Overcompensation and phase effects in a cyclic common vole population: between first and second-order cycles

1. Population cycles in voles are often thought to be generated by one-year delayed density-dependence on the annual population growth rate. In common voles, however, it has been suggested by Turchin (2003) that some populations exhibit first-order cycles, resulting from strong overcompensation (i.e. carrying capacity overshoots in peak years, with only an effect of the current year abundance on annual growth rates). 2. We focus on a common vole (Microtus arvalis) population from western France, that exhibits 3-year cycles. Several overcompensating nonlinear models for populations dynamics are fitted to the data, notably those of Hassell, and Maynard-Smith and Slatkin. 3. Overcompensating direct density-dependence (DD) provides a satisfactory description of winter crashes, and one-year delayed density-dependence is not responsible for the crashes, thus these are not classical second-order cycles. A phase-driven modulation of direct density-dependence maintains a low-phase, explaining wh...