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Fixation probabilities for multiallele Moran dynamics with weak selection

Ian Braga1,2, Lucas Wardil2, and Ricardo Martinez-Garcia1,3,4,*

  • *Contact author: r.martinez-garcia@hzdr.de
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Phys. Rev. Research 8, 043021 – Published 7 October, 2026

DOI: https://doi.org/10.1103/mcqq-jdwy

Abstract

Fixation probabilities are essential for characterizing stochastic evolutionary dynamics, but analytical results remain limited mainly to systems with two competing types. We develop a perturbative framework to compute fixation probabilities in multiallele Moran processes under weak selection. Exploiting the general structure of the backward Fokker-Planck operator in this regime, we show that fixation probabilities admit a systematic expansion around their neutral solution. We first introduce the framework for M competing alleles with multivariate polynomial fitness functions. We then apply it to three biologically motivated examples: a constant-fitness model, which we solve for an arbitrary number of alleles; a three-allele coordination game in which allele fitness increases with its frequency in the population; and a three-allele model of clonal interference between mutualistic alleles. These results extend the analytical understanding of fixation probabilities beyond pairwise interactions, establishing a framework for investigating multistrategy stochastic evolutionary dynamics.

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Phys. Rev. Research 8, 043021– Published 7 October, 2026
  • Received 13 April 2026
  • Accepted 22 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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