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We consider a single genetic locus with two alleles $A_1$ and $A_2$ in alarge haploid population. The locus is subject to selection and two-way, orrecurrent, mutation. Assuming the allele frequencies follow a Wright-Fisherdiffusion and have reached stationarity, we describe the asymptotic behaviorsof the conditional gene genealogy and the latent mutations of a sample withknown allele counts, when the count $n_1$ of allele $A_1$ is fixed, and wheneither or both the sample size $n$ and the selection strength$\lvert\beta\rvert$ tend to infinity. Our study extends previous work underneutrality to the case of non-neutral rare alleles, asserting that whenselection is not too strong relative to the sample size, even if it is stronglypositive or strongly negative in the usual sense ($\beta\to -\infty$ or$\beta\to +\infty$), the number of latent mutations of the $n_1$ copies ofallele $A_1$ follows the same distribution as the number of alleles in theEwens sampling formula. On the other hand, very strong positive selectionrelative to the sample size leads to neutral gene genealogies with a singleancient latent mutation. We also demonstrate robustness of our asymptoticresults against changing population sizes, when one of $\lvert\beta\rvert$ or$n$ is large.

Latent mutations in the ancestries of alleles under selection