Bowers R G, Boots M, Begon M
Department of Applied Mathematics and Theoretical Physics, University of Liverpool, U.K.
Proc Biol Sci. 1994 Sep 22;257(1350):247-53. doi: 10.1098/rspb.1994.0122.
The dynamics of a 'resistant' and a 'susceptible' strain of a self-regulated host species, in the presence of a directly transmitted pathogen, is investigated. The two strains trade off differences in pathogen transmissibility (as an aspect of pathogen resistance) against differences in birth rate and/or resistance to crowding. Depending on parameter values, either strain may be eliminated, or the two may coexist (along with the pathogen). Coexistence (polymorphism), unsurprisingly, requires an appropriate balance between the different advantages possessed by the two strains. The probability of coexistence through such a balance, however, varies nonlinearly with the degree of difference between the strains: coexistence is least likely between two very similar strains. Resistance is most likely to evolve in hosts with the characteristics of many insect pests. Moreover, with highly pathogenic pathogens, a 'susceptible' strain may exclude a 'resistant' strain because its higher growth rate is more effective against the pathogen than reduced transmissibility. 'Resistance' can reside in parameters other than those directly associated with the pathogen. Although no cycles arise and no chaotic behaviour is found, an oscillatory approach to equilibrium is commonly observed, signalling the possibility of observable oscillations in strain frequency in the (more variable) real world.
研究了在存在直接传播病原体的情况下，一个自我调节宿主物种的“抗性”和“敏感”菌株的动态变化。这两种菌株在病原体传播性差异（作为病原体抗性的一个方面）与出生率差异和/或对拥挤的抗性之间进行权衡。根据参数值，任一菌株都可能被淘汰，或者两者可能共存（与病原体一起）。不出所料，共存（多态性）需要两种菌株所具有的不同优势之间达到适当的平衡。然而，通过这种平衡实现共存的概率与菌株之间的差异程度呈非线性变化：两个非常相似的菌株之间共存的可能性最小。抗性最有可能在具有许多害虫特征的宿主中进化。此外，对于高致病性病原体，“敏感”菌株可能会排除“抗性”菌株，因为其较高的生长速率对病原体的作用比降低的传播性更有效。“抗性”可能存在于与病原体直接相关的参数之外的其他参数中。虽然没有出现周期，也没有发现混沌行为，但通常会观察到一种趋近平衡的振荡方式，这表明在（更具变化性的）现实世界中，菌株频率可能会出现可观测的振荡。
