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Infectious diseases have a major role in evolution by natural selection and pose a worldwide concern in livestock. Understanding quantitative genetics of infectious diseases, therefore, is essential both for understanding the consequences of natural selection and for designing artificial selection schemes in agriculture. The basic reproduction ratio, R0, is the key parameter determining risk and severity of infectious diseases. Genetic improvement for control of infectious diseases in host populations should therefore aim at reducing R0. This requires definitions of breeding value and heritable variation for R0, and understanding of mechanisms determining response to selection. This is challenging, as R0 is an emergent trait arising from interactions among individuals in the population. Here we show how to define breeding value and heritable variation for R0 for genetically heterogeneous host populations. Furthermore, we identify mechanisms determining utilization of heritable variation for R0. Using indirect genetic effects, next-generation matrices and a SIR (Susceptible, Infected and Recovered) model, we show that an individual's breeding value for R0 is a function of its own allele frequencies for susceptibility and infectivity and of population average susceptibility and infectivity. When interacting individuals are unrelated, selection for individual disease status captures heritable variation in susceptibility only, yielding limited response in R0. With related individuals, however, there is a secondary selection process, which also captures heritable variation in infectivity and additional variation in susceptibility, yielding substantially greater response. This shows that genetic variation in susceptibility represents an indirect genetic effect. As a consequence, response in R0 increased substantially when interacting individuals were genetically related.

On the definition and utilization of heritable variation among hosts in reproduction ratio R0 for infectious diseases