Department of Mathematics, The College ofWilliam and Mary,Williamsburg, VA 23187-8795, USA.
J Biol Dyn. 2007 Jul;1(3):273-88. doi: 10.1080/17513750701450235.
There is an emerging consensus that parasitoids are limited by the number of eggs which they can lay as well as the amount of time they can search for their hosts. Since egg limitation tends to destabilize host-parasitoid dynamics, successful control of insect pests by parasitoids requires additional stabilizing mechanisms such as heterogeneity in the distribution of parasitoid attacks and host density-dependence. To better understand how egg limitation, search limitation, heterogeneity in parasitoid attacks, and host density-dependence influence host-parasitoid dynamics, discrete time models accounting for these factors are analyzed. When parasitoids are purely egg-limited, a complete anaylsis of the host-parasitoid dynamics are possible. The analysis implies that the parasitoid can invade the host system only if the parasitoid's intrinsic fitness exceeds the host's intrinsic fitness. When the parasitoid can invade, there is a critical threshold, CV*>1, of the coefficient of variation (CV) of the distribution of parasitoid attacks that determines that outcome of the invasion. If parasitoid attacks sufficiently aggregated (i.e., CV>CV*), then the host and parasitoid coexist. Typically (in a topological sense), this coexistence is shown to occur about a periodic attractor or a stable equilibrium. If the parasitoid attacks are sufficiently random (i.e. CV<CV*), then the parasitoid drives the host to extinction. When parasitoids are weakly search-limited as well as egg-limited, coexistence about a global attractor occurs even if CV<CV*. However, numerical simulations suggest that the nature of this attractor depends critically on whether CV<1 or CV>1. When CV<1, the parasitoid exhibits highly oscillatory dynamics. Alternatively, when parasitoid attacks are sufficiently aggregated but not overly aggregated (i.e. CV>1 but close to 1), the host and parasitoid coexist about a stable equilibrium with low host densities. The implications of these results for classical biological control are discussed.
有一种新兴的共识认为，寄生蜂的产卵数量和搜索宿主的时间都会受到限制。由于产卵限制往往会使寄主-寄生蜂动态不稳定，因此成功地通过寄生蜂控制昆虫害虫需要额外的稳定机制，例如寄生蜂攻击的分布异质性和宿主密度依赖性。为了更好地理解产卵限制、搜索限制、寄生蜂攻击的异质性和宿主密度依赖性如何影响寄主-寄生蜂动态，分析了考虑这些因素的离散时间模型。当寄生蜂纯粹受到产卵限制时，可以对寄主-寄生蜂动态进行完整分析。分析表明，只有当寄生蜂的内在适合度超过宿主的内在适合度时，寄生蜂才能入侵宿主系统。当寄生蜂可以入侵时，寄生蜂攻击分布的变异系数 (CV) 存在一个临界阈值 CV*>1，该阈值决定了入侵的结果。如果寄生蜂的攻击足够聚集（即 CV>CV*），那么宿主和寄生蜂就会共存。通常（从拓扑意义上讲），这种共存发生在一个周期吸引子或稳定平衡点附近。如果寄生蜂的攻击足够随机（即 CV<CV*），那么寄生蜂就会将宿主推向灭绝。当寄生蜂受到弱搜索限制和产卵限制时，即使 CV<CV*，也会在全局吸引子附近共存。然而，数值模拟表明，这种吸引子的性质取决于 CV 是否小于 1 或大于 1。当 CV<1 时，寄生蜂表现出高度振荡的动力学。或者，当寄生蜂的攻击足够聚集但不过度聚集（即 CV>1 但接近 1）时，宿主和寄生蜂在宿主密度较低的稳定平衡点附近共存。这些结果对经典生物控制的意义进行了讨论。
