Evolution of dispersal in metapopulations with local density dependence and demographic stochasticity.

In this paper, we predict the outcome of dispersal evolution in metapopulations based on the following assumptions: (i) population dynamics within patches are density-regulated by realistic growth functions; (ii) demographic stochasticity resulting from finite population sizes within patches is accounted for; and (iii) the transition of individuals between patches is explicitly modelled by a disperser pool. We show, first, that evolutionarily stable dispersal rates do not necessarily increase with rates for the local extinction of populations due to external disturbances in habitable patches. Second, we describe how demographic stochasticity affects the evolution of dispersal rates: evolutionarily stable dispersal rates remain high even when disturbance-related rates of local extinction are low, and a variety of qualitatively different responses of adapted dispersal rates to varied levels of disturbance become possible. This paper shows, for the first time, that evolution of dispersal rates may give rise to monotonically increasing or decreasing responses, as well as to intermediate maxima or minima.

Invasion dynamics and attractor inheritance.

We study the dynamics of a population of residents that is being invaded by an initially rare mutant. We show that under relatively mild conditions the sum of the mutant and resident population sizes stays arbitrarily close to the initial attractor of the monomorphic resident population whenever the mutant has a strategy sufficiently similar to that of the resident. For stochastic systems we show that the probability density of the sum of the mutant and resident population sizes stays arbitrarily close to the stationary probability density of the monomorphic resident population. Attractor switching, evolutionary suicide as well as most cases of "the resident strikes back" in systems with multiple attractors are possible only near a bifurcation point in the strategy space where the resident attractor undergoes a discontinuous change. Away from such points, when the mutant takes over the population from the resident and hence becomes the new resident itself, the population stays on the same attractor. In other words, the new resident "inherits" the attractor from its predecessor, the former resident.

Necessary and sufficient conditions for evolutionary suicide.

Evolutionary suicide is an evolutionary process where a viable population adapts in such a way that it can no longer persist. It has already been found that a discontinuous transition to extinction is a necessary condition for suicide. Here we present necessary and sufficient conditions, concerning the bifurcation point, for suicide to occur. Evolutionary suicide has been found in structured metapopulation models. Here we show that suicide can occur also in unstructured population models. Moreover, a structured model does not guarantee the possibility of suicide: we show that suicide cannot occur in age-structured population models of the Gurtin-MacCamy type. The point is that the mutant's fitness must explicitly depend not only on the environmental interaction variable, but also on the resident strategy.

Evolution of migration in a metapopulation.

In this paper a general deterministic discrete-time metapopulation model with a finite number of habitat patches is analysed within the framework of adaptive dynamics. We study a general model and prove analytically that (i) if the resident populations state is a fixed point, then the resident strategy with no migration is an evolutionarily stable strategy, (ii) a mutant population with no migration can invade any resident population in a fixed point state, (iii) in the uniform migration case the strategy not to migrate is attractive under small mutational steps so that selection favours low migration. Some of these results have been previously observed in simulations, but here they are proved analytically in a general case. If the resident population is in a two-cyclic orbit, then the situation is different. In the uniform migration case the invasion behaviour depends both on the type of the residents attractor and the survival probability during migration. If the survival probability during migration is low, then the system evolves towards low migration. If the survival probability is high enough, then evolutionary branching can happen and the system evolves to a situation with several coexisting types. In the case of out-of-phase attractor, evolutionary branching can happen with significantly lower survival probabilities than in the in-phase attractor case. Most results in the two-cyclic case are obtained by numerical simulations. Also, when migration is not uniform we observe in numerical simulations in the two-cyclic orbit case selection for low migration or evolutionary branching depending on the survival probability during migration.