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1. Recombination-aware phylogeographic inference using the structured coalescent with ancestral recombination

   https://doi.org/10.1371/journal.pcbi.1010422  

   Guo, Fangfang; Carbone, Ignazio; Rasmussen, David A. (August 2022, PLOS Computational Biology)

   Schiffels, Stephan (Ed.)

   Movement of individuals between populations or demes is often restricted, especially between geographically isolated populations. The structured coalescent provides an elegant theoretical framework for describing how movement between populations shapes the genealogical history of sampled individuals and thereby structures genetic variation within and between populations. However, in the presence of recombination an individual may inherit different regions of their genome from different parents, resulting in a mosaic of genealogical histories across the genome, which can be represented by an Ancestral Recombination Graph (ARG). In this case, different genomic regions may have different ancestral histories and so different histories of movement between populations. Recombination therefore poses an additional challenge to phylogeographic methods that aim to reconstruct the movement of individuals from genealogies, although also a potential benefit in that different loci may contain additional information about movement. Here, we introduce the Structured Coalescent with Ancestral Recombination (SCAR) model, which builds on recent approximations to the structured coalescent by incorporating recombination into the ancestry of sampled individuals. The SCAR model allows us to infer how the migration history of sampled individuals varies across the genome from ARGs, and improves estimation of key population genetic parameters such as population sizes, recombination rates and migration rates. Using the SCAR model, we explore the potential and limitations of phylogeographic inference using full ARGs. We then apply the SCAR to lineages of the recombining fungus Aspergillus flavus sampled across the United States to explore patterns of recombination and migration across the genome. 

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2. Fractional coalescent

   https://doi.org/10.1073/pnas.1810239116  

   Mashayekhi, Somayeh; Beerli, Peter (March 2019, Proceedings of the National Academy of Sciences)

   An approach to the coalescent, the fractional coalescent (f-coalescent), is introduced. The derivation is based on the discrete-time Cannings population model in which the variance of the number of offspring depends on the parameter α. This additional parameter α affects the variability of the patterns of the waiting times; values of $\alpha <1$lead to an increase of short time intervals, but occasionally allow for very long time intervals. When $\alpha =1$, the f-coalescent and the Kingman’s n-coalescent are equivalent. The distribution of the time to the most recent common ancestor and the probability that n genes descend from m ancestral genes in a time interval of length T for the f-coalescent are derived. The f-coalescent has been implemented in the population genetic model inference software Migrate. Simulation studies suggest that it is possible to accurately estimate α values from data that were generated with known α values and that the f-coalescent can detect potential environmental heterogeneity within a population. Bayes factor comparisons of simulated data with $\alpha <1$and real data (H1N1 influenza and malaria parasites) showed an improved model fit of the f-coalescent over the n-coalescent. The development of the f-coalescent and its inclusion into the inference program Migratefacilitates testing for deviations from the n-coalescent. 

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3. The nested Kingman coalescent: speed of coming down from infinity

   Blancas, Airam; Rogers, Tim; Schweinsberg, Jason; Siri-Jegousse, Arno (January 2019, The Annals of applied probability)

   The nested Kingman coalescent describes the ancestral tree of a population undergoing neutral evolution at the level of individuals and at the level of species, simultaneously. We study the speed at which the number of lineages descends from infinity in this hierarchical coalescent process and prove the existence of an early-time phase during which the number of lineages at time t decays as 2γ/ct^2, where c is the ratio of the coalescence rates at the individual and species levels, and the constant γ ≈ 3.45 is derived from a recursive distributional equation for the number of lineages contained within a species at a typical time. 

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4. Multiple merger coalescent inference of effective population size

   https://doi.org/10.1098/rstb.2023.0306  

   Zhang, Julie; Palacios, Julia A (February 2025, Philosophical Transactions of the Royal Society B: Biological Sciences)

   NA (Ed.)

   Variation in a sample of molecular sequence data informs about the past evolutionary history of the sample’s population. Traditionally, Bayesian modelling coupled with the standard coalescent is used to infer the sample’s bifurcating genealogy and demographic and evolutionary parameters such as effective population size and mutation rates. However, there are many situations where binary coalescent models do not accurately reflect the true underlying ancestral processes. Here, we propose a Bayesian non-parametric method for inferring effective population size trajectories from a multifurcating genealogy under the Lambda-coalescent. In particular, we jointly estimate the effective population size and the model parameter for the Beta-coalescent model, a special type of Lambda-coalescent. Finally, we test our methods on simulations and apply them to study various viral dynamics as well as Japanese sardine population size changes over time. The code and vignettes can be found in the phylodyn package. This article is part of the theme issue ‘“A mathematical theory of evolution”: phylogenetic models dating back 100 years’. 

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5. Approximations to the expectations and variances of ratios of tree properties under the coalescent

   https://doi.org/10.1093/g3journal/jkac205  

   Lappo, Egor; Rosenberg, Noah A.; Hernandez, ed., R. (August 2022, G3 Genes|Genomes|Genetics)

   Abstract Properties of gene genealogies such as tree height (H), total branch length (L), total lengths of external (E) and internal (I) branches, mean length of basal branches (B), and the underlying coalescence times (T) can be used to study population-genetic processes and to develop statistical tests of population-genetic models. Uses of tree features in statistical tests often rely on predictions that depend on pairwise relationships among such features. For genealogies under the coalescent, we provide exact expressions for Taylor approximations to expected values and variances of ratios Xn/Yn, for all 15 pairs among the variables {Hn,Ln,En,In,Bn,Tk}, considering n leaves and 2≤k≤n. For expected values of the ratios, the approximations match closely with empirical simulation-based values. The approximations to the variances are not as accurate, but they generally match simulations in their trends as n increases. Although En has expectation 2 and Hn has expectation 2 in the limit as n→∞, the approximation to the limiting expectation for En/Hn is not 1, instead equaling π2/3−2≈1.28987. The new approximations augment fundamental results in coalescent theory on the shapes of genealogical trees. 

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