Genome-Wide Association Studies Reveal a Simple Genetic Basis of Resistance to Naturally Coevolving Viruses in

Summary

Variation in susceptibility to infectious disease often has a substantial genetic component in animal and plant populations. We have used genome-wide association studies (GWAS) in Drosophila melanogaster to identify the genetic basis of variation in susceptibility to viral infection. We found that there is substantially more genetic variation in susceptibility to two viruses that naturally infect D. melanogaster (DCV and DMelSV) than to two viruses isolated from other insects (FHV and DAffSV). Furthermore, this increased variation is caused by a small number of common polymorphisms that have a major effect on resistance and can individually explain up to 47% of the heritability in disease susceptibility. For two of these polymorphisms, it has previously been shown that they have been driven to a high frequency by natural selection. An advantage of GWAS in Drosophila is that the results can be confirmed experimentally. We verified that a gene called pastrel—which was previously not known to have an antiviral function—is associated with DCV-resistance by knocking down its expression by RNAi. Our data suggest that selection for resistance to infectious disease can increase genetic variation by increasing the frequency of major-effect alleles, and this has resulted in a simple genetic basis to variation in virus resistance.

Introduction

Variation in susceptibility to infectious disease often has a substantial genetic component in animal and plant populations [1]–[4]. As pathogens are a powerful selective force in the wild, natural selection is expected to play an important role in determining the nature of this genetic variation. Selection for resistance to infectious disease can change rapidly, as new pathogens appear in the population [5], or existing pathogens evolve, for example to evade or sabotage host defences [6]. This selection can result both in positive selection increasing the frequency of mutations that generate new resistance alleles [7], [8], and balancing selection stably maintaining resistant and susceptible alleles of a gene [9].

Over the last decade, genome-wide association studies (GWAS) have provided a more complete picture of the genetic architecture of disease susceptibility [10]. The majority of these studies have investigated non-communicable diseases in humans, and while many polymorphisms associated with susceptibility have been identified, these often have small effects and together can explain only a small proportion of the heritability [11] (but see [12]). It has been suggested that the reason for this is that new mutations that increase susceptibility to non-communicable disease may tend to be deleterious, so alleles that have large effects are either removed from the population or kept at a low frequency by purifying selection [11]. However, both GWAS and classical linkage mapping studies suggest that the genetic architecture of infectious disease susceptibility may be qualitatively different [13], as major effect polymorphisms that protect hosts against infection have been identified in many organisms, including plants [11], humans [3], [13] and insects [7], [14]. Furthermore, these polymorphisms are often under strong positive or balancing selection [7]–[9]. It has therefore been argued that natural selection may cause the variation in infectious disease susceptibility to have a simpler genetic architecture than non-communicable diseases as major-effect alleles can reach a higher frequency in populations [13].

In arthropods, several studies suggest that susceptibility to infectious disease may often be affected by major-effect polymorphisms (e.g.[7], [14], [15]). In Drosophila melanogaster, linkage mapping has been used to identify major effect resistance polymorphisms that affect susceptibility to both the sigma virus (DMelSV) [16], [17] and parasitoid wasps [18]. In the case of DMelSV, two of these loci have been identified at the molecular level (ref(2)P and CHKov1), and they have been found to be common in natural populations [7], [14], [19]. In addition, polymorphisms in known immunity genes have been found to affect susceptibility to bacterial infection, and some of these have substantial effects [2], [20], [21].

To understand how natural selection affects the genetics of disease susceptibility, we have used GWAS to examine the effects of selection for resistance to pathogens on patterns of genetic variation. To do this we infected D. melanogaster both with viruses that naturally occur in this species and viruses isolated from other species. The two of the viruses that naturally infect D. melanogaster are Drosophila C Virus (DCV), which is a positive sense RNA virus in the Dicistroviridae that infects a range of Drosophila species [22], [23], and the sigma virus DMelSV, which is a rhabdovirus that is a specialist on D. melanogaster [16]. The other two viruses naturally infect other insect species are DAffSV, which is another sigma virus that naturally infects Drosophila affinis [24], [25] and Flock House Virus (FHV), which is a nodavirus that was isolated from beetles but can infect an extremely broad range of organisms [26]. We found that the heritability of susceptibility to the two natural D. melanogaster viruses is high due to a small number of common major-effect polymorphisms. In contrast there is less genetic variation in susceptibility to viruses isolated from other species, and here there is no evidence of major effect polymorphisms.

Results

Genetic variation in virus resistance

To investigate genetic variation in resistance to viruses, we injected 47,220 flies from 185 different inbred lines from the Drosophila Genetic Reference Panel (DGRP) with four different viruses (Table 1; note that the DMelSV data, but not this analysis, has been published before [7]). The extent of genetic variation in susceptibility varied considerably between the different viruses, with the greatest genetic variation being present when flies are exposed to viruses that infect D. melanogaster in nature. Comparing the two viruses where resistance was measured in terms of survival time—DCV and FHV—we found DCV resistance has significantly greater heritability (Table 1). When the two sigma viruses, DMelSV and DAffSV, are compared, again the heritability is significantly greater in resistance to the naturally occurring virus DMelSV (Table 1). While differences in heritability can be caused by differences in genetic or environmental variation, it is clear that there is genetic variation in resistance to the natural pathogens of D. melanogaster. In the case of DCV and FHV, DCV has the greater coefficient of genetic variation (Table 1; CV_g) [27]. It is not possible to calculate the coefficient on variation for the sigma virus data as it is analysed on a logit scale. However, by inspecting V_e and V_g in Table 1, it is clear that the differences in the heritability of resistance to DMelSV and DAffSV are primarily driven by differences in V_g.

In all cases the genetic correlation in the level of resistance to different viruses is low, indicating that different genes are controlling resistance to different viruses (Table 2). In particular, the sigma viruses (DMelSV and DAffSV) showed no evidence of any genetic correlation, despite being relatively closely related [24], [25]. Despite being small, there is a significant positive genetic correlation in susceptibility between three pairs of viruses, indicating that there may be some variation in the ability to survive viral infection in general. The low genetic correlations also confirm that we are measuring susceptibility to the different viruses and not an artefact of the injection procedure.

Resistance to viruses that infect D. melanogaster in the wild has a simple genetic basis

To identify polymorphisms that are associated with resistance to the four viruses, we performed genome-wide association studies using the published genome sequences of the DGRP lines [28]. To correct for multiple tests and obtain a genome-wide significance threshold, we permuted the trait data across the lines and repeated the GWAS 400 times, each time recording the lowest P-value across the entire genome. Quantile-quantile (qq) plots of the P-values show that there are highly significant associations in the experiments using DCV and DMelSV — the two viruses that infect D. melanogaster in the wild — but not in the experiments using FHV and DAffSV (Figure 1).

When the P-values are plotted along the chromosomes, it is clear that the most significant P-values cluster together (Figure 2, Figure S1). In the case of DMelSV there is a cluster of significant SNPs around CHKov1 on chromosome arm 3R, which is a gene where we have previously shown that a transposable element insertion is associated with resistance to this virus [7] (Figure 2, Figure S1). The second most significant cluster of SNPs in this experiment falls just below the genome-wide significance threshold, and is on chromosome arm 2L (Figure 2, Figure S1). The SNPs in this cluster are all in strong linkage disequilibrium with a polymorphism in ref(2)P that is known to cause resistance (the causal polymorphism was genotyped by PCR and included in this analysis),[8], [14]. In the case of DCV there is a cluster of significant SNPs in and around a gene on chromosome arm 3L called pastrel, which has not previously been implicated in antiviral defence. There were no significant associations with susceptibility to FHV or DAffSV using a genome-wide significance threshold of P<0.05 (Figure 2, Figure S1).

We repeated the GWAS accounting for the effects of the polymorphisms in ref(2)P, CHKov1 and pastrel. The quantile-quantile plots of the resulting P-values (Figure 1, red points) show that these genes can account for all of the large excess of highly significant associations with DCV and DMelSV resistance. The resulting distribution of P-values resembles that seen for the other two viruses that do not naturally infect D. melanogaster.

To investigate how much of the genetic variation in susceptibility is explained by our GWAS, we calculated the proportion of the heritability that is explained by these genes. Assuming the polymorphisms have additive effects, then their contribution to additive genetic variation is 2pqa², where p and q are the frequencies of the alleles, and a and −a are the genotypic values of the resistant and susceptible homozygotes. In the case of DCV, pastrel (3L:7350895) can explain 47% of the heritability. In the case of DMelSV, ref(2)P explains 8% of the heritability, the doc element insertion in CHKov1 explains 29% of the heritability, and in combination these polymorphisms explain 37% of the heritability.

The proportion of the heritability explained by these polymorphisms may be biased by two factors. First, we are injecting the virus, which is an unnatural route of infection, and in the case of the sigma viruses we are assaying a symptom of infection rather than viral titres or effects on host survival. Second, we can only estimate the amount of genetic variation explained in inbred lines, and this can only be directly extrapolated to outcrossed populations if all the genes affecting resistance are additive. Unfortunately, we cannot estimate the importance or direction of this bias as we only used inbred lines (the only one of the three genes for which levels of dominance has been investigated is ref(2)P, where heterozygotes have intermediate levels of resistance when injected with the virus [29]). However, the bias could be substantial if we make the extreme assumptions about dominance. If the susceptible pastrel allele is recessive and only half the remaining genetic variance is additive, this polymorphism will explain 84% of V_a in an outcrossed population. Conversely, if the resistant pastrel allele is fully dominant and all the remaining genetic variance is additive, this polymorphism will explain just 7% of V_a in an outcrossed population.

In addition to these major-effect polymorphisms, there were also other suggestive results. The most significant association for DAffSV was a synonymous SNP in scavenger receptor C1 (2L:4123156 A/T; individual P = 6.41×10⁻⁸; genome-wide permutation P = 0.18). This gene functions both as a pattern recognition receptor of bacteria [30] and allows the uptake of dsRNA into cells [31]. A polymorphism in the gene Anaphase promoting complex 7 was associated with a 3.7 day increase in survival after injection with DCV (X:6491634 G/T; individual P = 1.95×10⁻¹⁵; genome-wide permutation P<0.05). This was at a low frequency, with the resistant variant present in 4 of 145 lines. Furthermore, it is a synonymous polymorphism, suggesting that it may not be a causal variant. The QQ plots also show that there is an excess of small P-values in three of the analyses (Figure 1), suggesting that there may be many more polymorphisms to be discovered, or that there is some unidentified population stratification.

As the polymorphisms in pastrel, CHKov1 and ref(2)P have a large effect on resistance, we repeated the GWAS taking account of these polymorphisms by including them as fixed effects in the model. However, this did not lead to the identification of additional SNPs associated with resistance (Figure S2). The most significant association with DCV resistance remained Anaphase promoting complex 7 (X:6491634 G/T). For DMelSV it was a SNP in the intron of off-track (2R:7899322 A/T, genome-wide P = 0.29), which is a transmembrane receptor that controls a variety of developmental and physiological processes [32].

Resistance genes are specific to different viruses

The polymorphisms in pastrel, CHKov1 and ref(2)P have highly specific effects, altering susceptibility to just one of the four viruses (Figure 3). Against these target viruses, the effect on the susceptibility of individual flies is considerable (Figure 3). Comparing flies that are homozygous for the resistant and susceptible alleles, the most significant SNP in pastrel increases survival times by 55%. The doc element insertion in CHKov1 reduces the proportion of infected flies by 39%, while the ref(2)P polymorphism is associated with a 24% reduction in infection rates (see also [7]). When large numbers of statistical tests are performed and the statistical power is low, as is the case in many genetic association studies, there is a tendency to overestimate effect sizes [33]. However, the extremely low P-values associated with our resistance genes suggest our statistical power was high and therefore these effect size estimates are reliable.

pastrel confers resistance to DCV

In pastrel there are six SNPs that are associated with resistance to DCV at P<10⁻¹². These include two adjacent SNPs in the 3′UTR (genome positions: 3L:7350452 T/G, 3L:7350453 A/G), two non-synonymous SNPs (3L:7350895 Ala/Thr, 3L:7352880 Glu/Gly) and two SNPs in introns (3L:7351494 C/T, 3L:7352966 T/G). All of these are in linkage disequilibrium, with the two SNPs in the 3′ UTR being perfectly associated (these are therefore considered as a single variant in subsequent analyses). To try and disentangle which of the polymorphisms might be a causal variant, we fitted a general linear mixed-effects model in which all five variants were included as fixed effects. This allows us to calculate the marginal significance of each polymorphism (i.e. the P-value after controlling for the effects of all the other SNPs). In this analysis only a non-synonymous SNP in the last coding exon of the pastrel remained highly significant (3L:7350895: F_1,116 = 18.2, P<0.0001; all other P-values>0.01). This SNP occurred in 21 of 142 lines that were sequenced at this site. We then tested the significance of each of the other four variants individually while controlling for the effects of 3L:7350895, by fitting general linear mixed-effects models and calculating sequential P-values from an ANOVA table. When we did this, all the other SNPs are significant (P<0.0001 in all cases). If we assume that we have included all the polymorphisms in this region in our analysis, this suggests that the non-synonymous polymorphism 3L:7350895 and at least one of the other sites are causal variants — but strong linkage disequilibrium prevents us from identifying which one(s). However, many polymorphisms, including indels, are missing from this dataset, so another polymorphism in this region that is not included in our analysis may be causing flies to be resistant to DCV.

To confirm the antiviral role of pastrel, we used RNAi to knock down the gene in flies that were homozygous for the susceptible allele. To do this, we expressed hairpin RNAs that target the pastrel gene under the control of a constitutively and ubiquitously expressed Gal4 driver. When the flies were infected with a high dose of DCV, this resulted in a large reduction in survival rates relative to both a control with a similar genetic background (Figure 4A; Cox proportional hazard mixed model: z = 3.62, P = 0.0003) and a control where we knocked down a gene unrelated to viral resistance (Figure 4A; Cox proportional hazard mixed model: z = 3.19 P = 0.001). To allow us to investigate viral titres, we also infected flies with a lower dose of DCV, which caused less mortality (Figure 4A). The viral titre in the flies where pastrel had been knocked down was ∼6 times greater than the background control and ∼15 times greater than the control gene (Figure 4B; F_2,18 = 23.3, P = 10⁻⁵).

Discussion

We have found that a small number of major-effect polymorphisms can explain a substantial proportion of the genetic variation in the susceptibility of D. melanogaster to viral infection. These genes have either been previously identified by linkage mapping, or, in the case of pastrel, were verified by RNAi in this study. These polymorphisms are only seen when flies were infected with the two viruses that occur naturally in D. melanogaster populations — we were unable to detect any significant associations when using viruses that naturally infect other insects. The consequence of this is that the genetic variation in susceptibility to the naturally occurring viruses is substantially greater than to viruses from other species. Combined with previous data showing that two of these resistance alleles have been driven to a high frequency by positive selection [7], [8], [34], these results suggest that selection by viruses in natural populations may be increasing genetic variation in disease susceptibility. As the resistance alleles that we detected have highly specific effects against a single virus, genetic variation in susceptibility to infection by viruses isolated from other species of insects has remained low.

Our results support the suggestion that the genetic architecture of infectious disease susceptibility may be different from non-communicable diseases due to selection by parasites [13], [35]. GWAS in humans have mostly focused on non-communicable disease, and have tended to find polymorphisms of modest effect. In contrast, work on infectious disease in humans has described numerous loci with a major-effect on susceptibility [3], [13], [35], and similar patterns have been reported by QTL studies in other animals [36]. This has led to the suggestion that variation in pathogen resistance may often be controlled by a mixture of major-effect polymorphisms and other loci that are difficult to detect because they are rare or have small effects [13]. Our results corroborate this pattern, as while we find a few major-effect genes, over half of the total genetic variation remains unexplained. Furthermore, our results provide support for the role of natural selection by parasites in increasing the frequency and effect size of disease susceptibility loci. If this pattern proves to apply to other species, then GWAS on susceptibility to infectious disease promises to be a productive direction for future research.

Parasites can result both in balancing selection maintaining polymorphisms in host resistance, and directional selection, which will ultimately fix the resistant allele [6]. Previous work has shown that the resistant alleles of CHKov1 and ref(2)P both arose recently by mutation and natural selection has caused them to increase in frequency [7], [8], [34], [37]. Therefore, it appears as though directional selection is driving new resistance genes through the population, and this is increasing genetic variation in disease susceptibility.

Directional selection on a trait can result in higher genetic variance when selection is acting on alleles that are initially at a low frequency [38]–[40]. If this is the case, selection will increase the frequency of rare alleles that previously contributed little to genetic variation in the population, and will therefore increase genetic variation in the trait [38]–[40]. For example, this process is thought to explain why selection by mate choice increases genetic variation in the cuticular hydrocarbons produced by Drosophila serrata [41]. In the case of the polymorphisms in ref(2)P and CHKov1, previous work has suggested that they have undergone a ‘hard’ selective sweep, where selection has been acting on new or rare polymorphisms [7], [8], [34], [37]. Therefore, they will have contributed little to genetic variation before selection, but now explain much of the heritability in this population. Certain traits, such as insecticide resistance, normally evolve in this way with selection acting on rare alleles [42]. This is thought to be because there are relatively few genetic changes that can cause insecticide resistance, and therefore there are too few mutations to generate much standing genetic variation [42]. If resistance to viruses also normally evolves due to selection on rare alleles, it may be common for directional selection to increase genetic variation. Fluctuating selection by parasites through time and space, or negatively frequency-dependent selection may also play an important role in increasing genetic variation.

In addition to the genes that we have identified, the bacterial symbiont Wolbachia also makes D. melanogaster more resistant to viral infection [43], [44]. Wolbachia occurs in natural populations, and protects flies against two of the viruses we studied — DCV and FHV [43], [44] (but not sigma viruses, Teixeira, Magwire and Wilfert, Pers. Comm.). As Wolbachia is transmitted vertically from mother to offspring, in many ways it can be regarded as another major-effect resistance polymorphism. We cured Wolbachia in our experiments with DCV and FHV and therefore have no data on its effects, but in natural populations of D. melanogaster it varies in prevalence from below 1% to near fixation [45]. This may affect how selection acts on the polymorphisms that we have identified, as our resistance genes may confer less of a benefit in populations where Wolbachia is common.

Will the genetic architecture of resistance to other classes of pathogens be similar to the pattern we have seen for viruses? In Drosophila, parasitoid wasps are one of the main causes of mortality in natural populations [46], and both linkage mapping and artificial selection experiments suggest that resistance against these parasites is controlled by a few major-effect loci [18], [47], [48]. There is also extensive variation in bacterial resistance, and polymorphisms in immune system genes explain a substantial proportion of this variation [49], [50]. It is difficult to compare these results directly to our own as comparatively few markers were genotyped and only known immune genes were investigated. Nonetheless, it would appear possible that bacterial resistance may have a more complex genetic architecture than virus resistance, involving more genes and epistatic interactions. Furthermore, there was not the clear difference between bacteria isolated from D. melanogaster and other organisms that we observed among our viruses [49], [50]. This may be because there is a broad-spectrum induced immune response against bacteria [51] but not viruses [52], or because the viruses may have a narrower host range, resulting in more rapid coevolution.

In the long term, the spread of the resistance genes through populations could either result in the virus evolving to overcome host resistance, or a permanent increase in the levels of resistance seen in the host population. Due to their high mutation rates, short generation times and large population sizes, RNA viruses can evolve rapidly [53]. Therefore, it is perhaps unsurprising that during the 1980s and 1990s sigma virus genotypes that were not affected by ref(2)P resistance spread through European populations of D. melanogaster [54]. This suggests that we may be observing one side of a coevolutionary arms race between hosts and parasites.

While the antimicrobial immune response of Drosophila is well-understood, we have only begun to understand in detail how Drosophila defends itself against viruses in the last six years [55]. Resistance to viruses could potentially evolve by altering the immune system (antiviral genes), or host factors that are usually exploited by viruses during the viral replication cycle (proviral genes). The only highly significant gene that we identified with a well-characterised function encodes ref(2)P, which is a homolog of the mammalian protein p62 [56]. This is a scaffold protein that has several functions, including in targeting cargoes such as protein aggregates and pathogens for destruction by autophagy — a process by which the cargo is wrapped in a double membrane vesicle called an autophagosome, which then fuses with the lysosome and is degraded [57], [58]. Autophagy was recently found to be an important component of antiviral immunity in D. melanogaster infected with vesicular stomatitis virus (VSV), which is another rhabdovirus that is related to DMelSV [24], [59]. Therefore, it is possible that this polymorphism is affecting the antiviral immune response. We also found suggestive evidence that a polymorphism in scavenger receptor C1 may be important in defence against DAffSV. This gene functions both as a pattern recognition receptor of bacteria [30] and allows the uptake of dsRNA into cells, resulting in an RNAi response [31]. The function of this gene therefore suggests it is a strong candidate as a component of antiviral immunity.

The functions of the two genes that have the largest effects on susceptibility, CHKov1 and pastrel, in antiviral defence remain unclear, although pastrel is thought to play a role in protein secretion [60]. Interestingly, knocking down the susceptible allele of this gene further increased susceptibility, suggesting that even the susceptible allele of the gene has some antiviral effect. Therefore, this gene may be part of the flies antiviral immune system. Characterising the role of CHKov1 and pastrel in the immune system or the viral life cycle promises to yield new insights into both how animals evolve resistance to infection, and how viruses interact with their hosts.

Methods

Resistance assays

Many of the DGRP lines are infected with Wolbachia bacteria [28], which affects susceptibility to DCV and FHV [44]. To clear the stocks of Wolbachia infection, flies were reared for two generations on food prepared by adding 6 ml of 0.05% w/v tetracycline to a vial containing 5 g instant Drosophila medium (Carolina Biological, Burlington, North Carolina, U.S.A.) and yeast. We checked the flies were uninfected by PCR as described in reference [61]. Lab fly stocks can also be naturally infected by DCV, so the lines were also cleared of natural virus infections by aging adult flies for 20 days and then dechorionating embryos with a ∼5% sodium hypochlorite solution [16]. A small number of the lines assayed for DAffSV were not treated in this way, but excluding these lines did not alter the results. Note that the DMelSV data was collected previously, before the lines were treated [7] (Wolbachia does not affect sigma viruses, Teixeira, Magwire and Wilfert, Pers. Comm.).

The generation prior to injecting the viruses, vials were set up containing two male and two female flies on cornmeal-agar food. For each fly line/virus combination, we set up 4 vials whenever possible. To maximise the level of cross-factoring, we always used different combinations of fly lines on each day of injecting. The flies were injected with 69 nl of the virus suspension intra-abdominally as described in detail in references [62], [63]. The infection of D. melanogaster by DAffSV has not been characterised before, so we first injected flies with the virus and monitored viral titres and the characteristic symptom of sigma virus infection — sensitivity to CO₂. These pilot experiments confirmed previous results that the virus can replicate in D. melanogaster [62], and also showed that infected flies are paralysed following exposure to CO₂ (Figure S3).

Therefore, to assay for infection by DAffSV, flies were exposed to pure carbon dioxide for 15 min at 12°C at 15 days post-injection. By 30 min post-exposure, flies are awake from this anaesthesia were classed as uninfected, but flies that were dead or paralysed were classed as infected [24]. To assay for susceptibility to DCV and FHV we recorded survival every 24 hours until all the flies had died. Due to a historical accident, the DCV and FHV experiments used male flies and the DAffSV and DMelSV experiments used females. Therefore, care should be taken in comparing these datasets (note that these pairs of experiments also differ in the trait being measured). The DMelSV data has been published previously [7], [8]. We have genotyped the DGRP lines for the polymorphisms in CHKov1 and ref(2)P by PCR as described in reference [7], [8].

We knocked down the pastrel gene by RNAi. Males from line UAS-pst (P{KK105159}VIE-260B) were crossed to Actin-GAL4 (w*;; P{GAL4-da.G32}UH1) virgins. As controls, males from a line with the same genetic background as UAS-pst (y,w¹¹¹⁸;P{attP,y⁺,w^3′}) and UAS-CG10669 (P{KK105150}VIE-260B) were also crossed to Actin-GAL4 virgins. F1 females were injected with DCV. We used two doses of DCV (high: TCID₅₀ = 1000 and low: TCID₅₀ = 690). We note that these were from different viral preparations, which may explain why this small difference in TCID₅₀ caused a large difference in mortality.

We measured DCV titres by quantitative PCR using the SensiFAST™ SYBR & Fluorescein Kit (Bioline, UK). DCV was amplified using the primers DCV 6060F (5′-CTTGCGGACCCTTTGTACGAC-3′) and DCV 7320R (5′-GCCATTCGAACTTGACCACGCAG-3′). As an endogenous control we amplified Actin5c using the primers qActin5c_for2 (5′GAGCGCGGTTACTCTTTCAC 3′) and qActin5c_rev2 (5′ AAGCCTCCATTCCCAAGAAC 3′).We performed three technical replicates of each PCR and used the mean of these in subsequent analyses. We calculated the titre of DCV relative to Actin5c as 2^ΔCt, where ΔCt is the critical threshold cycle of DCV minus the critical threshold cycle of Actin5c. This approach assumes near 100% primer efficiency, which was confirmed using a dilution series of the template cDNA.

Analysis of genetic variation

We fitted a series of linear models to estimate genetic variances and covariances. For FHV and DCV, our data consisted of the lifespan of individual flies, which we treat as a Gaussian response in a general linear model. We fitted separate models for each virus, which were formulated as follows. Let y_ijk be survival time (days after injection) of fly k from line i and vial j.

where β is the mean survival time across all lines, b_i is a random variable representing the deviation from the overall mean of the ith line, c_j is a random variable representing the deviation jth vial from the line mean, and ε_i,j,k is the residual error.

For DMelSV and DAffSV our data consist of numbers of infected and uninfected flies in each vial, which we treat as a binomial response in a generalized linear model. Let v_i,k be the probability of flies in vial k from line i being infected.

where β is the overall mean, b_i is a random variable representing the deviation from the overall mean of the ith line, and ε_ik is a residual which captures over-dispersion within each vial due to unaccounted for heterogeneity between vials in the probability of infection.

To estimate the genetic correlations between the viruses, we analysed data from all four viruses using a single model. To allow us to treat data from all four viruses as a binomial response in a generalized linear model, for FHV and DCV we used the numbers of dead and alive flies on a single day. Let v_i,j,k be the probability of flies, in vial k from line i and infected with virus j being dead.

where β is a vector of the mean survival times of the four virus types, and x_i is a row vector relating this fixed effect to vial i. b_i,j is the random effect of virus k on line j, and was assumed to be multivariate normally distributed, allowing us to estimate separate line variances for each virus type and covariances between all pairwise combinations of viruses. ε_i,j,k is the residual which captures over-dispersion within each vial. The residuals were assumed to be normally distributed with a separate variance estimated for each virus type.

The parameters of the models were estimated using the R library MCMCglmm [64], which uses Bayesian Markov chain Monte Carlo (MCMC) techniques. Each model was run for 1.3 million iterations with a burn-in of 300,000, a thinning interval of 100 and improper priors. We confirmed these results were not influenced by the choice of prior in the Bayesian analysis by also fitting models 1 and 2 using maximum likelihood (data not shown). Credible intervals on variances, correlations, and heritability were calculated from highest posterior density intervals.

As these fly lines are homozygous across most genes in the genome, the genetic variance, V_g, is half the between-line variance (assuming additive genetic variation). This allows us to calculate the heritability of DCV and FHV as:

Where V_v is the between vial variance and V_r is the residual variance. As the DMelSV and DAffSV parameters are on a logit scale, we calculated heritability as:

where is the variance of a logistic distribution (the cumulative distribution function of the logistic distribution is the inverse logit function, the link function used in the model; [65], [66]). Note that the between-vial variance is included in V_r in this model. In Table 1, we calculate V_e as V_r+. When calculating the proportion of the heritability explained by the polymorphisms we identified, we recalculated V_g after accounting for these polymorphisms, and then adjusted the numerators of equations (4) and (5) accordingly.

We also calculated the coefficient of genetic variation, CV_g, for DCV and FHV as , where β is the mean survival time [27]. To estimate the proportion of the heritability that is explained by these genes we assumed the polymorphisms have additive effects, so their contribution to additive genetic variation is 2pqa², where p and q are the frequencies of the alleles in the population used to calculate h², and a is half the difference in the survival or infection probability of flies that are homozygous for the resistant and susceptible alleles (i.e. a and −a are the genotypic values of the resistant and susceptible homozygotes). The maximum likelihood estimate of a, , was obtained by regressing genotype against the line means during the GWAS (see below). An unbiased estimate of a² was obtained as ² minus the square of the standard error of . In this calculation, the heritability of resistance to DMelSV was recalculated from the line means which were treated as Gaussian data.

We used robust statistics to analyse data on viral titres due to the presence of an outlier in the data. We fitted a linear model by robust regression using an M estimator and used a robust F test to assess significance [67].

Genome-wide association study

To identify single nucleotide polymorphisms (SNPs) that were associated to susceptibility, we performed a GWAS using the published DGRP genome sequences [28]. We only included biallelic SNPs where the minor allele occurred in at least 4 lines, and treated segregating sites within lines as missing data. In the case of DCV and FHV, the susceptibility of the line was measured as the mean survival time of flies in each line (with the vials of flies weighted by the number of flies in each vial). In the case of DMelSV and DAffSV, the susceptibility of the line was measured as the proportion of flies that were infected, as determined by the CO₂ assay. The DAffSV data was arcsine square root transformed to remove the dependence of the variance on the mean. To each SNP we fitted the linear model r_i,j = β+m_i+ε_i, where r_i,j is the susceptibility of flies with SNP genotype i from line j, β is the overall mean, m_i is the SNP i genotype, and ε_ik the residual. As major-effect polymorphisms affect the susceptibility of flies to DCV and DMelSV, the analysis was then repeated including the genotype of these genes as an additional explanatory variable.

Because we are performing multiple correlated tests, we determined a genome-wide significance threshold for the association between a SNP and phenotype by permutation. The phenotype data were permuted over the different recombinant lines, the genome-wide association study was repeated as described above, and the minimum P-value across the entire genome was recorded. This was carried out 400 times to generate a null distribution.

Supporting Information

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