Analysis of dispersal effects in metapopulation models

Ruiz-Herrera approaches the interaction between local dynamics and dispersal in spatially discrete populations analytically. Some of the mathematics in this paper were somewhat over my head, as such I will do my best to summarize the general modeling methods and main conclusions. They first define a relatively general metapopulation model with internal dynamics in which dispersal follows reproduction. They proceed to use this simple model to draw out a few general results: (1) all sub-populations are asymptotically identical and (2) the size of the total population is constant. They argue that this suggests that the classic conservation strategy of establishing corridors to increase connectivity may have little effect under the basic assumptions of this simple model (homogenous landscapes with simple local dynamics). They also note that though the identity of global attractors for the metapopulation is independent of dispersal distance the speed of convergence to an attractor depends heavily on it. Convergence occurs most rapidly at high and low dispersal distances.

He proceeds to consider the behavior of a metapopulation under chaotic local dynamics by simplifying to a 2 patch model. He demonstrates that metapopulations with small or large dispersal rates and oscillatory local dynamics display asynchronous chaotic dynamics. At intermediate dispersal rates there is instead global synchronization. In general this paper seems to largely analytically formalize concepts that have previously been studied numerically and with simulations. Perhaps the most interesting and non-intuitive result is the fact that speed of convergence to a global equilibrium is similar at high and low dispersal values.

 

Ruiz-Herrera, Alfonso. “Analysis of dispersal effects in metapopulation models.” Journal of mathematical biology 72.3 (2016): 683-698.