Search for: All records

Abstract Natural selection drives adaptive evolution and removes deleterious mutations; these effects are countervailing when a complex adaptation requires mutations that are initially deleterious when they arise, but beneficial in combination. While many models of this dynamic consider how genetic drift or other influences can aid valley crossing by weakening selection, we lack a general, analytical treatment of when relaxed selection might speed this type of adaptation. Here we use simulation and analysis to show that relaxed selection is generally favorable for valley-crossing when adaptive pathways require more than a single deleterious step. We also demonstrate that spatial heterogeneity in selection pressures could, by relaxing selection, allow populations to cross valleys much more rapidly than expected. These results relate to several applications of evolutionary theory to complex systems ranging from host-pathogen evolution to search algorithms in computer science. 

Despite considerable study of population cycles, the striking variability of cycle periods in many cyclic populations has received relatively little attention. Mathematical models of cyclic population dynamics have historically exhibited much greater regularity in cycle periods than many real populations, even when accounting for environmental stochasticity. We contend, however, that the recent focus on understanding the impact of long, transient but recurrent epochs within population oscillations points the way to a previously unrecognized means by which environmental stochasticity can create cycle period variation. Specifically, consumer–resource cycles that bring the populations near a saddle point (a combination of population sizes toward which the populations tend, before eventually transitioning to substantially different levels) may be subject to a slow passage effect that has been dubbed a ‘saddle crawlby'. In this study, we illustrate how stochasticity that generates variability in how close predator and prey populations come to saddles can result in substantial variability in the durations of crawlbys and, as a result, in the periods of population cycles. Our work suggests a new mechanistic hypothesis to explain an important factor in the irregular timing of population cycles and provides a basis for understanding when environmental stochasticity is, and is not, expected to generate cyclic dynamics with variability across periods.