The basic depression ratio of the host: the evolution of host resistance to microparasites

Abstract

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.