Source: J. Appl. Probab.
Volume 47, Number 3
Recurrence equations for the number of types and the frequency of each type in
a random sample drawn from a finite population undergoing discrete,
nonoverlapping generations and reproducing according to the Cannings
exchangeable model are deduced under the assumption of a mutation scheme with
infinitely many types. The case of overlapping generations in discrete time is
also considered. The equations are developed for the Wright-Fisher model and
the Moran model, and extended to the case of the limit coalescent with
nonrecurrent mutation as the population size goes to ∞ and the mutation
rate to 0. Computations of the total variation distance for the distribution of
the number of types in the sample suggest that the exact Moran model provides a
better approximation for the sampling formula under the exact Wright-Fisher
model than the Ewens sampling formula in the limit of the Kingman coalescent
with nonrecurrent mutation. On the other hand, this model seems to provide a
good approximation for a Λ-coalescent with nonrecurrent mutation as long
as the probability of multiple mergers and the mutation rate are small enough.
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