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

QST 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, FST . Thus, QST -FST comparison is used to infer selection: selective divergence when QST  > FST , or convergence when QST  < FST. 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 FIS  > 0 (higher when FIS  < 0). Then, we used an island model simulation approach to investigate the impact of inbreeding and dominance on the QST -FST framework in a hierarchical population structure. We show that, while differentiation at the lower hierarchical level (QSR ) is a monotonic function of migration, differentiation at the upper level (QRT ) is not. In the case of additive inheritance, we show that inbreeding inflates the variance of QRT , which can increase the frequency of QRT  > FRT 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.