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

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 biologically more realistic case.     

Joint effects of genetic hitchhiking and background selection on neutral variation

Due to relatively high rates of strongly selected deleterious mutations, directional selection on favorable alleles (causing hitchhiking effects on linked neutral polymorphisms) is expected to occur while a deleterious mutation-selection balance is present in a population. We analyze this interaction of directional selection and background selection and study their combined effects on neutral variation, using a three-locus model in which each locus is subjected to either deleterious, favorable, or neutral mutations. Average heterozygosity is measured by simulations (1) at the stationary state under the assumption of recurrent hitchhiking events and (2) as a transient level after a single hitchhiking event. The simulation results are compared to theoretical predictions. It is shown that known analytical solutions describing the hitchhiking effect without background selection can be modified such that they accurately predict the joint effects of hitchhiking and background on linked, neutral variation. Generalization of these results to a more appropriate multilocus model (such that background selection can occur at multiple sites) suggests that, in regions of very low recombination rates, stationary levels of nucleotide diversity are primarily determined by hitchhiking, whereas in regions of high recombination, background selection is the dominant force. The implications of these results on the identification and estimation of the relevant parameters of the model are discussed.     

Hitchhiking effect of a beneficial mutation spreading in a subdivided population

A central problem in population genetics is to detect and analyze positive natural selection by which beneficial mutations are driven to fixation. The hitchhiking effect of a rapidly spreading beneficial mutation, which results in local removal of standing genetic variation, allows such an analysis using DNA sequence polymorphism. However, the current mathematical theory that predicts the pattern of genetic hitchhiking relies on the assumption that a beneficial mutation increases to a high frequency in a single random-mating population, which is certainly violated in reality. Individuals in natural populations are distributed over a geographic space. The spread of a beneficial allele can be delayed by limited migration of individuals over the space and its hitchhiking effect can also be affected. To study this effect of geographic structure on genetic hitchhiking, we analyze a simple model of directional selection in a subdivided population. In contrast to previous studies on hitchhiking in subdivided populations, we mainly investigate the range of sufficiently high migration rates that would homogenize genetic variation at neutral loci. We provide a heuristic mathematical analysis that describes how the genealogical structure at a neutral locus linked to the locus under selection is expected to change in a population divided into two demes. Our results indicate that the overall strength of genetic hitchhiking--the degree to which expected heterozygosity decreases--is diminished by population subdivision, mainly because opportunity for the breakdown of hitchhiking by recombination increases as the spread of the beneficial mutation across demes is delayed when migration rate is much smaller than the strength of selection. Furthermore, the amount of genetic variation after a selective sweep is expected to be unequal over demes: a greater reduction in expected heterozygosity occurs in the subpopulation from which the beneficial mutation originates than in its neighboring subpopulations. This raises a possibility of detecting a "hidden" geographic structure of population by carefully analyzing the pattern of a selective sweep.     

Genetic Hitchhiking under Heterogeneous Spatial Selection Pressures

During adaptive evolutionary processes substantial heterogeneity in selective pressure might act across local habitats in sympatry. Examples are selection for drug resistance in malaria or herbicide resistance in weeds. In such setups standard population-genetic assumptions (homogeneous constant selection pressures, random mating etc.) are likely to be violated. To avoid misinferences on the strength and pattern of natural selection it is therefore necessary to adjust population-genetic theory to meet the specifics driving adaptive processes in particular organisms. We introduce a deterministic model in which selection acts heterogeneously on a population of haploid individuals across different patches over which the population randomly disperses every generation. A fixed proportion of individuals mates exclusively within patches, whereas the rest mates randomly across all patches. We study how the allele frequencies at neutral markers are affected by the spread of a beneficial mutation at a closely linked locus (genetic hitchhiking). We provide an analytical solution for the frequency change and the expected heterozygosity at the neutral locus after a single copy of a beneficial mutation became fixed. We furthermore provide approximations of these solutions which allow for more obvious interpretations. In addition, we validate the results by stochastic simulations. Our results show that the application of standard population-genetic theory is accurate as long as differences across selective environments are moderate. However, if selective differences are substantial, as for drug resistance in malaria, herbicide resistance in weeds, or insecticide resistance in agriculture, it is necessary to adapt available theory to the specifics of particular organisms.     

The Effect of Selective Sweeps on the Variance of the Allele Distribution of a Linked Multiallele Locus: Hitchhiking of Microsatellites

Microsatellite variation and the mechanisms which are responsible for this variation have received much attention in the last few years. Most theoretical studies of microsatellite allele distributions, however, did not incorporate the evolutionary dynamics of linked sites. The dynamics is usually modeled by invoking a special mutation mechanism such as stepwise mutation, which leads to a stepwise increase or decrease of the number of motif repeats on the occasion of mutation. It is shown here that selection at a locus, which itself is not subject to mutation, but which is adjacent to a microsatellite locus has an influence on statistics of the microsatellite allele distribution, provided that mutation rates are low to intermediate, when compared to 1/t1, the inverse of the time to fixation of a linked favorable substitution. If mutation rates are high, as for example in humans, a selective effect upon the microsatellite locus, such as hitchhiking, will quickly be obscured by mutations. In particular, in the latter case, the model shows that no correlation is to be expected between recombination rates and variability of microsatellites—such as had been predicted and experimentally demonstrated for nucleotide variability and recombination rates inDrosophila. The presented model is a generalization of the two locus two allele hitchhiking model which had been studied by Stephan and co-workers.     

Associations between malaria and MHC genes in a migratory songbird

Malaria parasites are a widespread and species-rich group infecting many wild populations of mammals, birds and reptiles. Studies on humans have demonstrated that genetic factors play a key role in the susceptibility and outcome of malaria infections. Until the present study, it has not been examined whether genetic variation in hosts is important for the outcome of malaria infections in natural avian populations. We investigated associations between major histocompatibility complex (MHC) genes and prevalence of three different avian malaria parasites (Haemoproteus payevskyi (GRW1), Plasmodium sp. (GRW2) and Plasmodium sp. (GRW4)) in a long-term study of great reed warblers Acrocephalus arundinaceus. We hypothesized that the MHC genes could either give full protection against a malaria infection, or confer protection against lethal malaria and direct the infection towards being milder. We found a positive association between numbers of MHC class I alleles (a measure of level of heterozygosity) and prevalence of the GRW2 parasite, suggesting the latter scenario. There was also a positive association between a specific MHC allele (B4b), previously shown to be under frequency-dependent selection in the study population, and prevalence of GRW2. These associations suggest that individuals carrying either a large number of MHC alleles or a specific MHC allele are protected against lethal malaria infections.     

Selective sweeps in the presence of interference among partially linked loci

Recurrent directional selection on a partially recombining chromosome may cause a substantial reduction of standing genetic variation in natural populations. Previous studies of this effect, commonly called selective sweeps, assumed that at most one beneficial allele is on the way to fixation at a given time. However, for a high rate of selected substitutions and a low recombination rate, this assumption can easily be violated. We investigated this problem using full-forward simulations and analytical approximations. We found that interference between linked beneficial alleles causes a reduction of their fixation probabilities. The hitchhiking effect on linked neutral variation for a given substitution also slightly decreases due to interference. As a result, the strength of recurrent selective sweeps is weakened. However, this effect is significant only in chromosomal regions of relatively low recombination rates where the level of variation is greatly reduced. Therefore, previous results on recurrent selective sweeps although derived for a restricted parameter range are still valid. Analytical approximations are obtained for the case of complete linkage for which interference between competing beneficial alleles is maximal.     

The Hill-Robertson effect and the evolution of recombination

In finite populations, genetic drift generates interference between selected loci, causing advantageous alleles to be found more often on different chromosomes than on the same chromosome, which reduces the rate of adaptation. This "Hill-Robertson effect" generates indirect selection to increase recombination rates. We present a new method to quantify the strength of this selection. Our model represents a new beneficial allele (A) entering a population as a single copy, while another beneficial allele (B) is sweeping at another locus. A third locus affects the recombination rate between selected loci. Using a branching process model, we calculate the probability distribution of the number of copies of A on the different genetic backgrounds, after it is established but while it is still rare. Then, we use a deterministic model to express the change in frequency of the recombination modifier, due to hitchhiking, as A goes to fixation. We show that this method can give good estimates of selection for recombination. Moreover, it shows that recombination is selected through two different effects: it increases the fixation probability of new alleles, and it accelerates selective sweeps. The relative importance of these two effects depends on the relative times of occurrence of the beneficial alleles.     

Clonal diversity of a lizard malaria parasite, Plasmodium mexicanum, in its vertebrate host, the western fence lizard: role of variation in transmission intensity over time and space

Within the vertebrate host, infections of a malaria parasite (Plasmodium) could include a single genotype of cells (single-clone infections) or two to several genotypes (multiclone infections). Clonal diversity of infection plays an important role in the biology of the parasite, including its life history, virulence, and transmission. We determined the clonal diversity of Plasmodium mexicanum, a lizard malaria parasite at a study region in northern California, using variable microsatellite markers, the first such study for any malaria parasite of lizards or birds (the most common hosts for Plasmodium species). Multiclonal infections are common (50-88% of infections among samples), and measures of genetic diversity for the metapopulation (expected heterozygosity, number of alleles per locus, allele length variation, and effective population size) all indicated a substantial overall genetic diversity. Comparing years with high prevalence (1996-1998 = 25-32% lizards infected), and years with low prevalence (2001-2005 = 6-12%) found fewer alleles in samples taken from the low-prevalence years, but no reduction in overall diversity (H = 0.64-0.90 among loci). In most cases, rare alleles appeared to be lost as prevalence declined. For sites chronically experiencing low transmission intensity (prevalence approximately 1%), overall diversity was also high (H = 0.79-0.91), but there were fewer multiclonal infections. Theory predicts an apparent excess in expected heterozygosity follows a genetic bottleneck. Evidence for such a distortion in genetic diversity was observed after the drop in parasite prevalence under the infinite alleles mutation model but not for the stepwise mutation model. The results are similar to those reported for the human malaria parasite, Plasmodium falciparum, worldwide, and support the conclusion that malaria parasites maintain high genetic diversity in host populations despite the potential for loss in alleles during the transmission cycle or during periods/locations when transmission intensity is low.     

The Red Queen lives: Epistasis between linked resistance loci

A popular theory explaining the maintenance of genetic recombination (sex) is the Red Queen Theory. This theory revolves around the idea that time‐lagged negative frequency‐dependent selection by parasites favors rare host genotypes generated through recombination. Although the Red Queen has been studied for decades, one of its key assumptions has remained unsupported. The signature host‐parasite specificity underlying the Red Queen, where infection depends on a match between host and parasite genotypes, relies on epistasis between linked resistance loci for which no empirical evidence exists. We performed 13 genetic crosses and tested over 7000 Daphnia magna genotypes for resistance to two strains of the bacterial pathogen Pasteuria ramosa. Results reveal the presence of strong epistasis between three closely linked resistance loci. One locus masks the expression of the other two, while these two interact to produce a single resistance phenotype. Changing a single allele on one of these interacting loci can reverse resistance against the tested parasites. Such a genetic mechanism is consistent with host and parasite specificity assumed by the Red Queen Theory. These results thus provide evidence for a fundamental assumption of this theory and provide a genetic basis for understanding the Red Queen dynamics in the Daphnia–Pasteuria system.     

Genetic mapping of determinants in drug resistance,virulence, disease susceptibility,and interaction of host-rodent malaria parasites

Genetic mapping has been widely employed to search for genes linked to phenotypes/traits of interest. Because of the ease of maintaining rodent malaria parasites in laboratory mice, many genetic crosses of rodent malaria parasites have been performed to map the parasite genes contributing to malaria parasite development, drug resistance, host immune response, and disease pathogenesis. Drs. Richard Carter, David Walliker, and colleagues at the University of Edinburgh, UK, were the pioneers in developing the systems for genetic mapping of malaria parasite traits, including characterization of genetic markers to follow the inheritance and recombination of parasite chromosomes and performing the first genetic cross using rodent malaria parasites. Additionally, many genetic crosses of inbred mice have been performed to link mouse chromosomal loci to the susceptibility to malaria parasite infections. In this chapter, we review and discuss past and recent advances in genetic marker development, performing genetic crosses, and genetic mapping of both parasite and host genes. Genetic mappings using models of rodent malaria parasites and inbred mice have contributed greatly to our understanding of malaria, including parasite development within their hosts, mechanism of drug resistance, and host-parasite interaction.     

Rapid parasite adaptation drives selection for high recombination rates

The Red Queen hypothesis proposes that sex is maintained through selection pressure imposed by coevolving parasites: susceptible hosts are able to escape parasite pressure by recombining their genome to create resistant offspring. However, previous theoretical studies have shown that the Red Queen typically selects against sex unless selection is strong, arguing that high rates of recombination cannot evolve when parasites are of low virulence. Here we show that under the biologically plausible assumption of a severe fitness cost for parasites that fail to infect, the Red Queen can cause selection for high recombination rates, and that the strength of virulence is largely irrelevant to the direction of selection for increased recombination rates. Strong selection on parasites and short generation times make parasites usually better adapted to their hosts than vice versa and can thus favor higher recombination rates in hosts. By demonstrating the importance of host-imposed selection on parasites, our findings resolve previously reported conflicting results.     

Recombination suppression at the dominant <Emphasis Type="Italic">Rhg1/Rfs2</Emphasis> locus underlying soybean resistance to the cyst nematode

Host resistance to “yellow dwarf” or “moonlight” disease cause by any population (Hg type) of Heterodera glycines I., the soybean cyst nematode (SCN), requires a functional allele at rhg1. The host resistance encoded appears to mimic an apoptotic response in the giant cells formed at the nematode feeding site about 24–48 h after nematode feeding commences. Little is known about how the host response to infection is mediated but a linked set of 3 genes has been identified within the rhg1 locus. This study aimed to identify the role of the genes within the locus that includes a receptor-like kinase (RLK), a laccase and an ion antiporter. Used were near isogeneic lines (NILs) that contrasted at their rhg1 alleles, gene-based markers, and a new Hg type 0 and new recombination events. A syntenic gene cluster on Lg B1 was found. The effectiveness of SNP probes from the RLK for distinguishing homolog sequence variants on LgB1 from alleles at the rhg1 locus on LgG was shown. The resistant allele of the rhg1 locus was shown to be dominant in NILs. None of the recombination events were within the cluster of the three candidate genes. Finally, rhg1 was shown to reduce the plant root development. A model for rhg1 as a dominant multi-gene resistance locus based on the developmental control was inferred.     

Reduced variation around drug-resistant dhfr alleles in African Plasmodium falciparum

We have measured microsatellite diversity at 26 markers around the dhfr gene in pyrimethamine-sensitive and -resistant parasites collected in southeast Africa. Through direct comparison with diversity on sensitive chromosomes we have found significant loss of diversity across a region of 70 kb around the most highly resistant allele which is evidence of a selective sweep attributable to selection through widespread use of pyrimethamine (in combination with sulfadoxine) as treatment for malaria. Retrospective analysis through four years of direct and continuous selection from use of sulfadoxine-pyrimethamine as first-line malaria treatment on a Plasmodium falciparum population in KwaZulu Natal, South Africa, has revealed how recombination significantly narrowed the margins of the selective sweep over time. A deterministic model incorporating selection coefficients measured during the same interval indicates that the transition was toward a state of recombination-selection equilibrium. We compared loss of diversity around the same resistance allele in two populations at either extreme of the range of entomological inoculation rates (EIRs), namely, under one infective bite per year in Mpumalanga, South Africa, and more than one per day in southern Tanzania. EIRs determine effective recombination rates and are expected to profoundly influence the dimensions of the selective sweep. Surprisingly, the dimensions were broadly consistent across both populations. We conclude that despite different recombination rates and contrasting drug selection histories in neighboring countries, the region-wide movement of resistant parasites has played a key role in the establishment of resistance in these populations and the dimensions of the selective sweep are dominated by the influence of high initial starting frequencies.     

The classical hitchhiking model with continuous mutational pressure and purifying selection

Detecting selective sweeps driven by strong positive selection and localizing the targets of selection in the genome play a major role in modern population genetics and genomics. Most of these analyses are based on the classical model of genetic hitchhiking proposed by Maynard Smith and Haigh (1974, Genetical Research, 23, 23). Here, we consider extensions of the classical two‐locus model. Introducing mutation at the strongly selected site, we analyze the conditions under which soft sweeps may arise. We identify a new parameter (the ratio of the beneficial mutation rate to the selection coefficient) that characterizes the occurrence of multiple‐origin soft sweeps. Furthermore, we quantify the hitchhiking effect when the polymorphism at the linked locus is not neutral but maintained in a mutation‐selection balance. In this case, we find a smaller relative reduction of heterozygosity at the linked site than for a neutral polymorphism. In our analysis, we use a semi‐deterministic approach; i.e., we analyze the frequency process of the beneficial allele in an infinitely large population when its frequency is above a certain threshold; however, for very small frequencies in the initial phase after the onset of selection we rely on diffusion theory.     

The Evolution of the Y Chromosome with X-Y Recombination

A theoretical population genetic model is developed to explore the consequences of X-Y recombination in the evolution of sex chromosome polymorphism. The model incorporates one sex-determining locus and one locus subject to natural selection. Both loci have two alleles, and the rate of classical meiotic recombination between the loci is r. The alleles at the sex-determining locus specify whether the chromosome is X or Y, and the alleles at the selected locus are arbitrarily labeled A and a. Natural selection is modeled as a process of differential viabilities. The system can be expressed in terms of three recurrence equations, one for the frequency of A on the X-bearing gametes produced by females, one for each of the frequency of A on the X- and Y-bearing gametes produced by males. Several special cases are examined, including X chromosome dominance and symmetric selection. Unusual equilibria are found with the two sexes having very different allele frequencies at the selected locus. A significant finding is that the allowance of recombination results in a much greater opportunity for polymorphism of the Y chromosome. Tighter linkage results in a greater likelihood for equilibria with a large difference between the sex chromosomes in allele frequency.     

Statistical properties of polymorphism in host—parasite genetics

Summary Host—parasite interactions often have complex dynamics. At the level of individual allele frequencies, the dynamics are difficult to predict and difficult to measure. However, aggregate properties of polymorphism, such as allelic diversity or the frequency of resistance, may be relatively easy to work with. I study this problem with computer simulations of a host—parasite model. In one example, the simulations show that the allelic diversity at a locus is similar in a host—parasite model and a neutral model in which drift is the only evolutionary process. Allelic diversity is similar in the two models, even though the temporal dynamics of individual allele frequencies are very different. In a second example, the genetic system that would be inferred from analysing samples of hosts and parasites is quite different from the actual specificity that determines the dynamics of the system. Thus, general conclusions about the specificity of host—parasite genetics must be analysed in the context of the expected statistical distributions of polymorphism. The final example shows that the frequency of resistance provides an interesting aggregate measure of host—parasite polymorphism. If the ratio of parasite generation time to the time between the reproductive seasons of the hosts is small, then no regular periodicity in the frequency of resistance occurs. However, if parasites have many generations per reproductive season of the host, then resistance fluctuates with a period equal to the seasonality of the host. The important role of seasonality shown here differs from the emphasis in previous theories on the relative generation times of host and parasite.     

Hookworm infection,anaemia and genetic variability of the New Zealand sea lion

Hookworms are intestinal blood-feeding nematodes that parasitize and cause high levels of mortality in a wide range of mammals, including otariid pinnipeds. Recently, an empirical study showed that inbreeding (assessed by individual measures of multi-locus heterozygosity) is associated with hookworm-related mortality of California sea lions. If inbreeding increases susceptibility to hookworms, effects would expectedly be stronger in small, fragmented populations. We tested this assumption in the New Zealand sea lion, a threatened otariid that has low levels of genetic variability and high hookworm infection rates. Using a panel of 22 microsatellites, we found that average allelic diversity (5.9) and mean heterozygosity (0.72) were higher than expected for a small population with restricted breeding, and we found no evidence of an association between genetic variability and hookworm resistance. However, similar to what was observed for the California sea lion, homozygosity at a single locus explained the occurrence of anaemia and thrombocytopenia in hookworm-infected pups (generalized linear model, F = 11.81, p < 0.001) and the effect was apparently driven by a particular allele (odds ratio = 34.95%; CI: 7.12–162.41; p < 0.00001). Our study offers further evidence that these haematophagus parasites exert selective pressure on otariid blood-clotting processes.     

Pathogens and sex in plants

Summary Extant theories that attribute the evolution of sex to pathogen attack depend on the assumption that pathogens are narrowly specialized, so that high fitness on one host genotype results in poor fitness on hosts with other allele combinations. This assumption is necessary in order for frequency-dependent selection to produce sustained cycling of gametic disequilibrium across the host's disease resistance loci, which makes recombination advantageous. However, a review of numerous genetic studies on plant disease resistance failed to uncover a single example consistent with this assumption. Instead, the empirical results provide strong support for a different pattern of pathogen specificity, in which adaptation by pathogens to one resistance allele does not preclude high fitness on alternate host genotypes lacking that allele. Modification of traditional models for pathogen-mediated evolution of sex showed that for conditions close to the empirical pattern of genotypic specificity, sex is almost never favoured. For plants, these results cast doubt on current theories arguing that pathogens are the primary selective agent responsible for sexual reproduction.