Coupled fast and slow feedbacks lead to continual evolution: A general modeling approach

The Red Queen Hypothesis, which suggests that continual evolution can result from solely biotic interactions, has been studied in macroevolutionary and microevolutionary contexts. While the latter has been effective in describing examples in which evolution does not cease, describing which properties lead to continual evolution or to stasis remains a major challenge. In many contexts it is unclear which assumptions are necessary for continual evolution, and whether described behavior is robust under perturbations. Our aim here is to prove continual evolution under minimal conditions and in a general framework, thus automatically obtaining robustness. We show that the combination of a fast positive and a slow negative feedback causes continual evolution with a single evolving trait, provided the ecological timescale is sufficiently separated from the timescales of mutations and negative feedback. Our approach and results form a next step towards a deeper understanding of the evolutionary dynamics resulting from biotic interactions.