Whither Pst? The approximation of Qst by Pst in evolutionary and conservation biology

Local adaptation through natural selection can be inferred in case the additive genetic divergence in a quantitative trait across populations (Q(st)) exceeds the neutral expectation based on differentiation of neutral alleles across these populations (e.g. F-st). As such, measuring Q(st) in relation to neutral differentiation presents a first-line investigation applicable in evolutionary biology (selection on functional genes) and conservation biology (identification of locally adapted coding genes). However, many species, especially those in need of conservation actions, are not amenable for the kind of breeding design required to estimate either narrow- or broad-sense Q(st). In such cases, Q(st) has been approximated by the phenotypic divergence in a trait across populations (P-st). I here argue that the critical aspect for how well P-st approximates Q(st) depends on the extent that additive genetic effects determine variation between populations relative to within populations. I review how the sensitivity of conclusions regarding local adaptation based on P-st have been evaluated in the literature and find that many studies make a anticonservative null assumption in estimating P-st and/or use a nonconservative approach to explore sensitivity of their conclusions. Data from two studies that have provided a second, independent assessment of selection in their system suggest that P-st-F-st comparisons should be interpreted very conservatively. I conclude with recommendations for improving the robustness of the inferences drawn from comparing P-st with neutral differentiation.