Pest outbreaks can cause large scale defoliation of forest trees or destruction of crops, leading to various ecosystem and economic losses. Some outbreaks occur simultaneously across large geographic scales and some outbreaks occur alternatively every few years across space. Parasitoids are a natural enemy of these pests (hosts) and could help mitigate these pest outbreaks. A holistic understanding of the host-parasitoid interactions in a spatial context would thus enhance our ability to understand, predict and prevent these outbreaks. We use a discrete time deterministic model of the host parasitoid system with populations migrating between patches to study host outbreaks. In particular, we explore the conditions under which host outbreaks across patches are in phase and out of phase. We examine when these steady states are dependent on initial conditions. Lastly, we also examine how migration affects the time between successive outbreaks.
Results/Conclusions
We found that at low migration rates, the outbreaks in the patches are out of phase. As we increase the rate of migration, the outbreaks in the patches are in phase, with intermediate phase differences along the way. We found that at intermediate migration rates, both in phase and out of phase solutions are possible in steady state, depending on the initial conditions. We show these results to be robust across different growth rates of host and parasitoids, although at high parasitoid growth rates, parasitoid extinctions become increasingly likely at steady state. We also show that time between successive outbreaks first decreases (when the patches are out of phase) and later increases with increasing migration rates (as patches are in phase). We plan to expand our model in 2 ways - by introducing the dynamics of producers (producer - host - parasitoid model) and by analyzing these results in light of environmental stochasticity.
