Individuals with different phenotypes can have widely-varying responses to natural selection, yet many classical approaches to evolutionary dynamics emphasize how a population's average phenotype increases in fitness over time. However, recent experimental results have produced examples of populations that have multiple fitness peaks, or that experience frequency-dependence that affects the direction and strength of selection on certain individuals. Here, we extend classical fitness gradient formulations of natural selection in order to describe the dynamics of a phenotype distribution in terms of its moments---such as the mean, variance, skewness, etc. The number of governing equations in our model can be adjusted in order to capture different degrees of detail about the population. We compare our simplified model to direct Wright-Fisher simulations of evolution in several canonical fitness landscapes, we find that our model provides a low-dimensional description of complex dynamics not typically explained by classical theory, such as cryptic selection forces due to selection on trait ranges, time-variation of the heritability, and nonlinear responses to stabilizing or disruptive selection due to asymmetric trait distributions. In addition to providing a framework for extending general understanding of common qualitative concepts in phenotypic evolution---such as fitness gradients, selection pressures, and heritability---our approach has practical importance for studying evolution in contexts in which genetic analysis is infeasible.
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