Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Carnivores hunt in groups, birds breed in colonies, and fish
school together. While living in groups can confer benefits to a population, it
also promotes adverse effects such as increased disease risk. In this talk I
will present a mathematical model that combines both hunting cooperation and
disease transmission in the predator population. The model is simple in
structure and consists of three nonlinear differential equations, yet it shows
complex bifurcation behavior leading to bistability, limit cycle oscillations,
and homoclinic loops. We find that there is a critical level of group
cooperation, beyond which large enough populations withstand disease mortality
and survive even though they would go extinct in the absence of cooperation
(strong Allee effect). On the other hand, cooperation can reduce predator
population size due to overexploitation of prey and also destabilize the
community dynamics.