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Host-parasitoid population dynamics is often probed using asemi-discrete/hybrid modeling framework. Here, the update functions in thediscrete-time model connecting year-to-year changes in the population densitiesare obtained by solving ordinary differential equations that mechanisticallydescribe interactions when hosts become vulnerable to parasitoid attacks. Weuse this semi-discrete formalism to study two key spatial effects: localmovement (migration) of parasitoids between patches during the vulnerableperiod; and yearly redistribution of populations across patches outside thevulnerable period. Our results show that in the absence of any redistribution,constant density-independent migration and parasitoid attack rates are unableto stabilize an otherwise unstable host-parasitoid population dynamics.Interestingly, inclusion of host redistribution (but not parasitoidredistribution) before the start of the vulnerable period can lead to stablecoexistence of both species. Next, we consider a Type-III functional response(parasitoid attack rate increases with host density), where the absence of anyspatial effects leads to a neutrally stable host-parasitoid equilibrium. Asbefore, density-independent parasitoid migration by itself is againinsufficient to stabilize the population dynamics and host redistributionprovides a stabilizing influence. Finally, we show that a Type-III functionalresponse combined with density-dependent parasitoid migration leads to stablecoexistence, even in the absence of population redistributions. In summary, wehave systematically characterized parameter regimes leading to stable/unstablepopulation dynamics with different forms of spatial heterogeneity coupled tothe parasitoid's functional response using mechanistically formulatedsemi-discrete models.

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