Fredericton, 1 - 4 juin 2018
The second example models complex predator-swarm interactions. Here, each prey within a swarm is represented by a point particle, with near repulsion and far-field attraction, in addition to the repulsion from the predator. The resulting system of ODE's can be approximated by a nonlocal PDE whose analysis yields insight about whether swarming behaviour helpful in avoiding a predator.
This work is joint with Starrlight Augustine, Suzanne C. Dufour and Amy Hurford.
Vital rates and dispersal rates also vary according to an individual’s sex, and for many animal species, fertility depends on the formation of breeding pairs, which in turn depends on the relative frequency of the sexes. We have developed an invasion model that accounts for both the age- and the sex-structure of the population, and includes the pair formation process and sex bias in the vital and dispersal rates.
We have derived, and will present, a formula for the invasion speed obtained from the model using low-population-density approximations. Our comparison of this formula with the results of numerical simulations suggests that the formula is correct for a class of reasonable nonlinear models and initial conditions as well. Using the formula, we will show that the invasion speed depends in complex ways upon the model parameters and on the nature of the pair-formation process that governs mating.