Fixation probabilities for multi-allele Moran dynamics with weak selection
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915935295635456 |
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| author | Braga, Ian Wardil, Lucas Martinez-Garcia, Ricardo |
| author_facet | Braga, Ian Wardil, Lucas Martinez-Garcia, Ricardo |
| contents | 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 multi-allele 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 in a general case with $M$ competing alleles and arbitrary fitness functions, and then apply it to three biologically motivated examples: a simple model of three competing alleles with a constant fitness function, a coordination game in which allele fitness increases with its frequency in the population, and a model of clonal interference between mutualistic alleles. These results extend the analytical understanding of fixation probabilities beyond pairwise interactions, establishing a framework for investigating multi-strategy stochastic evolutionary dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_12004 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fixation probabilities for multi-allele Moran dynamics with weak selection Braga, Ian Wardil, Lucas Martinez-Garcia, Ricardo Populations and Evolution Statistical Mechanics 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 multi-allele 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 in a general case with $M$ competing alleles and arbitrary fitness functions, and then apply it to three biologically motivated examples: a simple model of three competing alleles with a constant fitness function, a coordination game in which allele fitness increases with its frequency in the population, and a model of clonal interference between mutualistic alleles. These results extend the analytical understanding of fixation probabilities beyond pairwise interactions, establishing a framework for investigating multi-strategy stochastic evolutionary dynamics. |
| title | Fixation probabilities for multi-allele Moran dynamics with weak selection |
| topic | Populations and Evolution Statistical Mechanics |
| url | https://arxiv.org/abs/2604.12004 |