The coalescent in finite populations with arbitrary, fixed structure
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916305959911424 |
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| author | Allen, Benjamin McAvoy, Alex |
| author_facet | Allen, Benjamin McAvoy, Alex |
| contents | The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial, age, and class structure, along with other features of real-world populations. To further extend the range of population structures to which coalescent theory applies, we formulate a coalescent process for a broad class of neutral drift models with arbitrary -- but fixed -- spatial, age, sex, and class structure, haploid or diploid genetics, and any fixed mating pattern. Here, the coalescent is represented as a random sequence of mappings $\mathcal{C} = \left(C_t\right)_{t=0}^\infty$ from a finite set $G$ to itself. The set $G$ represents the ``sites'' (in individuals, in particular locations and/or classes) at which these alleles can live. The state of the coalescent, $C_t:G \to G$, maps each site $g \in G$ to the site containing $g$'s ancestor, $t$ time-steps into the past. Using this representation, we define and analyze coalescence time, coalescence branch length, mutations prior to coalescence, and stationary probabilities of identity-by-descent and identity-by-state. For low mutation, we provide a recipe for computing identity-by-descent and identity-by-state probabilities via the coalescent. Applying our results to a diploid population with arbitrary sex ratio $r$, we find that measures of genetic dissimilarity, among any set of sites, are scaled by $4r(1-r)$ relative to the even sex ratio case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_02880 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The coalescent in finite populations with arbitrary, fixed structure Allen, Benjamin McAvoy, Alex Populations and Evolution Probability 92D15 The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial, age, and class structure, along with other features of real-world populations. To further extend the range of population structures to which coalescent theory applies, we formulate a coalescent process for a broad class of neutral drift models with arbitrary -- but fixed -- spatial, age, sex, and class structure, haploid or diploid genetics, and any fixed mating pattern. Here, the coalescent is represented as a random sequence of mappings $\mathcal{C} = \left(C_t\right)_{t=0}^\infty$ from a finite set $G$ to itself. The set $G$ represents the ``sites'' (in individuals, in particular locations and/or classes) at which these alleles can live. The state of the coalescent, $C_t:G \to G$, maps each site $g \in G$ to the site containing $g$'s ancestor, $t$ time-steps into the past. Using this representation, we define and analyze coalescence time, coalescence branch length, mutations prior to coalescence, and stationary probabilities of identity-by-descent and identity-by-state. For low mutation, we provide a recipe for computing identity-by-descent and identity-by-state probabilities via the coalescent. Applying our results to a diploid population with arbitrary sex ratio $r$, we find that measures of genetic dissimilarity, among any set of sites, are scaled by $4r(1-r)$ relative to the even sex ratio case. |
| title | The coalescent in finite populations with arbitrary, fixed structure |
| topic | Populations and Evolution Probability 92D15 |
| url | https://arxiv.org/abs/2207.02880 |