Browsing by Author "Takebayashi, Naoki"

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Open Access
Allele frequency spectra in structured populations: Novel-allele probabilities under the labelled coalescent.
(Theoretical population biology, 2020-06) Uyenoyama, Marcy K; Takebayashi, Naoki; Kumagai, Seiji
We address the effect of population structure on key properties of the Ewens sampling formula. We use our previously-introduced inductive method for determining exact allele frequency spectrum (AFS) probabilities under the infinite-allele model of mutation and population structure for samples of arbitrary size. Fundamental to the sampling distribution is the novel-allele probability, the probability that given the pattern of variation in the present sample, the next gene sampled belongs to an as-yet-unobserved allelic class. Unlike the case for panmictic populations, the novel-allele probability depends on the AFS of the present sample. We derive a recursion that directly provides the marginal novel-allele probability across AFSs, obviating the need first to determine the probability of each AFS. Our explorations suggest that the marginal novel-allele probability tends to be greater for initial samples comprising fewer alleles and for sampling configurations in which the next-observed gene derives from a deme different from that of the majority of the present sample. Comparison to the efficient importance sampling proposals developed by De Iorio and Griffiths and colleagues indicates that their approximation for the novel-allele probability generally agrees with the true marginal, although it may tend to overestimate the marginal in cases in which the novel-allele probability is high and migration rates are low.
Open Access
Evolution of the sex ratio and effective number under gynodioecy and androdioecy.
(Theoretical population biology, 2017-12) Uyenoyama, Marcy K; Takebayashi, Naoki
We address the evolution of effective number of individuals under androdioecy and gynodioecy. We analyze dynamic models of autosomal modifiers of weak effect on sex expression. In our zygote control models, the sex expressed by a zygote depends on its own genotype, while in our maternal control models, it depends on the genotype of its maternal parent. Our analysis unifies full multi-dimensional local stability analysis with the Li-Price equation, which for all its heuristic appeal, describes evolutionary change over a single generation. We define a point in the neighborhood of a fixation state from which a single-generation step indicates the asymptotic behavior of the frequency of a modifier allele initiated at an arbitrary point near the fixation state. A concept of heritability appropriate for the evolutionary modification of sex emerges from the Li-Priceframework. We incorporate our theoretical analysis into our previously-developed Bayesian inference framework to develop a new method for inferring the viability of gonochores (males or females) relative to hermaphrodites. Applying this approach to microsatellite data derived from natural populations of the gynodioecious plant Schiedea salicaria and the androdioecious killifish Kryptolebias marmoratus, we find that while female and hermaphrodite S. salicaria appear to have similar viabilities, male K. marmoratus appear to survive to reproductive age at less than half the rate of hermaphrodites.
Open Access
Inductive determination of allele frequency spectrum probabilities in structured populations.
(Theoretical population biology, 2019-10) Uyenoyama, Marcy K; Takebayashi, Naoki; Kumagai, Seiji
We present a method for inductively determining exact allele frequency spectrum (AFS) probabilities for samples derived from a population comprising two demes under the infinite-allele model of mutation. This method builds on a labeled coalescent argument to extend the Ewens sampling formula (ESF) to structured populations. A key departure from the panmictic case is that the AFS conditioned on the number of alleles in the sample is no longer independent of the scaled mutation rate (θ). In particular, biallelic site frequency spectra, widely-used in explorations of genome-wide patterns of variation, depend on the mutation rate in structured populations. Variation in the rate of substitution across loci and through time may contribute to apparent distortions of site frequency spectra exhibited by samples derived from structured populations.