Global redistribution and local migration in semi-discrete host–parasitoid population dynamic models

Abstract

Host–parasitoid population dynamics is often probed using a semi-discrete/hybrid modeling framework. Here, the update functions in the discrete-time model connecting year-to-year changes in the population densities are obtained by solving ordinary differential equations that mechanistically describe interactions when hosts become vulnerable to parasitoid attacks. We use this semi-discrete formalism to study two key spatial effects: local movement (migration) of parasitoids between patches during the vulnerable period; and yearly redistribution of populations across patches outside the vulnerable period. Our results show that in the absence of any redistribution, constant density-independent migration and parasitoid attack rates are unable to stabilize an otherwise unstable host–parasitoid population dynamics. Interestingly, inclusion of host redistribution (but not parasitoid redistribution) before the start of the vulnerable period can lead to stable coexistence of both species. Next, we consider a Type-III functional response (parasitoid attack rate increases with host density), where the absence of any spatial effects leads to a neutrally stable host–parasitoid equilibrium. As before, density-independent parasitoid migration by itself is again insufficient to stabilize the population dynamics and host redistribution provides a stabilizing influence. Finally, we show that a Type-III functional response combined with density-dependent parasitoid migration leads to stable coexistence, even in the absence of population redistributions. In summary, we have systematically characterized parameter regimes leading to stable/unstable population dynamics with different forms of spatial heterogeneity coupled to the parasitoid’s functional response using mechanistically formulated semi-discrete models.