The genetic underpinnings of population cyclicity: establishing expectations for the genetic anatomy of cycling populations

Despite extensive research into the mechanisms underlying population cyclicity, we have little understanding of the impacts of numerical fluctuations on the genetic variation of cycling populations. Thus, the potential implications of natural and anthropogenically‐driven variation in population cycle dynamics on the diversity and evolutionary potential of cyclic populations is unclear. Here, we use Canada lynx Lynx canadensis matrix population models, set up in a linear stepping‐stone, to generate demographic replicates of biologically realistic cycling populations. Overall, increasing cycle amplitude predictably reduced genetic diversity and increased genetic differentiation, with cyclic effects increased by population synchrony. Modest dispersal rates (1–3% of the population) between high and low amplitude cyclic populations did not diminish these effects suggesting that spatial variation in cyclic amplitude should be reflected in patterns of genetic diversity and differentiation at these rates. At high dispersal rates (6%) groups containing only high amplitude cyclic populations had higher diversity and lower differentiation than those mixed with low amplitude cyclic populations. Negative density‐dependent dispersal did not impact genetic diversity, but did homogenize populations by reducing differentiation and patterns of isolation by distance. Surprisingly, temporal changes in diversity and differentiation throughout a cycle were not always consistent with population size. In particular, negative density‐dependent dispersal simultaneously decreased differences in genetic diversity while increasing differences in genetic differentiation between numerical peaks and nadirs. Combined, our findings suggest demographic changes at fine temporal scales can impact genetic variation of interacting populations and provide testable predictions relating population cyclicty to genetic variation. Further, our results suggest that including realistic demographic and dispersal parameters in population genetic models and using information from temporal changes in genetic variation could help to discern complex demographic scenarios and illuminate population dynamics at fine temporal scales.