2025/04/16 by Marta Dai Pra, Pra, Marta Dai, Alison Etheridge +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Medicine · Social Sciences · #60J70 #60J90 #60K35 #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2504.11875
openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We introduce an individual-based model for structured populations undergoing demographic bottlenecks, i.e. drastic reductions in population size that last many generations and can have arbitrary shapes. We first show that the (non-Markovian) allele-frequency process converges to a Markovian diffusion process with jumps in a suitable relaxation of the Skorokhod J1 topology. Backward in time we find that genealogies of samples of individuals are described by multi-type Ξ-coalescents presenting multiple simultaneous mergers with simultaneous migrations. These coalescents are also moment-duals of the limiting jump diffusions. We then show through a numerical study that our model is flexible and can predict various shapes for the site frequency spectrum, consistent with real data, using a small number of interpretable parameters.