Lambdakoalescentu

Lambdakoalescentu is a Latinized designation for the Lambda-coalescent, a family of stochastic processes used in population genetics to model the ancestral relationships of a gene sample. Unlike the classical Kingman coalescent, which allows only binary mergers of lineages, the Lambda-coalescent permits multiple ancestral lineages to merge in a single event. This framework captures skewed offspring distributions and sweepstakes reproduction found in some species, leading to genealogies with multifurcations.

The process runs backward in time, and for a sample of n lineages the coalescent events occur with rates determined by a finite measure Lambda on the interval [0,1]. If b lineages merge at once, the event rate is lambda_{n,b} = ∫_0^1 x^{b-2} (1-x)^{n-b} Λ(dx). When Lambda concentrates at 0, only binary mergers occur and the Lambda-coalescent reduces to the Kingman coalescent. Different choices of Lambda yield a variety of genealogical shapes, including rapid multiple mergers.

Key properties include the potential for simultaneous mergers and, depending on Lambda, whether the process comes down from infinity (a finite number of ancestral lineages after any positive time). Notable subclasses include Beta-coalescents, where Lambda arises from Beta distributions, modeling different degrees of reproductive skew.

Applications of lambdakoalescentu concepts appear in population-genomic analyses to infer population size histories, selection, and demographic events in species with high fecundity or temporally variable reproduction. The Lambda-coalescent framework links to coalescent theory, ancestral recombination graphs, and other models used to interpret genetic variation under non-Kingman genealogies.