Labelled partitions in action: recombination, selection, mutation, and more
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913525715173376 |
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| author | Alberti, Frederic |
| author_facet | Alberti, Frederic |
| contents | In this paper, we consider the evolution of an (infinitely large) population under recombination and additional evolutionary forces, modelled by a measure-valued ordinary differential equation. We provide a stochastic representation for the solution of this model via duality to a new labelled partitioning process with Markovian labels. In the special case of single-crossover, this leads to a recursive solution formula. This extends (and unifies) previous results on the selection-recombination equation. As a concrete example, we consider the selection-mutation-recombination equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2203_10874 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Labelled partitions in action: recombination, selection, mutation, and more Alberti, Frederic Probability Populations and Evolution 60J25, 92D15 In this paper, we consider the evolution of an (infinitely large) population under recombination and additional evolutionary forces, modelled by a measure-valued ordinary differential equation. We provide a stochastic representation for the solution of this model via duality to a new labelled partitioning process with Markovian labels. In the special case of single-crossover, this leads to a recursive solution formula. This extends (and unifies) previous results on the selection-recombination equation. As a concrete example, we consider the selection-mutation-recombination equation. |
| title | Labelled partitions in action: recombination, selection, mutation, and more |
| topic | Probability Populations and Evolution 60J25, 92D15 |
| url | https://arxiv.org/abs/2203.10874 |