Disease-induced natural selection in a diploid host.
Using for each genotype an SIR-type model of disease transmission dynamics, we describe natural selection in a continuously breeding diploid host whose disease susceptibility and resistance are carried at one locus with two alleles. The system is transformed into variables that for each disease class describe the number of individuals, the gene frequency, and the deviation from Hardy-Weinberg proportions as measured by Wright's fixation index. An assumption of small variation in disease response among genotypes (slow selection) separates the system to first-order into three blocks. One block describes the population-wide disease dynamics, the second considers the fixation index in each class, and the third block provides the change in gene frequencies. The first two blocks settle to equilibrium at a rate determined by the population turnover time while the last block after a while is dominated by a slowly changing variable, the average gene frequency. The dynamics of the gene frequency take the usual form for a continuous time slow selection model, and this provides explicit, epidemiologically justified expressions for the genotypic fitnesses. We apply the method to other disease transmission patterns (SEI and SIS) and discuss how suitable time averages extend our results to diseases with temporally varying incidence.
Andreasen
V
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Department of Mathematics and Physics, Roskilde University, Denmark.
Christiansen
F B
FB
D000483:Alleles; D001723:Birth Rate; D003141:Communicable Diseases / Q000453:epidemiology* / Q000235:genetics / Q000635:transmission; D004171:Diploidy; D005787:Gene Frequency; D020022:Genetic Predisposition to Disease; D005838:Genotype; D006801:Humans; D007113:Immunity, Innate / Q000235:genetics*; D015994:Incidence; D008957:Models, Genetic; D012641:Selection, Genetic