Strong amplification of quantitative genetic variation under a balance between mutation and fluctuating stabilizing selection

The observation of high heritability in most quantitative traits has been a long-standing puzzle. There is a general consensus that simple models of quantitative genetic variation, which are mostly founded on the assumption of mutation-selection balance in a constant environment, have failed to explain high heritability. To make matters worse, the reasons for failure are unknown, leaving little to guide future model developments. Here we revisit this puzzle by taking the canonical Latter-Bulmer model and relaxing the assumption of perfect environmental stasis. Instead we assume that the trait optimum changes slowly but steadily in a random walk (specifically, an Ornstein-Uhlenbeck process), similar to standard models used for phylogenetic comparative methods. We show that our model behaves qualitatively differently to its stationary optimum counterpart even though the optimum only changes slowly. This is the result of a feedback between the adaptation rate and selection coefficient fluctuations. The heritability predictions resulting from this feedback are more consistent with observations and also less sensitive to evolutionary parameters than the classical LB model. We derive a simple formula to predict genetic variation under random walk optimum fluctuations which helps to explain some of our counter-intuitive results and which should be useful for understanding the potential influence of fluctuations in future work. Since the feedback driving our results should also occur in more complex models e.g. with multiple traits, we argue that environmental change has been an essential biological ingredient missing in previous mutation-selection balance models of quantitative trait heritability.