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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. [ABSTRACT FROM AUTHOR]

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 . 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., (© 2017 John Wiley & Sons Ltd.)