REV IEW AND SYNTHES IS Moving forward in circles: challenges and opportunities in modelling population cycles

Fr ed eric Barraquand, Stilianos Louca, Karen C. Abbott, Christina A. Cobbold, Flora Cordoleani, Donald L. DeAngelis, Bret D. Elderd, Jeremy W. Fox, Priscilla Greenwood, Frank M. Hilker, Dennis L. Murray, Christopher R. Stieha, Rachel A. Taylor, Kelsey Vitense, Gail S.K. Wolkowicz and Rebecca C. Tyson Abstract Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research.