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

The basic reproduction ratio R-0 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 characterization using the basic depression ratio D-0 This quantity is the number of host individuals per infected 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 D-0. This parallels the result for pathogen virulence where R-0 is maximized. The tension between these two criteria is noted. The framework established allows a discussion of tradeoffs 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 D-0. The evolutionary attainment of the results is discussed.