Asynchronous and Synchronous Dispersals in Spatially Discrete Population Models

This study is on the role of synchronous and asynchronous dispersals in a discrete-time single-species population model with dispersal between two patches, where predispersal dynamics are compensatory or overcompensatory and dispersal is synchronous or asynchronous or mixed synchronous and asynchronous. It is known that single-species dispersal-linked population models behave as singlespecies single-patch models whenever all predispersal local dynamics are compensatory and dispersal is synchronous. However, the dynamics of the corresponding model connected by asynchronous and mixed synchronous-asynchronous dispersals depend on the dispersal rates, intrinsic growth rates, and the parameter that models the possible modes of dispersal. The species becomes extinct on at least one patch when the asynchronous dispersal rates are high, while it persists when the rates are low. In mixed synchronous-asynchronous systems, depending on the model parameters, the pioneer species either becomes extinct on all patches or persists on all patches. Overcompensatory predispersal dynamics with synchronous dispersal can lead to multiple attractors with fractal basin boundaries. However, the associated models with either asynchronous or mixed synchronous and asynchronous dispersals exhibit multiple attractors with fewer numbers of distinct attractors. That is, the long-term dynamics of synchronous dispersal-linked systems can be more sensitive to initial population sizes than that of the corresponding asynchronous and mixed synchronous-asynchronous systems. Also, synchronous, asynchronous, and mixed synchronous-asynchronous dispersals can “stabilize” the local patch dynamics from overcompensatory to compensatory dynamics. In our mixed synchronous-asynchronous model, the dominant mode of dispersal usually drives the dynamics of the full system.