a theory of eco-evolutionary dynamics. Classical ecological and evolutionary models largely ignore the interplay between ecological and evolutionary processes. However, experiments in microbial ecosystems suggest that ecology and evolution can occur on similar time scales. To address this gap, we develop a theory of ecological invasions that can be used to analyze a wide variety of ecological models including the Lotka-Volterra model, consumer resource models (CRMs), and models with cross feeding. Importantly, our framework is valid even when the community being invaded is evolved (non-random) and in the presence of invasion-driven species extinctions. Using our theory, we obtain analytical expressions relating invasion fitness to the final invader abundance, species and resource abundance shifts, and extinction probabilities. Our results can be naturally understood in terms of a new quantity we call the "dressed invasion fitness" that augments the traditional notion of invasion fitness by incorporating the effect of ecological feedback. We use our formalism to analyze short-term evolutionary dynamics by modeling mutations as invasions by an invader that is correlated with an existing parent species. We show that, generically, mutants and parents can co-exist, often by driving the extinction of low-abundance species. Collectively, these results show the important role played by eco-evolutionary feedbacks in shaping ecological invasions and short-term evolutionary dynamics in complex communities.