The coalescent in finite populations with arbitrary, fixed structure
Abstract
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 C=Ctt=0∞ 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, Ct:G→G, maps each site g∈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.
- Publication:
-
Theoretical Population Biology
- Pub Date:
- August 2024
- DOI:
- 10.1016/j.tpb.2024.06.004
- arXiv:
- arXiv:2207.02880
- Bibcode:
- 2024TPBio.158..150A
- Keywords:
-
- Coalescent theory;
- Identity-by-descent;
- Genetic drift;
- Random mapping;
- Quantitative Biology - Populations and Evolution;
- Mathematics - Probability;
- 92D15
- E-Print:
- 71 pages, 2 figures