Effect of migration and environmental heterogeneity on the maintenance of quantitative variation: a simulation study

The paradox of high genetic variation observed in traits under stabilizing selection is a longstanding problem in evolutionary theory, as mutation rates are 10-100 times too low to explain observed levels of standing genetic variation under classic models of mutation-selection balance. Here, we use individual-based simulations to explore the effect of various types of environmental heterogeneity on the maintenance of genetic variation (V A ) for a quantitative trait under stabilizing selection. We find that V A is maximized at intermediate migration rates in spatially heterogeneous environments, and that the observed patterns are robust to changes in population size. Spatial environmental heterogeneity increased variation by as much as 10-fold over mutation-selection-balance alone, whereas pure temporal environmental heterogeneity increased variance by only 45% at max. Our results show that some combinations of spatial heterogeneity and migration can maintain considerably more variation than mutation-selection balance, potentially reconciling the discrepancy between theoretical predictions and empirical observations. However, given the narrow regions of parameter space required for this effect, this is unlikely to provide a general explanation for the maintenance of variation. Nonetheless, our results suggest that habitat fragmentation may affect the maintenance of V A and thereby reduce the adaptive capacity of populations.