Regular ArticleSimulating Probability Distributions in the Coalescent
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A characterisation of the reconstructed birth–death process through time rescaling
2020, Theoretical Population BiologyCitation Excerpt :We briefly review relevant known results which we will rely on throughout the paper. Secondly, the coalescent with variable population size, as described by Griffiths and Tavaré (1994), can be described as an inhomogeneous pure-death process, where the death rate is quadratic in the number of lineages and depends on a population size function. Because the death rate of the RRP is linear in the number of lineages, there is no population size function which would equate the two models.
Allele frequency spectra in structured populations: Novel-allele probabilities under the labelled coalescent
2020, Theoretical Population BiologyCitation Excerpt :Restricted to the infinite-alleles model of mutation, it can be solved inductively, by progressively incrementing sample size, number of distinct allelic classes, and number of singleton alleles, to produce AFS probabilities for samples derived from structured populations (Uyenoyama et al., 2019). A number of works have explored methods for approximating the distribution of the immediate ancestor of an observed sample in a variety of demographic contexts (e.g., Hoppe, 1987; Griffiths and Tavaré, 1994a,b; Stephens and Donnelly, 2000; Tavaré, 2004; De Iorio and Griffiths, 2004b). By addressing the distribution of the next-sampled gene, Stephens and Donnelly (2000) developed a more efficient class of importance sampling (IS) proposal distributions for generating genealogical histories.
Developments in coalescent theory from single loci to chromosomes
2020, Theoretical Population BiologyInductive determination of allele frequency spectrum probabilities in structured populations
2019, Theoretical Population BiologyAncestral inference from haplotypes and mutations
2018, Theoretical Population BiologyComputing the joint distribution of the total tree length across loci in populations with variable size
2017, Theoretical Population BiologyCitation Excerpt :Moreover, ancient and contemporary population structure can lead to the accumulation of private genetic variation in certain sub-populations. Methods to study genetic variation, or perform inference, in populations with varying size or more complex demographic histories have been developed based on the Wright–Fisherdiffusion, describing the evolution of population allele frequencies forward in time (Griffiths, 2003; Živković, et al., 2015; Gutenkunst et al., 2009; Excoffier et al., 2013), or the Coalescent process, a model for the genealogical relationship in a sample of individuals (Griffiths and Tavaré, 1994; Griffiths and Marjoram, 1996; Griffiths and Tavaré, 1998; Živković and Wiehe, 2008; Bhaskar et al., 2015; Kamm et al., 2017). A powerful representation of genetic variation data that has been used in this context is the Site-Frequency-Spectrum.