An analytical model for genetic hitchhiking in the evolution of antimalarial drug resistance

Abstract

We analytically study a deterministic model for the spread of drug resistance among human malaria parasites. The model incorporates all major characteristics of the complex malaria-transmission cycle and accounts for the fact that only a fraction α of infected hosts receive drug treatment. Furthermore, the model incorporates that hosts can be co-infected. The number m of parasites co-infecting a host is either a constant or, more generally, follows a given frequency distribution. Although the model is formulated in a multilocus setup, for our results we assume that drug resistance is caused by a single locus with two alleles - a sensitive one and a resistant one. We assume that the resistant allele has a selective advantage only in treated hosts and pays metabolic costs, which causes this allele to be deleterious in untreated hosts. We provide necessary and sufficient conditions for the fixation of the resistant allele. Moreover, provided the resistant allele will sweep through the population, we derive a formula for the time until it reaches a given frequency and in particular for the time until quasi-fixation. Furthermore, we establish an analytical solution for allele frequency changes at a linked neutral biallelic locus due to the rapid increase in frequency of the resistant allele. Our solution describes a local reduction in heterozygosity among parasite chromosomes around the resistant allele, the effect commonly referred to as the hitchhiking effect, as a function of α and m. The result therefore allows the investigation of selective sweep patterns under specific demographic settings. We find that the hitchhiking effect is similar but different from the standard model of genetic hitchhiking that assumes random mating and homogeneous selection. In particular, the process of recombination and selection cannot be decoupled. We further explain why standard hitchhiking theory cannot be applied to drug resistance in malaria. Furthermore, we will show that a genome-wide reduction in relative heterozygosity can occur provided a fraction of hosts is infected by a single parasite haplotype. Finally, we show how to incorporate host heterogeneity, and generalize our results to this bio logically more realistic case.

Malaria life cycle intensifies both natural selection and random genetic drift

“…As well, the proportion of multiple infections differs among geographical locations, and therefore the level of inbreeding differs. Previous theoretical work has reported the effect of hitchhiking and partial selfing on genetic variation (37), modeled the hitchhiking effect of drug-resistant alleles, and demonstrated that selection and recombination cannot be decoupled in the malaria life cycle (27). Although the observed level of linkage disequilibrium in the Senegal population is very low (4), the next step in the modeling will be to allow for the possibility of mixed infections in a multilocus model to examine the relation between transmission intensity and linkage disequilibrium.…”

“…Their results highlight the importance of studying the effect of various reproductive mechanisms on basic evolutionary outcomes. Although there has been research on the evolution of drug resistance in malaria parasites, in both mathematical models and computational simulations (24)(25)(26)(27), it has not been ascertained whether the underlying processes of random genetic drift, natural selection, and their interactions yield outcomes in the malaria life cycle that are congruent with those of the WF model.…”

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

“…Recently, Schneider and Kim (2010) introduced an analytical feasible model for the spread of antimalarial-drug resistance, which allows to study genetic hitchhiking. The model covers the important characteristics of the transmission cycle, incorporates host heterogeneity, i.e., different classes of treated and untreated hosts, and accounts for the fact that hosts can be infected by differently many parasites.…”

“…Moreover, the model allows simple conditions for the spread of resistance and its speed in terms of the fitness parameters and α . Hence, it is useful to find ‘optimal’ treatment strategies to prevent or slow down the spread of resistance (for more discussion see Schneider and Kim 2010). …”

“…However, Schneider and Kim (2010) discuss in detail why the application of the standard selective-sweep model to a malaria-parasite population is highly problematic. In particular, the high degree of selfing among malaria parasites will lead to a genome-wide reduction of heterozygosity if selection is sufficiently strong (cf.…”