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Universality of evolutionary trajectories under arbitrary competition dynamics

View ORCID ProfileAndrea Mazzolini, View ORCID ProfileJacopo Grilli
doi: https://doi.org/10.1101/2021.06.17.448795
Andrea Mazzolini
1Laboratoire de physique de l’École normale supérieure (PSL University), CNRS, Sorbonne Université, and Université de Paris, 75005 Paris, France
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Jacopo Grilli
2Quantitative Life Sciences, The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste 34151, Italy
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  • For correspondence: jgrilli@ictp.it
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Abstract

The assumption of constant population size is central in population genetics. It led to a large body of results, that are robust to modeling choices and that have proven successful to understand evolutionary dynamics. In reality, allele frequencies and population size are both determined by the interaction between a population and the environment. Relaxing the constant-population assumption have two big drawbacks. It increases the technical difficulty of the analysis, and it requires specifying a mechanism for the saturation of the population size, possibly making the results contingent on model details. Here, we develop a framework that encompasses a great variety of systems with an arbitrary mechanism for population growth limitation. By using techniques based on scale separation for stochastic processes, we are able to calculate analytically properties of evolutionary trajectories, such as the fixation probability. Remarkably, these properties assume a universal form with respect to our framework, which depends on only three parameters related to the inter-generation timescale, the invasion fitness, and the carrying capacity of the strains. In other words, different systems, such as Lotka-Volterra or a chemostat model (contained in our framework), share the same evolutionary outcomes after a proper re-mapping of their parameters. An important and surprising consequence of our results is that the direction of selection can be inverted, with a population evolving to reach lower values of invasion fitness.

Competing Interest Statement

The authors have declared no competing interest.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted May 06, 2022.
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Universality of evolutionary trajectories under arbitrary competition dynamics
Andrea Mazzolini, Jacopo Grilli
bioRxiv 2021.06.17.448795; doi: https://doi.org/10.1101/2021.06.17.448795
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Universality of evolutionary trajectories under arbitrary competition dynamics
Andrea Mazzolini, Jacopo Grilli
bioRxiv 2021.06.17.448795; doi: https://doi.org/10.1101/2021.06.17.448795

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