Generalization of the Q ST framework in hierarchically structured populations: Impacts of inbreeding and dominance.

Q _ST is a differentiation parameter based on the decomposition of the genetic variance of a trait. In the case of additive inheritance and absence of selection, it is analogous to the genic differentiation measured on individual loci, F _ST . Thus, Q _ST -F _ST comparison is used to infer selection: selective divergence when Q _ST  > F _ST , or convergence when Q _ST  < F _{ST .} The definition of Q-statistics was extended to two-level hierarchical population structures with Hardy-Weinberg equilibrium. Here, we generalize the Q-statistics framework to any hierarchical population structure. First, we developed the analytical definition of hierarchical Q-statistics for populations not at Hardy-Weinberg equilibrium. We show that the Q-statistics values obtained with the Hardy-Weinberg definition are lower than their corresponding F-statistics when F _IS  > 0 (higher when F _IS  < 0). Then, we used an island model simulation approach to investigate the impact of inbreeding and dominance on the Q _ST -F _ST framework in a hierarchical population structure. We show that, while differentiation at the lower hierarchical level (Q _SR ) is a monotonic function of migration, differentiation at the upper level (Q _RT ) is not. In the case of additive inheritance, we show that inbreeding inflates the variance of Q _RT , which can increase the frequency of Q _RT  > F _RT cases. We also show that dominance drastically reduces Q-statistics below F-statistics for any level of the hierarchy. Therefore, high values of Q-statistics are good indicators of selection, but low values are not in the case of dominance.
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