Approximations for the hitchhiking effect caused by the evolution of antimalarial-drug resistance

An analytically feasible, deterministic model for the spread of drug resistance among human malaria parasites, which incorporates all characteristics of the complex malaria-transmission cycle was introduced by Schneider and Kim (Theor. Popul Biol, 2010). The model accounts for the fact that only a fraction of infected hosts receive drug treatment and that hosts can be co-infected by differently many parasites. Furthermore, the model also incorporates host heterogeneity. Antimalarial-drug resistance is assumed to be caused by a single locus with two alleles-a sensitive one and a resistance one. The most important result for this model is that an analytical solution for the frequencies of a linked neutral biallelic locus exists. However, the exact solution does not admit an explicit form, and cannot straightforwardly be interpreted in terms of the model parameters. Here, we establish simple approximations for the equilibrium frequency at the neutral locus. Under the assumption that the resistant allele is initially rare-the biologically most relevant assumption in this context-and that recombination is weak, the approximations become similar to the approximations in the standard hitchhiking model. However, there are crucial differences. In particular, because of the high degree of selfing among malaria parasites in their sexual phase, a genome-wide reduction of relative heterozygosity occurs if selection is sufficiently strong. It turns out that the approximations are accurate even if the recombination rates are not small and the resistant allele is initially not very rare. The main advantage of our approximations is that they are easy to interpret in terms of model parameters. Moreover, they allow to make predictions of the size of the valley of reduced heterozygosity around the selected locus for given model parameters. Reversely, for a given reduction of heterozygosity, it is possible to identify the corresponding parameters. Moreover, we will show that incorporating host heterogeneity leads to an increased hitchhiking effect.