Mathematics and Computer Science Department, Valdosta State University, Valdosta, GA 31698, USA.
J Biol Dyn. 2012;6:80-95. doi: 10.1080/17513758.2011.578758. Epub 2011 May 24.
In two models of pest control using a pesticidal crop along with a non-pesticidal refuge to prevent the development of resistance, we numerically compute the bifurcations that bound the region in parameter space where control is sustainable indefinitely. An exact formula for one of the bifurcation surfaces in one of the models is also found. One model is conceptual and as simple as possible. The other is realistic and very detailed. Despite the great differences in the models, we find the same distinctive bifurcation structure. We focus on the parameters that determine: (i) the restriction of pest exchange between the crop and the refuge, which we call 'screening' the refuge, and (ii) the recessiveness of the resistance trait. The screened refuge technique is seen to work in the models up to quite high values of fitness of resistant heterozygotes, that is, even when resistance is not strongly recessive.
在利用杀虫作物和非杀虫避难所来防止抗药性发展的两种害虫防治模型中，我们通过数值计算来确定控制能够无限期持续的参数空间的分岔边界。我们还找到了其中一个模型中一个分岔面的精确公式。一个模型是概念性的，尽可能简单。另一个则是现实的，非常详细。尽管模型有很大的差异，但我们发现了相同的独特分岔结构。我们关注的是决定以下两个参数的值：（i）作物和避难所之间的害虫交换限制，我们称之为“屏蔽”避难所，以及（ii）抗药性性状的隐性。在模型中，屏蔽避难所技术可以在抗性杂合子适应度相当高的情况下（即，即使抗性不是很强的隐性）工作。
