Ringland John, George Prasanth
Department of Mathematics, University at Buffalo Buffalo, NY, USA.
Department of Mathematics, University of Rhode Island Kingston, RI, USA.
Evol Appl. 2011 May;4(3):459-70. doi: 10.1111/j.1752-4571.2010.00160.x. Epub 2010 Oct 18.
We describe and analyze a 'screened refuge' technique for indefinitely sustaining control of insect pests using transgenic pesticidal crops or an applied pesticide, even when resistance is not recessive. The screen is a physical barrier that restricts pest movement. In a deterministic discrete-time model of the use of this technique, we obtain asymptotic analytical formulas for the two important equilibria of the system in terms of the refuge size and the pest fitnesses, mutation rates, and mobility out of and into the refuge. One of the equilibria is stable and is the point at which the pest population is controlled. The other is a saddle whose stable manifold bounds the basin of attraction of the former: its location provides a measure of the tolerance of the control mechanism to perturbations in the resistant allele density.
我们描述并分析了一种“筛选庇护所”技术，该技术可使用转基因杀虫作物或施用农药无限期地维持对害虫的控制，即使抗性并非隐性。筛选是一种限制害虫移动的物理屏障。在使用该技术的确定性离散时间模型中，我们根据庇护所大小、害虫适合度、突变率以及进出庇护所的迁移率，得出了系统两个重要平衡点的渐近解析公式。其中一个平衡点是稳定的，是害虫种群得到控制的点。另一个是鞍点，其稳定流形界定了前者的吸引域：它的位置提供了一种衡量控制机制对抗性等位基因密度扰动的容忍度的方法。
