The roles of the Moran effect and dispersal in synchronizing oscillating populations

Patterns of spatial synchrony of population dynamics are dramatic phenomena that provide the potential for unraveling forces controlling the dynamics of natural populations in time and space. Prior ecological research has focused on attention to either deterministic or stochastic forces acting separately, with an emphasis on long term behavior, or on small systems consisting often of two interacting spatial locations. Using ideas from the dynamics of weakly coupled oscillators with an emphasis on the temporal dynamics of synchrony we develop a synthetic approach that explains patterns of synchrony as the result of an interplay between deterministic and stochastic forces. The temporal scale of convergence can provide a useful tool for determining the relative importance of deterministic and stochastic influences. Our approach applies both to specific systems that have been previously analyzed such as disease dynamics, and to a range of exploiter victim systems.