Understanding how mutations evolve on Y chromosomes is central to explaining the origin, diversity and persistence of sex chromosomes. Mutations occurring on the Y chromosome in sexual populations experience selective dynamics that differ markedly from those on autosomes, due to a reduced effective population size and the presence of large non-recombining regions containing alleles maintained in a permanently heterozygous state. These specific features alter gene transmission in the Y chromosome population compared to autosomes, even within the same pedigree. Here, we provide a two-sex diploid Wright-Fisher model that explicitly incorporates both sex chromosomes and autosomes within a unified population framework, in order to capture the influence of these specificities on the fate of mutations, not only considering fixation probabilities but also segregation times. We use diffusion approximations and provide analytical and numerical tools to compute these quantities across a wide range of parameters and selection regimes. We recover classical results on fixation probabilities in various scenarios, including purely beneficial, deleterious or overdominant mutations, and extend them in the light of mean segregation time, a key but often overlooked determinant of evolutionary outcomes over finite timescales. In particular, our analyses show that overdominant mutations are overall more likely to fix in observable time windows on the Y chromosome than on autosomes. Individual-based simulations corroborate our approximations and highlight parameter regimes where the theoretical approach is particularly useful, especially for parameter values inducing long segregation times or small fixation probabilities, for which simulations are impractical. Our results provide a comprehensive and tractable framework for clarifying how chromosome-specific features shape evolutionary dynamics beyond fixation probabilities alone.
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