Extent of selection

An initial application of our method found extensive evidence of positive selection in the viral genome, with 74 (out of 387) nucleotide sites in p24 and 81 (out of 324) nucleotide sites in gp41 being inferred to evolve under positive selection in at least one individual (S1 Table and S1 Fig). Our method explicitly accounts for linkage disequilibrium between alleles observed in the sequencing data[27,32]; a potential remains for interactions between observed alleles in the targeted sequence region, and non-observed alleles in flanking regions of the genome (Fig 1). To estimate the effect of these interactions on our results, we ran simulations to replicate the dynamics of real infections. In a multi-locus system where all alleles under selection are observed (i.e. in which the full data of the system are available), our approach performs very well, identifying the majority of variants under selection with very few false positive inferences. However, when non-observed selected alleles interact with observed alleles via linkage disequilibrium (i.e. where only partial data of the system is available), our approach is prone to generating false positive inferences of selection (S1 Text, S3 and S4 Tables). Data from our simulation study allowed us to set statistical criteria via which we could combine inferences from multiple patients and confidently identify sites under selection, despite the presence of false positive calls.

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Fig 1. Linkage disequilibrium between alleles in the virus.

Here positive selection at locus A affects the behaviour of alleles at locus B due to linkage. Our method of inference corrects for such effects if A is observed, whereas a single-locus method could lead to incorrectly inferring selection at B. However, in the system shown linkage disequilibrium also exists between alleles at A and B and those at the unobserved locus C. Such effects cannot be accounted for by our approach. We used a simulation-based approach to estimate the importance of such effects, so as to account for their influence upon the results generated by our method.

https://doi.org/10.1371/journal.ppat.1008171.g001

Strength and time of onset of selection

Inferred variants generally evolved under weak selection. In constructing a distribution of the strength of selection among selected variants, we first assessed the degree of precision with which this statistic could be inferred at each locus. The uncertainty in a given estimate depends upon the extent to which data are available. For example, when a variant emerges and fixes between two time points, only a lower bound on the strength of selection can be inferred[33]. We therefore generated confidence intervals for each inferred magnitude of selection using a likelihood-based method, retaining only variants for which the upper and lower bounds of this interval differed by no more than an order of magnitude. Distributions of fitness effects compiled from these variants showed that most of the identified alleles under selection experienced very weak selective effects, with long tails of alleles evolving under strong positive selection (Fig 2). Application of our method to simulated data highlighted an undercalling of very weakly selected variants, and an underestimation of the magnitude of selection affecting the strongest variants (S2 Fig), however the overall inferred distribution of selection coefficients was not statistically different to the ‘true’ distribution used to generate simulations (S3 Fig). Further statistical details and notes on these simulations are provided in S1 Text, S4, S5 and S6 Figs.

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Fig 2. Histograms of inferred strengths of selection and times in days of onset of selection across 34 individuals.

The maximum likelihood estimates are shown in each case, for the subset of the data where the upper and lower bound confidence intervals on the strength of selection are within an order of magnitude of each other. Bars indicate variants at nucleotide sites, and are coloured according to whether they are within AA positions associated with differences in susceptibility to CTLs (pink) or susceptibility to NAbs (blue). Where a codon is implicated in both a NAb and CTL response, for clarity it is coloured blue (see S2 Table).

https://doi.org/10.1371/journal.ppat.1008171.g002

In p24, around 65% of inferred selected variants had a strength of selection of less than 5% per generation, while in gp41 approximately half of variants were under this threshold. In our model, selection of 5% per generation would cause, in the absence of interference effects, a change in allele frequency from 5% to 95% in a period of just under eight months. Most selection acting upon variants was inferred to kick in during the first year of infection and almost all within two years, and we found no evidence of a correlation between the strength and time of onset of selection (S7 Fig). Our approach underestimates the proportion of variants under weak selection; very weak selection would not produce a change in the population sufficient to be identified from the data. The extreme beneficial end of the distribution may also be under-represented because variants which fixed within individuals before the first sample was collected cannot be identified from our data. Finally, the finite period of time over which sequencing was performed could restrict the inference of more lately selected variation because a selected variant arising later in infection would have less time to affect the composition of the population in an observable way.

Distribution of selected variants among individuals

Using the simulated data, we identified a statistical threshold at which we could robustly identify specific sites in the genome containing variants under selection despite the presence of false positive inferences of selection. A unique aspect of this dataset is the large number of untreated individuals included in the study. Where alleles at the same locus were inferred to be under selection in multiple individuals, a statistical approach was used to infer loci at which, under conservative assumptions, at least one of the inferred variants is genuinely under selection. Taking into account different patterns for nonsynonymous and synonymous mutations, we estimated per-site false-positive rates for nonsynonymous and synonymous mutations, which were subsequently used to identify with statistical confidence sites that were under selection in at least one individual in our dataset. The process used for estimation is described in full in S1 Text. Taking all 34 individuals into consideration, we calculated that in p24 we could be confident that a site is under selection in at least one individual if mutations were inferred to be under selection in at least five individuals, and/or if nonsynonymous mutations were inferred to be under selection in two or more individuals, while in gp41 we could be confident if at least five mutations and/or three nonsynonymous mutations were inferred to be under selection. This is a conservative approach, and will exclude sites genuinely under selection in only one or a few individuals, for example sites associated with escape from rare HLA alleles or NAbs, or other less common forms of selection.

Applying these criteria, we identified 11 specific nucleotide sites, representing 10 amino acid (AA) positions, under selection in p24, and likewise we identified 11 such sites, representing 8 AA positions, in gp41. All but four mutations at these AA positions represented nonsynonymous changes (see Table 1). Occasionally two different codons at the same AA position were found to be subject to selection in a single individual, but in general repeated inferences of selection at an AA position occurred in distinct individuals (S1 Table). The positions of the identified mutations in their respective protein structure are shown in Fig 3.

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Fig 3. Locations of selected positions on the protein structures of p24 and gp41.

Protein structures with pdb identities and 3J34 and 6NIJ were used to plot these figures [103,104]. Parts of proteins that were covered by sequence data are shown in gray, with the remainder of the protein in white van der Waals representation. Amino acid positions identified by our analysis are shown in red. The gp41 structure does not show the entirety of the sequenced region, with amino acids at positions 670 and 674 also identified in our analysis, but not in the protein structure. Other nearby proteins are shown in white surface representation. Figures were created using the VMD software package [105].

https://doi.org/10.1371/journal.ppat.1008171.g003

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Table 1. Summary of amino acid positions containing sites under selection.

https://doi.org/10.1371/journal.ppat.1008171.t001

Using the Los Alamos HIV database (http://www.hiv.lanl.gov), for all of the AA positions in our study, we determined whether they have previously been associated with changes in CTL susceptibility or NAbs (see Methods, Fig 4, S2 Table). In p24, 43% of sites have previously been associated with changes in CTL susceptibility and/or compensatory mutations, whilst 69% of the variants we inferred to be under selection were associated with CTL and/or compensatory mutations. For the 10 AA positions identified as almost certainly under selection, nine have previously been associated with changes in CTL susceptibility and/or compensatory mutations, and lie in epitope regions recognised by multiple HLA alleles present in the Ugandan population[66–68]. The remaining codon (residue 286 in HXB2 gag) lies within CTL epitopes recognised by human leukocyte antigen (HLA) alleles that are relatively common in the Ugandan population (A1101 and B27[66]) and therefore mutations at this site probably affect sensitivity to CTLs, or possibly compensatory mutations. In gp41, 44% of AA sites have previously been associated with NAbs, whilst 61% of the variants we inferred to be under selection were associated with NAbs. Of the eight AA positions identified as being almost certainly under selection, five (residues 620, 624, 655, 674 and 677 of env) have previously been associated with NAbs, including broadly neutralising antibodies (bNAbs). These are associated with the gp120/g41 interface and the membrane-proximal external region (MPER). The other three codons (residues 641, 644 and 648 of env) all lie within an epitope region that is targeted by the monoclonal antibody HGF24, which has been shown to neutralise some viruses isolated from the African continent[58]. Although we cannot rule out other sources of selection in env, given the position of these codons on the genome, we believe selection due to humoral immune pressure is more likely. As such, all of the sites we identified as under selection in p24 probably affect susceptibility to CTLs or associated compensatory mutations, whereas all of the sites under selection in gp41 probably affect susceptibility to NAbs or associated compensatory mutations.

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Fig 4. Amino Acid (AA) positions containing nucleotide sites that with confidence were inferred to be under selection in at least one individual.

Codon positions are in relation to the HXB2 reference sequence and the vertical y-axis gives the number of times that codon was inferred to be under selection across 34 individuals. Occasionally the same AA position was inferred to be under selection twice in the same individual. Pink: AA positions associated with changes in susceptibility to CTLs or compensatory mutations; Blue: AA positions associated with susceptibility to NAbs. Selection at Gag residue 286 possibly reflects CTL escape in one individual and reversion in another. Selection at Env residues 641, 644, and 648 possibly reflect selection associated with NAbs; these are all within an epitope region targeted by the neutralising antibody HGF24 in some African Isolates[58]. Where an AA position is implicated in CTL and NAb responses, for clarity they are coloured in blue.

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Direction of selection

Since mutations that enable the virus to evade host immune responses are often costly in terms of viral replication[69,70], sites harbouring escape mutations are likely to evolve towards the population-level consensus when transmitted to a new host since the selective pressure of a specific immune response is removed, but costs associated with the mutation remain [2,31,71–74]. This hypothesis is supported by the observation that allelic substitutions during the course of untreated infection occur towards population consensus much more frequently than expected by chance [2,31]. If analysis is restricted to sites where substitutions are observed, this bias is confined mainly to nonsynonymous substitutions[31], which is expected if immune escape mutations are generally nonsynonymous.

Since the HLA types of the 34 individuals in our study are unknown, we followed previous studies by classifying variants we confidently inferred to be under selection as escapes or reversions depending on the population-level consensus[2,71]. Specifically, we classified selected variants as escapes if they resulted in an AA change away from the subtype-specific population-level consensus in Uganda during the period the individuals were being sampled (see Methods for full details). Conversely, inferred selected variants were classified as reversions if they resulted in change towards the subtype-specific population-level consensus. Of the 32 selected nonsynonymous mutations identified in p24, 13 were classified as escapes, 14 as reversions, and five as neither. The similar number of escapes and reversions observed is expected if CTL immune escape mutations are costly in non-HLA matched hosts, with escape in one individual followed by reversion in the next. The observation of one escape and one reversion in residue 286 of gag supports our prediction that this locus likely affects CTL susceptibility. Of the 40 nonsynonymous mutations identified in gp41, 18 were classified as escapes, 11 as reversions, and 11 as neither. The fact that over a quarter of AA changes are towards population consensus suggests that in many cases antibody escape mutations are deleterious in hosts without a matching antibody, but the stereotypical pattern of adaptation in one individual followed by reversion in another found at CTL immune epitopes is likely more complex for antibody-escape evolution, where escape mutations are sometimes, but not always costly in the absence of an antibody response [75,76]. Among the three residues 641, 644 and 648 of env, five of the nine nonsynonymous variants are escapes, three are reversions, and two are neither, supporting our prediction that these sites affect susceptibility to host (probably NAb) immune responses.

We also determined the direction of change for all variants inferred to be under selection, which will likely include variants under direct selection and variants changing in frequency due to hitch-hiking, and whether they represented synonymous or nonsynonymous changes (S8 Fig). We found a clear correlation between the number of times that selection was inferred at an AA position and the proportion of selected variants that were nonsynonymous (linear regression, p24 p = 0.009, r² = 0.85; gp41 p = 0.007, r² = 0.67). For gp41, a correlation was also found between repeated selection at an AA position and a pattern of evolution towards the population consensus (p = 0.011, r² = 0.63); around half of inferred selection events were towards population consensus at the AA position most frequently inferred to be under selection. Although for p24 the linear regression did not reveal a significant trend (p = 0.400, r² = 0.18), there is a distinction between AA positions selected 2 or more times, which have a high probability of being towards subtype-specific population consensus (44%), and AA positions selected once, which have only a small probability of being towards the consensus (5%). Our interpretation is that AA positions represented once in our analysis disproportionately represent mutations increasing in frequency due to hitch-hiking, with these mutations tending to be synonymous and away from population level consensus. AA positions represented multiple times, on the other hand, are more likely to represent immune escapes and reversions, and therefore tend to be nonsynonymous but with only around half of mutations away from consensus.

Comparing codon diversity at the within-host and population scale

Our data showed a strong relationship between within- and between-host sequence diversities, where the diversity of codons was measured at each AA position. Within-host diversity was measured approximately three years after seroconversion for each of the 34 individuals, and the mean calculated. Diversity at the population scale was calculated as the mean of the diversities for each of the subtypes A, D, and C, using virus sequences from a large number of individuals living in Uganda around the same time as the 34 individuals in our study (see Methods). Consistent with previous studies [2], we identified a strong relationship between measurements of sequence diversity calculated at the within-host and population scales (Fig 5, S2 Table), with all AA positions found to be highly diverse at the within-host level also highly diverse at the population level. Moreover, all but one of the AA positions containing nucleotide sites that we are confident are under selection are also diverse at the population level (the exception being residue 302 in gag). Given that most changes at these sites probably reflect escape from host immune responses, compensatory mutations, or reversions of these escapes in subsequent individuals, diversity at the population scale at these AA positions is likely maintained by the differing selection pressures faced by variants in different hosts due to different immunological backgrounds.

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Fig 5. Within- and between-host codon diversity.

For every AA position in our region of analysis we determined the within- and between-host codon diversity. Large markers denote AA positions in which we are confident selection is occurring in at least one individual. Markers are coloured if they are associated with changes in sensitivity to CTLs or compensatory mutations (pink) or NAbs (blue). The site confidently under selection in p24 but which is unspecified (Gag residue 286) is possibly associated with CTL escape. The sites confidently under selection in gp41 but which are unspecified (Env residues 641, 644, and 648) possibly reflect selection associated with NAbs; these are all within an epitope region targeted by the neutralising antibody HGF24 in some African Isolates[58]. Where an AA position is implicated in CTL and NAb responses, for clarity they are coloured in blue.

https://doi.org/10.1371/journal.ppat.1008171.g005

Not all AA positions found to be highly diverse at the population level were detected as being under selection, with a high degree of confidence, at the within-host scale. This observation could arise if codons at these positions are under selection in some individuals in the population, but we failed to observe it with confidence, either because we sampled too few individuals, selection was too weak to be detected, and/or selection drove fixation events before the first sampling time point. In addition, at unconstrained sites experiencing little or no selection, diversity might gradually accumulate at the population scale due to drift, exacerbated by small bottleneck sizes at transmission. This could explain the high levels of population diversity at positions 235 in gag and 609 in env; almost all of the diversity observed at these codon positions is due to the presence of synonymous variants.

Model outline

Our model proceeds through a number of steps (see below for full details). (1) We identified variant alleles from the sequence data using a simple frequency cutoff. Measurements of the frequencies of variant alleles over time were collected into trajectories, each trajectory describing the frequency of a single allele over time. (2) Sets of alleles with similar trajectories were identified, and under the assumption that all of the differences between these similar trajectories resulted from noise in the data, the extent of noise, modelled as a single parameter, was estimated. The noise parameter defines a likelihood function for the data, the existence of which allows for fits to be made between the data and a number of models describing the evolution of the population. (3) Models of evolution at a single locus were used to assess all of the derived trajectories. Comparing the likelihoods of models describing evolution under selective neutrality, and under selection, we identified, using model selection, a subset of trajectories which potentially evolved under non-neutral selection. Such selection could arise either from intrinsic selection for or against the allele, or via linkage disequilibrium with an intrinsically selected allele elsewhere in the genome. (4) We combined the alleles present at each locus that had a potentially non-neutral trajectory into haplotypes, with these haplotypes only describing alleles at the loci identified to have potentially non-neutral trajectories (S9 Fig). (5) For each patient, the number of reads with each observed haplotype at each time of sampling was counted, forming a multi-locus dataset describing the evolution of the virus in that patient over time. (6) A series of multi-locus evolutionary models were fitted to the data from each patient, identifying the most parsimonious explanation of the data in terms of time-dependent selection acting on individual alleles in each dataset. (7) Confidence intervals for the inferred selection parameters were generated, again making use of the likelihood function. The model is thus identical to that described in a previous publication [33] with differences only in the approach to identifying noise in step two, in the models used to fit the data in step six, and in the calculation of confidence intervals for selection.

Sequencing data

For our evolutionary analysis we used previously generated deep-sequence data from 34 longitudinally sampled individuals participating in the Rakai Community Cohort study and co-enrolled in the Molecular Epidemiology Research (MER) seroconverter study. Targeted short-read deep-sequence data from the p24 region of gag (390 bp; HXB2 reference genome positions 1429–1816) and the gp41 region of env (324 bp; HXB2 7941–8264) had been sequenced using the 454 sequencing platform (Roche, Branford, CT). All individuals were untreated, with a first sampling time point around one year since seroconversion, and typically 3 or 4 subsequent time points spanning between two and seven years of infection (see Table 1 in Raghwani et al 2019). Aligned sequences can be found at https://github.com/katrinalythgoe/

RakaiHIV. Further details on the individuals, including viral loads and CD4 counts, and sequencing methods used have been given elsewhere[31,93].

Calling of variant alleles and trajectories from sequence data

Single-locus variants were identified in the data using the SAMFIRE software package[94]. Variants with a minimum allele frequency of at least 1% for at least one time point in the course of infection were identified. Variant frequencies collected over time were described in terms of trajectories. By way of notation, in a given patient we denote the trajectory comprising the observed frequencies of allele a at locus i across all recorded times t_k. Here K is the total number of points in time at which the population was observed via sequencing, which varied between 2 and 5. We note that the frequency is calculated simply as, the number of observations of allele a at locus i at time t_k divided by the total number of alleles observed at locus i at time t_k.

Estimating the extent of noise in the data

Noise in sequence data can arise either through the collection of an unrepresentative sample of viruses from a patient, or via errors induced in the experimental processing and sequencing of that sample [93]. We here applied a heuristic method to derive a conservative estimate of the extent of noise in the data from the data itself. This was achieved by exploiting effects caused by genetic hitch-hiking[95]. If two alleles appear uniquely upon a shared genetic background, they will initially share an identical allele frequency. Over time the allele frequencies will change in a very similar manner, differences arising over time as a result of recombination between distinct haplotypes. We thus identified putatively hitch-hiking trajectories to derive an estimate of noise in the sequence dataset.

For this analysis, we considered loci at which a minor allele frequency of at least 10% was observed in samples collected at two points in time. Loci in HIV can potentially have multiple alleles satisfying this condition. For each pair of such loci, i, and j, we found the alleles a*, b* minimising the statistic where the minimisation was calculated over all polymorphic alleles at the loci i and j. Initially, pairs of trajectories (i,a*) and (j,b*) were denoted as being ‘similar’ if

A set of further heuristic steps was then applied to refine these sets of trajectories. On timescales close to those over which the data for this study was measured, recombination in HIV-1 has been noted as being of importance over genetic distances greater than 100 nucleotides [2]; here a distance cutoff of less than or equal to 50 nucleotides was imposed between trajectories, that is |i-j| ≤ 50.

Next, under the assumption that pairs of our variants initially arose on the same background, pairs were required to have similar frequencies at the first time of observation, requiring that

Further, so as to remove pairs of trajectories for which only one was polymorphic at a given time, it was required that the maximum ratio between minor allele frequencies did not exceed 10³ for the duration of the trajectories; the framework of a Dirichlet multinomial model we subsequently use to estimate the extent of noise does not perform well on very low frequencies. Remaining sets of pairs identified in each patient were clustered into sets via an iterative process; beginning with an initial pair of trajectories (i₁, a₁) and (i₂, a₂), a trajectory (i_m, a_m) was added to the set if, following filtering, (i_m, a_m) was similar to a trajectory (i_n, a_n) already in the set. Sets of trajectories generated by the above process are shown in S10 Fig.

Having identified sets of trajectories, an inference process was used to evaluate the extent of noise in the data. Conservatively, the ‘true’ allele frequencies of each set were calculated as a simple mean of the observations, thereby assuming that all differences in frequencies result from ‘noise’ in the sequencing process. Given a set of trajectories S from a single viral population, recalling that was calculated as , the inferred frequency at time t_k was calculated as the mean fraction of variant alleles across all loci with trajectories in S. That is,

A Dirichlet multinomial model was then parameterised across all trajectory sets, finding the value of C satisfying Where the summations are, respectively, calculated over sets of similar trajectories S, trajectories m in each set S, and samples k in each trajectory, and where the likelihood is the Dirichlet multinomial function in which the sums and products with index a are calculated over all alleles at a specific locus, or equivalently over all haplotypes within a population, while G indicates the gamma function.

The derived value of C provides a proxy measurement of the extent of noise in the data and was used in further likelihood calculations; we inferred the value C = 100.359. Qualitatively, this value represents the extent to which the variance of a sample of haplotypes is overdispersed in relation to a simple multinomial sample; a small value of Crepresents an increased amount of uncertainty in the data, tending towards a uniform distribution, in which samples are fully uninformative, while a high value of C represents increased uncertainty, tending towards a multinomial sample in which every read precisely identifies a haplotype in a perfectly representative sample from the population. We note that patterns of noise in genome sequence data may be substantially more complex than represented by our model; our likelihood, combined with the BIC model selection framework, provides a simple yet analytically tractable approach for the inference of selection parameters from real genome sequence data.

Identification of potentially non-neutral loci

Considering frequency data from each variant allele, ‘potentially non-neutral’ loci [92] at which significant changes in allele frequency were observed over time were identified. In this process, where q¹(t) denotes the frequency of the variant allele at locus i at time t, deterministic models of evolution at a single locus were fitted to the single-locus trajectories, using the equation for neutral (σ_k = 0), constant (σ_k = s), and time dependent models of selection, retaining trajectories for which the constant or time-dependent models of selection outperformed the neutral model. This was evaluated using the Bayesian Information Criterion (BIC) to account for the increased complexity of the models including selection [96].

Construction of haplotypes

For each individual, only potentially non-neutral loci were retained for the rest of the analysis, with each combination of alleles at these sites representing a haplotype. We converted the sequence data into a set describing the number of times each haplotype was observed in the sequence data, at each sampling time point. For example, if three non-neutral loci were identified, we might count the number of reads with the alleles G, A, and C at these loci at a given time point; the proportion of such reads would specify the observed frequency of the haplotype GAC. Only viral haplotypes which were observed in the sequencing data were considered, generally representing a small fraction of the haplotypes that could potentially exist. This approximation is equivalent to the assumption that non-observed viral haplotypes were under sufficiently strong purifying selection to prevent them from reaching an observable frequency.

Multi-locus evolutionary models

Our evolutionary models considered the effect of mutation, selection, and recombination upon the population. Within a model the frequency of the haplotype a at generation t_k of the within-host viral population was specified by the frequency q_a(t_k), frequencies changing according to the three evolutionary processes. The model system was propagated within the space of observed haplotypes using a Wright-Fisher approach of discrete generations, with successive steps of mutation, recombination and selection.

Mutation was approximated as occurring between haplotypes that differ by a single nucleotide with rate μ per generation. Recombination was approximated as occurring in a pairwise manner between haplotypes with rate ρ per base per generation. That is, if a recombination event occurring between the loci indexed i and i+1, and involving the haplotypes a and b, were to produce the haplotype c, then in our model the new haplotype was produced at rate Δ_i,i+1ρq_a(t_k)q_b(t_k) where Δ_i,i+1 is the sequence distance between loci i and i+1.

A time-dependent model of selection acting upon haplotypes was applied, simulating the changing selection acting upon HIV during an infection. The time-dependent fitness w_a of a haplotype a at time t was modelled via a hierarchical model of single-locus terms where the sum is calculated over all loci i in the set of potentially non-neutral loci identified above. The parameter s_i denotes selection acting for or against all haplotypes with a variant at locus i, and the parameter I_{i,a,Ti} is a binary indicator function. Here, T_i is the time at which selection begins to act upon the variant allele at locus i. The indicator function is set so that I_{i,a,Ti} = 1 if t>T_i, and if the haplotype a contains the variant allele at locus i, while I_{i,a,Ti} = 0 if it is true either that a does not contain the variant allele at i, or if t ≤ T_i.

Selection then modifies the frequency of each haplotype according to the equation where the sum with index b indicates a sum over all haplotypes, including a. In this manner the frequency of a haplotype changes according to the relation between its fitness and the mean fitness of the total viral population.

On the basis of previous studies[77,97–100], parameters for mutation and recombination were set at μ = 3 x 10⁻⁵ per generation and ρ = 10⁻⁵ per base per generation, with a generation time of two days[101], reflecting parameters derived from studies of chronic infection. Parameters σ_i and T_i, and initial frequencies q^a(t₀), were learnt from the data according to a hierarchical model framework. An initial, neutral model contained no selection parameters, every haplotype having equal fitness. Next, single-locus selection models were considered. Such a model uses the set of parameters i, a, σ_i, and T_i, to describe the locus and allele at which selection acted, the magnitude of selection and the time at which selection took effect. In each model, given the loci and allele under selection, the optimal values for the magnitudes and times of selection were identified, using a simple likelihood optimisation process. The Dirichlet multinomial likelihood described above, with the inferred noise parameter C, was used in this process, matching the observed haplotype frequencies to those produced by the evolutionary model. To improve coding efficiency a model lacking mutation and recombination was used to derive reasonable starting parameters for selection and haplotype frequencies; the subsequent application of a model with the addition of mutation, then the full model with mutation and recombination gave the final likelihood and maximum likelihood parameters. Replicate calculations with different random seeds were used to validate likelihood calculations. By means of an iterative process, more complex models of selection were considered. Initially, selection parameters were added, taking the best n-locus models and adding selection at an additional locus to each one. Upon the discovery of a model for which adding selection at a further locus did not improve the model, a process involving both the addition and subtraction of parameters was initiated, to the point of discovering a model for which neither adding a further pair of selection parameters, or removing an existing pair of parameters, improved the model. The comparison of models was performed using the Bayesian Information Criterion. As a conservative step, a model with an additional pair of selection parameters was required to significantly outperform a simpler model to be accepted, this being denoted by an improvement of 10 units of BIC given a maximum likelihood set of parameters for each model. Compared to an earlier model of selection at multiple loci [28], our approach has the advantage of parsimony, inferring selection at a locus only where there is specific evidence for non-neutrality at that site. Our model of time-dependent selection accounts for the expected behaviour of the host immune system against HIV. No prior distribution of selection coefficients was assumed.

Estimating confidence intervals for selection coefficients

Confidence intervals were calculated for each parameter s_i inferred in the maximum likelihood calculation. Supposing the maximum log likelihood for a given inferred system to be equal to some value L, error bars were generated via a constrained exploration of the model space, in which a change in model parameters was accepted if the resulting likelihood was not greater than L-2, and for which changes to the parameter of concern, σ_i, were constrained so that this parameter could only change in a specific direction; forcing this parameter to increase generated an estimate, after repeated iteration, for the upper error bar of this parameter, while forcing this parameter to decrease generated an estimate of the lower error bar of this parameter.

Reporting selection coefficients

In our study we report the respective fitness advantage conferred by each beneficial mutation as a percentage per generation. This statistic, s, is calculated from an inferred selection coefficient as

Direction of selection

For each of the selected mutations identified in our analysis, we determined whether evolution was towards or away from the subtype-specific population consensus. The subtype of each gene region for each individual and the population consensus for subtypes A, D and C in Uganda during a similar period to which the individuals were sampled was previously determined[31].

Amino Acid position association with immune escape

Using the Los Alamos HIV database (http://www.hiv.lanl.gov), we determined for each of the AA positions in the p24 and gp41 regions that we analysed whether they have previously been associated with changes in CTL susceptibility or neutralising antibodies. For CTL susceptibility we used the Epitope Variant and Escape Mutation Database CTL variant search tool (https://www.hiv.lanl.gov/content/immunology/variants/variant_search.html?db=ctl). AA positions were marked as being associated with susceptibility to CTLs if susceptible and/or resistant variants were returned in the search tool. We excluded codons inferred to be susceptible to CTLs if the only evidence was high levels of diversity at the population level. For neutralising antibodies we used the Neutralizing Antibody Contacts and Features search tool (https://www.hiv.lanl.gov/components/sequence/HIV/featuredb/search/env_ab_search_pub.comp), marking codons as associated with susceptibility if variants were shown or predicted to affect neutralisation by antibodies, or binding to neutralising antibodies.

Codon diversity

We used the diversity statistic π to measure mean intra- and inter-host diversity at the codon level. Given a locus a at which the read depth is N, where n_a of each codon a was where n_i of each of the three-nucleotide codons i have been observed, we define the diversity statistic π as

This diversity statistic has been shown to be less prone than some other metrics to biases at the intra-host scale[102], and using codons (nucleotide triplet motifs) rather than amino acids or single nucleotides means our measure incorporates synonymous and nonsynonymous diversity whilst still enabling comparison with information on sensitivity to host immune responses, which is typically given at the amino acid level. To determine the mean intra-host diversity at a given codon position, we calculated π for each individual and then took the mean for all 34 individuals. To determine the mean inter-host diversity at a given codon position we calculated π for each subtype and then took the mean for all three subtypes (A, C and D).

Application of the method to simulated data

The performance of our method was evaluated using simulated data, generated in order to be as close in nature as possible to the real data. A complete discussion of the methods used is given in S1 Text.