Abstract: Despite considerable study of population cycles, the striking variability of cycle periods in many cyclic populations remains largely unexplained. Mathematical models of cyclic population dynamics seem to exhibit much greater regularity in cycle periods than many real populations, even when accounting for environmental stochasticity. We contend, however, that recent advances in understanding the origins of long transient dynamics point 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 recovering away) 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 a significant 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.