Betacoalescent

A betacoalescent is a class of stochastic processes used in the study of coalescent theory, which models the genealogical relationships within a sample of individuals from a population. These processes generalize the classical coalescent models, such as Kingman's coalescent, by allowing multiple lineages to merge simultaneously, capturing phenomena like sweepstakes reproduction or highly skewed offspring distributions.

The defining feature of a betacoalescent is its coalescence mechanism, characterized by a measure that determines the rates at which different numbers of lineages coalesce. Specifically, for a sample of n lineages, the process specifies the probabilities of multiple mergers occurring at each coalescent event. This flexibility provides a richer framework to model real-world populations where reproductive success is highly uneven.

Betacoalescents are mathematically formalized as Markov processes on the space of partitions of the sample. They are characterized by a Λ-measure, which governs the rates and sizes of multiple mergers. These processes are related to Λ-coalescents, introduced by Pitman and Sagitov in the early 2000s, and include well-known models like the Beta-coalescent, where the measure is a Beta distribution.

Applications of betacoalescents span population genetics, epidemiology, and evolutionary biology, offering insights into ancestral genealogy under diverse reproductive strategies. They provide a flexible modeling framework for genetic variation and help interpret observed genetic data, especially in populations with non-standard reproduction patterns.

Overall, betacoalescents represent an important extension of classical coalescent theory, broadening the scope of ancestral process models to accommodate complex biological realities.