Theoretical impacts of habitat loss and generalist predation on predator-prey cycles

Certain herbivores and their predators undergo high amplitude periodic fluctuations in abundance in northern latitudes but exhibit damped cyclic dynamics in their respective southern ranges. Generalist predators and habitat disturbance have been identified as two features of southern habitats that may contribute to the attenuation of cycles in southern latitudes. Using the snowshoe hare and Canada lynx as model species, we employed a reaction-diffusion-advection framework with reaction terms taken from the May and Rosenzweig-MacArthur models to study the relative and joint damping impacts of generalist predation and habitat loss on predator-prey cycles. We found that generalist predation has consistently strong stabilizing effects and may represent a threat to the persistence of specialized predators. Habitat loss also ultimately results in the loss of cycles, but cycle amplitude and animal densities may not always decrease monotonically with habitat loss. The joint damping impacts of generalists and habitat loss can be severe, consistent with observations of low cycle amplitude, high predation rates, and significant habitat loss in the southern ranges of cyclic species. Elevated generalist predation rates at patch edges and in the surrounding matrix hasten cycle attenuation in situations that lead to increased prey exposure to generalists, including small patch sizes, higher movement rates into the matrix, and increased prey density at patch edges. The dominant driver of cycle attenuation, as well as cycle response to habitat disturbance, may vary between regions and systems. Field data that help clarify the relationships between habitat loss and fragmentation, generalist density and behavior, and cyclic activity would be invaluable in informing future modeling and conservation efforts.