On the evolution of virulence and the relationship between various measures of mortality

Troy Day

Abstract

Smallpox causes roughly 20% mortality whereas chickenpox causes less than 0.1%. Most ‘verbal’ (i.e. non–mathematical) discussions using a mortality definition of virulence would therefore label smallpox as more virulent. Indeed, the virulence of many diseases is measured using such case mortalities, 𝛘, or related measures such as expected host lifespan, T, or lethal dose, LDx. But 𝛘, T and LDx are only indirectly related to parasite–induced instantaneous mortality rate, α, which is the mortality measure used in much of the theory developed to explain virulence evolution. Here I point out that relatively deadly pathogens can actually have lower values of α than benign pathogens, demonstrating that α does not, by itself, reflect the extent to which a parasite causes host mortality. I present mathematical relationships between α and 𝛘, T and LDx, and use these to demonstrate that predictions about virulence evolution can be qualitatively altered depending upon which measure is used as the definition of virulence. Two simple examples are presented to illustrate this point, one of which demonstrates that the well–cited prediction that virulence should evolve to be higher when disease–independent host mortality increases need not hold. This prediction has been made in terms of parasite–induced instantaneous mortality, α, but if virulence is measured using case mortality (or T or LDx) then this prediction can easily be reversed. Theoretical and empirical researchers must use compatible mortality measures before a productive exchange between the two can take place, and it is suggested that case mortality (or lethal dose) is best suited as a single (mortality) measure of parasite virulence.