Investigating the importance of migration and spatial heterogeneity in emerging spatial patterns of host-parasitoid populations

Understanding the cause of Insect outbreaks has always been a complex problem. Often these outbreaks are linked to environmental effects or trophic interactions and not migration. Migration amongst these insects are often at length scales much smaller than the length scales of outbreaks and thus aren’t considered a major factor in insect outbreaks. We use a discrete time metapopulation model on a square lattice, with diffusive migration to adjacent sites. We incorporate the competition for resources and parasitism to model the host-parasitoid population dynamics at each site. Furthermore, we use absorbing boundaries for the sites present at the edge of the lattice (as opposed to periodic boundaries) as ecosystems have sharply defined boundaries. At steady state, we show that outbreaks can occur at length scales much larger than the scale of migrations. In addition, we show that many interesting qualitative patterns like spiral waves emerge in our model at different parameter regimes. Lastly, we investigate how these patterns change in the presence of spatial heterogeneity as spatial heterogeneities are inherent to natural ecosystems.