Frequency dependence and the predictability of evolution in a changing environment.

Frequency-dependent (FD) selection, whereby fitness and selection depend on the genetic or phenotypic composition of the population, arises in numerous ecological contexts (competition, mate choice, crypsis, mimicry, etc.) and can strongly impact evolutionary dynamics. In particular, negative frequency-dependent selection (NFDS) is well known for its ability to potentially maintain stable polymorphisms, but it has also been invoked as a source of persistent, predictable frequency fluctuations. However, the conditions under which such fluctuations persist are not entirely clear. In particular, previous work rarely considered that FD is unlikely to be the sole driver of evolutionary dynamics when it occurs, because most environments are not static but instead change dynamically over time. Here, we investigate how FD interacts with a temporally fluctuating environment to shape the dynamics of population genetic change. We show that a simple metric introduced by Lewontin, the slope of frequency change against frequency near equilibrium, works as a key criterion for distinguishing microevolutionary outcomes, even in a changing environment. When this slope D is between 0 and -2 (consistent with the empirical examples we review), substantial fluctuations would not persist on their own in a large population occupying a constant environment, but they can still be maintained indefinitely as quasi-cycles fueled by environmental noise or genetic drift. However, such moderate NFDS buffers and temporally shifts evolutionary responses to periodic environments (e.g., seasonality). Stronger FD, with slope D < -2, can produce self-sustained cycles that may overwhelm responses to a changing environment, or even chaos that fundamentally limits predictability. This diversity of expected outcomes, together with the empirical evidence for both FD and environment-dependent selection, suggests that the interplay of internal dynamics with external forcing should be investigated more systematically to reach a better understanding and prediction of evolution.