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.

通常使用半离散/混合建模框架来研究宿主-拟寄生物种群的动态。在这里，离散时间模型中的更新函数连接了人口密度的逐年变化，这是通过求解常微分方程获得的，该方程以机械方式描述了当宿主变得易受寄生虫袭击时的相互作用。我们使用这种半离散的形式主义来研究两个关键的空间影响：脆弱时期斑块之间的寄生虫的局部运动（迁移）；以及在脆弱时期之外跨补丁的年度人口重新分配。我们的结果表明，在没有任何重新分布的情况下，恒定的密度无关的迁移和寄生虫的发生率无法稳定原本不稳定的宿主－寄生虫种群动态。有趣的是 在脆弱期开始之前包含宿主的重新分布（但不包括寄生虫的重新分布）可以导致两个物种的稳定共存。接下来，我们考虑一种III型功能性反应（类寄生物的侵袭率随宿主密度的增加而增加），在这种情况下，任何空间效应的缺乏都会导致中性稳定的宿主－类寄生虫平衡。像以前一样，密度独立的类寄生虫迁移本身再次不足以稳定种群动态，宿主的重新分布提供了稳定的影响。最后，我们显示了III型功能响应与密度依赖性寄生类寄生虫迁移相结合，即使在没有人口重新分配的情况下，也能导致稳定的共存。综上所述，