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Continual Evolution in Nonreciprocal Ecological Models

Feedbacks between evolution and ecology are ubiquitous, with ecological interactions determining which mutants are successful, and these mutants in turn modifying community structure. We study the evolutionary dynamics of several ecological models with overlapping niches, including consumer resource and Lotka-Volterra models. Evolution is assumed slow and extinctions are permanent, with ecological dynamics reaching a stable fixed point between introductions of invaders or mutants. When new strains are slowly added to the community, the ecosystem converges, after an initial evolutionary transient, to a diverse eco-evolutionary steady state. In this "Red Queen" phase of continual evolution, the biodiversity continues to turn over without the invasion probability of new variants getting any smaller. For resource-mediated interactions, the Red Queen phase obtains for any amount of asymmetry in the interactions between strains, and is robust to "general fitness" differences in the intrinsic growth rates of strains. Via a dynamical mean field theory framework valid for high-dimensional phenotype space, we analytically characterize the Red Queen eco-evolutionary steady state in a particular limit of model parameters. Scaling arguments enable a more general understanding of the steady state and evolutionary transients toward it. This work therefore establishes simple models of continual evolution in an ecological context without host-pathogen arms races, and points to the generality of Red Queen evolution. However, we also find other eco-evolutionary phases in simple models: For generalized Lotka-Volterra models with weakly asymmetric interactions an "oligarch" phase emerges in which the evolutionary dynamics continually slow down and a substantial fraction of the community's abundance condenses into a handful of slowly turning-over strains.

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