A general multi-scale description of metastable adaptive motion across fitness valleys.

Autor: Esser M; Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität, Endenicher Allee 60, 53115, Bonn, Germany. manuel.esser@uni-bonn.de., Kraut A; Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität, Endenicher Allee 60, 53115, Bonn, Germany.; School of Mathematics, University of Minnesota - Twin Cities, 206 Church St SE, Minneapolis, MN, 55455, USA.
Jazyk: angličtina
Zdroj: Journal of mathematical biology [J Math Biol] 2024 Oct 01; Vol. 89 (4), pp. 46. Date of Electronic Publication: 2024 Oct 01.
DOI: 10.1007/s00285-024-02143-3
Abstrakt: We consider a stochastic individual-based model of adaptive dynamics on a finite trait graph G = ( V , E ) . The evolution is driven by a linear birth rate, a density dependent logistic death rate and the possibility of mutations along the directed edges in E. We study the limit of small mutation rates for a simultaneously diverging population size. Closing the gap between Bovier et al. (Ann Appl Probab 29(6):3541-358, 2019) and Coquille et al. (Electron J Probab 26:1-37, 2021) we give a precise description of transitions between evolutionary stable conditions (ESC), where multiple mutations are needed to cross a valley in the fitness landscape. The system shows a metastable behaviour on several divergent time scales, corresponding to the widths of these fitness valleys. We develop the framework of a meta graph that is constituted of ESCs and possible metastable transitions between them. This allows for a concise description of the multi-scale jump chain arising from concatenating several jumps. Finally, for each of the various time scales, we prove the convergence of the population process to a Markov jump process visiting only ESCs of sufficiently high stability.
(© 2024. The Author(s).)
Databáze: MEDLINE
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