The probability distribution under a population divergence model of the number of genetic founding lineages of a population or species

The composition of genetic variation in a population or species is shaped by the number of events that led to the founding of the group. We consider a neutral coalescent model of two populations, where a derived population is founded as an offshoot of an ancestral population. For a given locus, using both recursive and nonrecursive approaches, we compute the probability distribution of the number of genetic founding lineages that have given rise to the derived population. This number of genetic founding lineages is defined as the number of ancestral individuals that contributed at the locus to the present-day derived population, and is formulated in terms of interspecific coalescence events. The effects of sample size and divergence time on the probability distribution of the number of founding lineages are studied in detail. For 99.99% of the loci in the derived population to each have one founding lineage, the two populations must be separated for 9.9N generations. However, only approximately 0.87N generations must pass since divergence for 99.99% of the loci to have <6 founding lineages. Our results are useful as a prior expectation on the number of founding lineages in scenarios that involve the evolution of one population from the splitting of an ancestral group, such as in the colonization of islands, the formation of polyploid species, and the domestication of crops and livestock from wild ancestors.