Group defence and the predator's functional response.

We derive from first principles the functional response of the predator and the reproduction rate of the prey in the case that the prey form groups as a defence against the predator and the latter captures only single prey. We also give some examples of the resulting predator-prey population dynamics.

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.

The efficacy of dispersal in relation to safe site area and seed production.

A model is developed to define the efficacy of dispersal in relation to safe site area and seed production. Efficacy is measured as the expected number of progeny from one parent. It is shown that maximization of efficacy does not depend on the density of safe sites. When safe sites are confined to a restricted area around the parent, and safe sites are small or few propagules are produced, dispersal curves with short tails are most efficacious; when safe sites are larger or when more propagules are produced, distributions with longer tails become more advantageous.