Ecological and evolutionary dynamics of communities are inexorably intertwined. The ecological state determines the fate of newly arising mutants, and mutations that increase in frequency can reshape the ecological dynamics. Evolutionary game theory and its extensions within adaptive dynamics have been the mathematical frameworks for understanding this interplay, leading to notions such as evolutionarily stable states (ESS) in which no mutations are favoured, and evolutionary branching points near which the population diversifies. A central assumption behind these theoretical treatments has been that mutations are rare so that the ecological dynamics has time to equilibrate after every mutation. A fundamental question is whether qualitatively new phenomena can arise when mutations are frequent. Here, we describe an adaptive diversification process that robustly leads to complex ESS, despite the fact that such communities are unreachable through a step-by-step evolutionary process. Rather, the system as a whole tunnels between collective states over a short timescale. The tunnelling rate is a sharply increasing function of the rate at which mutations arise in the population. This makes the emergence of ESS communities virtually impossible in small populations, but generic in large ones. Moreover, communities emerging through this process can spatially spread as single replication units that outcompete other communities. Overall, this work provides a qualitatively new mechanism for adaptive diversification and shows that complex structures can generically evolve even when no step-by-step evolutionary path exists.
Abstract:Ecological and evolutionary dynamics of communities are inexorably intertwined. The ecological state determines the fate of newly arising mutants, and mutations that increase in frequency can reshape the ecological dynamics. Evolutionary game theory and its extensions within adaptive dynamics (AD) have been the mathematical frameworks for understanding this interplay, leading to notions such as Evolutionary Stable States (ESS) in which no mutations are favored, and evolutionary branching points near which the population diversifies. A central assumption behind these theoretical treatments has been that mutations are rare so that the ecological dynamics has time to equilibrate after every mutation. A fundamental question is whether qualitatively new phenomena can arise when mutations are frequent. Here we describe an adaptive diversification process that robustly leads to complex ESS, despite the fact that such communities are unreachable through a step--by--step evolutionary process. Rather, the system as a whole tunnels between collective states over a short time scale. The tunneling rate is a sharply increasing function of the rate with which mutations arise in the population. This makes the emergence of ESS communities virtually impossible in small populations, but generic in large ones. Moreover, communities emerging through this process can spatially spread as single replication units that outcompete other communities. Overall, this work provides a qualitatively new mechanism for adaptive diversification and shows that complex structures can generically evolve even when no step--by--step evolutionary path exists.. CC-BY 4.0 International license peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/271015 doi: bioRxiv preprint first posted online Feb. 24, 2018; Main TextUnderstanding the consequences of the feedback between ecological and evolutionary dynamics is a fundamental challenge 1--6 , particularly in asexual microbial communities, where new strains with altered ecological interactions can readily arise through mutational events such as replication errors and horizontal gene transfer 7--14 . In the absence of mutations, the strain abundance dynamics can be represented as a non--linear dynamical system with fixed dimensionality determined by the number of strains 15--18 , which allows us to understand and classify long--term community composition in terms of dynamical attractors. It is far less clear, however, how to analyze the dynamics when mutations stochastically introduce new dimensions and ecological interactions 19--22 .Important progress was made with the advent of Evolutionary Game Theory 23--26 , which established the notion of evolutionary stable states as long--term endpoints of the eco--evolutionary dynamics. An evolutionary stable state is a community that has reached an ecological attractor that cannot be invaded by any possible mutant. Therefore, an evolutionary stable communit...
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