Gubbins S, Gilligan CA
Churchill College, Cambridge, UK.
Proc Biol Sci. 1999 Dec 22;266(1437):2539-49. doi: 10.1098/rspb.1999.0957.
Fungicide resistance is an important practical problem, but one that is poorly understood at the population level. Here we introduce a simple nonlinear model for fungicide resistance in botanical epidemics which includes the dynamics of the chemical control agent and the host population, while also allowing for demographic stochasticity in the host-parasite dynamics. This provides a mathematical framework for analysing the risk of fungicide resistance developing by including the parameters for the amount applied, longevity and application frequency of the fungicide. The model demonstrates the existence of thresholds for the invasion of the resistant strain in the parasite population which depend on two quantities: the relative fitness of the resistant strain and the effectiveness of control. This threshold marks a change from definite elimination of the resistant strain below the threshold to a finite probability of invasion which increases above the threshold. The fungicide decay rate, the amount of fungicide applied and the period between applications affect the effectiveness of control and, consequently, they influence whether or not resistance develops and the time taken to achieve a critical frequency of resistance. All three parameters are amenable to control by the grower or by coordinating the activity of a population of growers. Providing crude estimates of the effectiveness of control and relative fitness are available, the results can be used to predict the consequences of changing these parameters for the risk of invasion and the proportion of sites at which this might be expected to occur. Although motivated for fungicide resistance, the model has broader application to herbicide, antibiotic and antiviral resistance. The modelling approach and results are discussed in the context of resistance to chemical control in general.
杀菌剂抗性是一个重要的实际问题，但在种群层面上人们对此了解甚少。在此，我们引入一个用于植物病害流行中杀菌剂抗性的简单非线性模型，该模型包括化学防治剂和寄主种群的动态变化，同时还考虑了寄主 - 寄生物动态中的种群统计学随机性。这提供了一个数学框架，通过纳入杀菌剂的施用量、持效期和施用频率等参数来分析杀菌剂抗性产生的风险。该模型表明，寄生物种群中抗性菌株入侵存在阈值，这取决于两个量：抗性菌株的相对适合度和防治效果。这个阈值标志着从低于阈值时抗性菌株肯定被消除到高于阈值时入侵概率有限增加的转变。杀菌剂的衰减率、施用量和施用间隔会影响防治效果，进而影响抗性是否会产生以及达到抗性临界频率所需的时间。这三个参数都可以由种植者控制，或者通过协调一群种植者的活动来控制。如果能提供防治效果和相对适合度的粗略估计值，这些结果可用于预测改变这些参数对入侵风险以及预期可能发生入侵的地点比例的影响。尽管该模型是基于杀菌剂抗性提出的，但它在除草剂、抗生素和抗病毒抗性方面有更广泛的应用。本文将在一般化学防治抗性的背景下讨论建模方法和结果。
