Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Applied Mathematics


Wild, Geoff


Dispersal plays a key role in the persistence of metapopulations, as the balance between local extinction and colonization is affected by dispersal. Herein, I present three pieces of work related to dispersal. The first two are devoted to the ecological aspect of delayed dispersal in metapopulations. The first one focuses on how dispersal may disrupt the social structure on patches from which dispersers depart. Examinations of bifurcation diagrams of the dynamical system show a metapopulation will, in general, be either in the state of global extinction or persistence, and dispersal only has a limited effect on metapopulation persistence. The second one examines multiple models with time delays. Investigating critical delays and the absolute stability of equilibrium shows that: 1) delays associated with dispersal only cannot destabilize the population; 2) reducing local extinction in metapopulations with delays associated with available territories or establishment leads to oscillations; 3) metapopulations with a structure for occupied patches suffer less from the problem in 2) caused by establishment delays. The third work studies how dispersal evolves in environments with temporal global-scale fluctuations. Methods from theoretical evolutionary biology are applied, and perturbation methods, numerical procedures and individual-based simulations show that difference between conditional dispersal probabilities for poor and good environment states increases as fluctuation frequency and disparity of dispersal cost increase. At last, conclusions and discussion of the implication of the above studies to cooperative breeding are presented, as well as a future direction to construct a kin selection model and investigate the evolution of helping.