We model the population dynamics of two host species attacked by a common parasitoid using a discrete-time formalism that captures their population densities from year to year. It is well known starting from the seminal work of Nicholson and Bailey that a constant parasitoid attack rate leads to an unstable host-parasitoid interaction. However, a Type III functional response, where the parasitoid attack rate accelerates with increasing host density stabilizes the population dynamics. We first consider a scenario where both host species are attacked by a parasitoid with the same Type III functional response. Our results show that sufficient fast acceleration of the parasitoid attack rate stabilizes the population dynamics of all three species. For two symmetric host species, the extent of acceleration needed to stabilize the three-species equilibrium is exactly the same as that needed for a single host-parasitoid interaction. However, asymmetry can lead to scenarios where the removal of a host species from a stable interaction destabilizes the interaction between the remaining host species and the parasitoid. Next, we consider a situation where one of the host species is attacked at a constant rate (i.e., Type I functional response), and the other species is attacked via a Type III functional response. We identify parameter regimes where a Type III functional response to just one of the host species stabilizes the three species interaction. In summary, our results show that a generalist parasitoid with a Type III functional response to one or many host species can play a key role in stabilizing population dynamics of host-parasitoid communities in apparent competition.

我们使用离散时间形式来模拟被常见寄生蜂攻击的两种宿主物种的种群动态，该形式可以捕捉它们逐年的种群密度。众所周知，从 Nicholson 和 Bailey 的开创性工作开始，恒定的寄生蜂攻击率会导致不稳定的寄主-寄生蜂相互作用。然而，一种 III 型功能反应，其中寄生蜂攻击率随着宿主密度的增加而加速，稳定了种群动态。我们首先考虑两种寄主物种都受到具有相同 III 型功能反应的寄生蜂攻击的场景。我们的结果表明，寄生蜂攻击率的足够快的加速稳定了所有三个物种的种群动态。对于两个对称的宿主物种，稳定三个物种平衡所需的加速程度与单个寄主-寄生蜂相互作用所需的加速程度完全相同。然而，不对称会导致从稳定的相互作用中去除宿主物种会破坏剩余宿主物种与寄生蜂之间的相互作用的情况。接下来，我们考虑一种情况，其中一个宿主物种以恒定速率受到攻击（即 I 型功能反应），而另一个物种通过 III 型功能反应受到攻击。我们确定了参数机制，其中对宿主物种之一的 III 型功能响应稳定了三个物种的相互作用。总之，