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Abstract We consider a simple diploid population-genetic model with potentially high variability of offspring numbers among individuals. Specifically, against a backdrop of Wright–Fisher reproduction and no selection, there is an additional probability that a big family occurs, meaning that a pair of individuals has a number of offspring on the order of the population size. We study how the pedigree of the population generated under this model affects the ancestral genetic process of a sample of size two at a single autosomal locus without recombination. Our population model is of the type for which multiple-merger coalescent processes have been described. We prove that the conditional distribution of the pairwise coalescence time given the random pedigree converges to a limit law as the population size tends to infinity. This limit law may or may not be the usual exponential distribution of the Kingman coalescent, depending on the frequency of big families. But because it includes the number and times of big families, it differs from the usual multiple-merger coalescent models. The usual multiple-merger coalescent models are seen as describing the ancestral process marginal to, or averaging over, the pedigree. In the limiting ancestral process conditional on the pedigree, the intervals between big families can be modeled using the Kingman coalescent but each big family causes a discrete jump in the probability of coalescence. Analogous results should hold for larger samples and other population models. We illustrate these results with simulations and additional analysis, highlighting their implications for inference and understanding of multilocus data.
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This content will become publicly available on February 13, 2026
Multiple merger coalescent inference of effective population size
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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- Award ID(s):
- 2143242
- PAR ID:
- 10589235
- Editor(s):
- NA
- Publisher / Repository:
- The Royal Society Publishing
- Date Published:
- Journal Name:
- Philosophical Transactions of the Royal Society B: Biological Sciences
- Volume:
- 380
- Issue:
- 1919
- ISSN:
- 0962-8436
- Subject(s) / Keyword(s):
- Multiple mergers coalescent, Gaussian processes,Lambda-coalescent, Beta-coalescent
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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