2021/12/17 by Claus Vogl, Vogl, Claus, Sandra Peer +3
Biochemistry, Genetics and Molecular Biology · #Applications (stat.AP) #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Computer and information sciences #Genetic Associations and Epidemiology #Genetic and phenotypic traits in livestock #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.2112.09394
openalex publication_date 2021/12/17 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
Inference of the marginal likelihood of sample allele configurations using backward algorithms yields identical results with the Kingman coalescent, the Moran model, and the diffusion model (up to a scaling of time). For inference of probabilities of ancestral population allele frequencies at any given point in the past - either of discrete ancestral allele configurations as in the coalescent, or of ancestral allele proportions as in the backward diffusion - backward approaches need to be combined with corresponding forward ones. This is done in so-called forward-backward algorithms. In this article, we utilize orthogonal polynomials in forward-backward algorithms. They enable efficient calculation of past allele configurations of an extant sample and probabilities of ancestral population allele frequencies in equilibrium and in non-equilibrium. We show that the genealogy of a sample is fully described by the backward polynomial expansion of the marginal likelihood of its allele configuration.