Source: Adv. in Appl. Probab. Volume 44, Number 2
(2012), 408-428.
Many applications in genetic analyses utilize sampling distributions, which
describe the probability of observing a sample of DNA sequences randomly drawn
from a population. In the one-locus case with special models of mutation, such
as the infinite-alleles model or the finite-alleles parent-independent mutation
model, closed-form sampling distributions under the coalescent have been known
for many decades. However, no exact formula is currently known for more general
models of mutation that are of biological interest. In this paper, models with
finitely-many alleles are considered, and an urn construction related to the
coalescent is used to derive approximate closed-form sampling formulae for an
arbitrary irreducible recurrent mutation model or for a reversible recurrent
mutation model, depending on whether the number of distinct observed allele
types is at most three or four, respectively. It is demonstrated empirically
that the formulae derived here are highly accurate when the per-base mutation
rate is low, which holds for many biological organisms.
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