Abstract
The paradox of high genetic variation observed in traits under stabilizing selection is a long-standing problem in evolutionary theory, as mutation rates appear too low to explain observed levels of standing genetic variation under classic models of mutation-selection balance. Spatially or temporally heterogeneous environments can maintain more standing genetic variation within populations than homogeneous environments, but it is unclear whether such conditions can resolve the above discrepancy between theory and observation. Here, we use individual-based simulations to explore the effect of various types of environmental heterogeneity on the maintenance of genetic variation (VA ) for a quantitative trait under stabilizing selection. We find that VA 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 VA and thereby reduce the adaptive capacity of populations.
Highlights
As genetic variation is the fundamental basis upon which evolution acts, it is important to understand how variation is maintained in order to provide a foundation for answering various questions in biology and related fields, such as missing heritability (Maher, 2008), conservation of biodiversity (Cook & Sgrò, 2017), and population potential to respond to change (Houle, 1992)
There is minimal response to rate of migration between the two patches, except for a small increase at low to intermediate m, which is consistent with predictions of Goldstein and Holsinger (1992), and arises due to an interaction between effects of genetic redundancy and genetic drift
For the combination of spatial and temporal heterogeneity, there is little change for most parameter combinations compared to spatial heterogeneity alone (Figure 4B); for those where there is a noticeable deviation, whether the parameter set falls in or out of the target range remains unchanged. The results of these simulations show that environmental heterogeneity can have a large impact on the maintenance of additive genetic variation (VA) under a variety of parameters
Summary
As genetic variation is the fundamental basis upon which evolution acts, it is important to understand how variation is maintained in order to provide a foundation for answering various questions in biology and related fields, such as missing heritability (Maher, 2008), conservation of biodiversity (Cook & Sgrò, 2017), and population potential to respond to change (Houle, 1992). The most widely studied explanation for this paradox is mutation-selection balance ( referred to as MSB), the appeal of which lies in its intuitive logic: mutation, as the ultimate source of genetic variation, provides enough input to offset the eroding effect of selection, leading to a state of equilibrium. Under such models, stabilizing selection is assumed according to a Gaussian fitness function with parameter VS setting the strength of selection on genotypes (where large values result in weaker selection). Multiple MSB models have been proposed, most notably the continuum-of-alleles model from Kimura and Crow (1964) of which two main approximations have been put forth: the Gaussian approximation (Kimura 1965; later expanded by Lande 1976), and the House-of-cards approximation (Turelli, 1984; Burger et al, 1989)
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