Linear response theory for eco-evolutionary dynamics

Ecological and evolutionary processes often unfold on overlapping timescales, making an integrated theory of eco-evolutionary dynamics indispensable. Traditional evolutionary theories typically focus on single-species dynamics and only crudely account for niche-based competition. Conversely, niche theory captures ecological interactions but lacks evolutionary processes. Here, we bridge this gap by incorporating evolutionary dynamics into niche theory. Our framework models mutations as small phenotypic perturbations to existing species and computes the community's linear response to such perturbations. This approach illuminates two key aspects of eco-evolutionary processes. First, it mathematically decomposes a mutant's fitness into three easily interpretable components: strategy (competitive ability), innovation (novelty), and naive fitness (mortality/maintenance rate). Each of these components have clear geometric interpretations as vectors in niche space. Second, our theory can predict how a successful mutant will affect the community, including changes in species abundances and resource levels. We illustrate the explanatory power of our framework using a variety of consumer-resource models, including the MacArthur, linear resource, and microbial consumer resource models.