Bowers R G
Department of Mathematics Sciences, University of Liverpool, UK.
Proc Biol Sci. 2001 Feb 7;268(1464):243-50. doi: 10.1098/rspb.2000.1360.
The basic reproduction ratio R0 occupies a central position in the theory of host pathogen interactions. However, this quantity stresses the role of the pathogen. This paper proposes an additional, more host-centred char acterization using the basic depression ratio D0. This quantity is the number of host individuals per infected by which the infected host population is depressed below its uninfected level. This paper shows that a baseline criterion for the evolution of host resistance to microparasites is that resistance evolves to minimize D0. This parallels the result for pathogen virulence where R0 is maximized. The tension between these two criteria is noted. The framework established allows a discussion of trade-offs between aspects of the pathogen-free host biology and the host pathogen interaction. For certain linear and convex trade-offs it is shown that the strain with the lowest transmission parameter beta wins (despite the fact that it has the lowest intrinsic birth rate a). For corresponding concave trade-offs, either the strain with minimum beta and a or the strain with maximum beta and a wins. Finally the connection with the techniques of adaptive dynamics is made. Evolutionary singular points are shown to occur at extrema of D0. The evolutionary attainment of the results is discussed.
基本繁殖数R0在宿主-病原体相互作用理论中占据核心地位。然而，这个量强调的是病原体的作用。本文提出了一种额外的、更以宿主为中心的特征描述，即使用基本抑制率D0。这个量是指每个受感染宿主个体感染的宿主数量，通过这些宿主数量，受感染宿主种群被压低到未感染水平以下。本文表明，宿主对微寄生虫抗性进化的一个基线标准是抗性进化到使D0最小化。这与病原体毒力的结果相似，在病原体毒力方面R0被最大化。注意到这两个标准之间的矛盾。所建立的框架允许讨论无病原体宿主生物学方面与宿主-病原体相互作用之间的权衡。对于某些线性和凸性权衡，结果表明具有最低传播参数β的菌株获胜（尽管它具有最低的内在出生率α）。对于相应的凹性权衡，要么是具有最小β和α的菌株获胜，要么是具有最大β和α的菌株获胜。最后建立了与自适应动力学技术的联系。进化奇点显示出出现在D0的极值处。讨论了结果的进化实现。
