Dispersal and the environment drive asynchronous modulation of frequency and amplitude of predator-prey abundance with implications for metacommunity stability

Frederic Guichard, Department of Biology, McGill University, Montreal, QC, Canada and Russell Milne, Applied Mathematics, University of Waterloo, Waterloo, ON, Canada

Background/Question/Methods
Spatial synchrony of population fluctuations is an important tool for predicting regional stability. It can be applied to biological oscillations such as those displayed by predator-prey interactions, or to environmentally forced fluctuations. Theory generally predicts that limited dispersal can promote stability by preventing spatial synchrony. These studies and the analysis of ecological time series have largely focused on either statistical covariance or phase analysis to infer spatial synchrony. However, natural systems can display complex fluctuations of abundance with important variations in the frequency and amplitude of population fluctuations, which are not fully resolved by current ecological theories of spatial synchrony. In particular, while environmental fluctuations and limited dispersal can each control the dynamics of frequency and amplitude of population fluctuations, ecological theories of spatial synchrony still need to resolve their role on synchrony and stability in heterogeneous metacommunities. Here, we adopt a heterogeneous predator-prey metacommunity model and study the response of dispersal-driven phase locking and frequency-amplitude modulation to among-patch heterogeneity in carrying capacity.
Results/Conclusions
We find that frequency modulation, which corresponds to the periodic and spontaneous fluctuation of the period of predator-prey cycles, occurs at intermediate values of dispersal and habitat heterogeneity. Frequency-amplitude modulation can emerge in metacommunities of autonomously oscillating populations. With sufficient habitat heterogeneity in carrying capacity, frequency-amplitude modulation can also emerge through the forcing of oscillations in otherwise equilibrium communities via dispersal from oscillating communities. Under frequency-amplitude modulation, frequency and amplitude are coupled and correlated, with periods of low amplitude associated with higher frequency predator-prey cycles. This frequency-amplitude coupling is found to promote both local and regional stability through cyclic and long-term patterns of local and regional variability. Our results highlight the importance of approaching spatial synchrony as a non-stationary phenomenon, and to provide metrics of stability that capture its dependence on spatial and temporal scales. We will finally discuss the implications of our results for the assessment and interpretation of spatial synchrony observed in experimental and natural systems.