Introduction

Human interventions perturb microbial populations in many ways. Most obviously, the use of antibiotics or vaccines that target some strains and not others provide opportunities for new strains to emerge and become established. Examples include vaccines for antigenically diverse human pathogens like influenza, Neisseria meningitidis, Haemophilus influenzae, Streptococcus pneumoniae, and human papillomavirus [1–3]. Predicting these changes is a central goal of population genomic and evolutionary studies of pathogens as these data may inform vaccine development, surveillance activities, and drug discovery [4–7]. For bacteria in particular, detailed predictions of how a population will respond to a selective pressure are challenging. Models that specify how mutations with a given fitness change in frequency over time are often hard to apply in practice, as we typically do not know in advance important parameters such as the fitness value of particular alleles or how this is affected by their frequency (frequency-dependent selection) or genetic background (epistasis) [8,9].

Ongoing efforts to control disease caused by S. pneumoniae (the pneumococcus), a colonizer of the human nasopharynx and a cause of pneumonia, bacteremia, meningitis, and otitis media, underscore the difficulties of predicting changes after introduction of a vaccine [10]. Pneumococcal conjugate vaccines (PCVs) target only a fraction of this antigenically diverse species, which contains over 90 distinct serotypes defined by the antigenic properties of the polysaccharide capsule [11]. In the United States, the 7-valent PCV7 vaccine was introduced in 2000 and targeted 7 serotypes (4, 6B, 9V, 14, 18C, 19F, and 23F) that were responsible for the greatest proportion of invasive pneumococcal disease, whereas the successor 13-valent pneumococcal conjugate vaccine (PCV13), was introduced in 2010 and targeted 13 serotypes (1, 3, 4, 5, 6A, 6B, 7F, 9V, 14, 18C, 19A, 19F, and 23F) [12]. Following widespread introduction of PCVs among children, the carriage prevalence of pneumococci remained largely unchanged (approximately 30% of the general US population) [13,14] and nonvaccine serotypes (NVTs) benefited from the removal of their vaccine-serotype (VT) competitors and became more common in carriage and disease, with the gains from reducing VT disease partly offset by increases in NVT disease [14–16]. In some instances, this led to an increase in NVT serotypes capable of causing severe disease or that harbored genes conferring antimicrobial resistance [17,18]. These changes in the pathogen population varied by location and were not fully appreciated until retrospective analysis [19–21].

Our recent study of pneumococcal carriage isolates that were collected before and after PCV7 vaccine introduction in the Southwest US [21] illustrates the complexity in post-vaccine population dynamics, echoing findings from other studies. Pneumococcal populations contain multiple “sequence clusters,” which are closely related lineages, defined on the basis of sequence variation in loci present among all isolates (i.e., the core genome) [22]. We henceforth use the term strains to refer to these lineages/sequence clusters and note that different isolates of a single strain may exhibit different serotypes. In general, although their frequencies vary markedly between locations, the dominant S. pneumoniae strains are widespread [23,24]. Variation in genome content due to horizontal gene transfer is a hallmark of prokaryotes; therefore, in addition to the core genome, we can define the accessory genome, as those genes not found in all isolates in the sample [25,26]. Consistent with their close phylogenetic relatedness in terms of core genome sequence variation, each strain we identify is composed of isolates that are fairly homogeneous—but not completely so—in the presence/absence of accessory genes as well as phenotypic properties such as serotype and antibiotic resistance [27].

Previous work showed that post-vaccine success of pneumococcal strains may depend on the accessory genome [24,28]. In many bacteria, this can be a large fraction of the total number of genes found in a species (i.e., the “pangenome”) [29,30]. A population genomic study of pneumococci in Massachusetts children found that vaccination had remarkably little effect, after 6 years, on the overall frequencies of individual accessory genes (defined as clusters of orthologous groups [COGs]) [28]. Despite the fact that nearly half the pre-vaccine population had serotypes targeted by the vaccine, only 2 of >3,000 loci in the accessory genome significantly decreased in frequency 6 years post-vaccine, and none increased [28]. More recently, a geographically diverse sample of pneumococcal genomes showed that although the distribution of strains varied widely across the globe, the proportion of isolates in each sample containing each individual accessory gene was highly consistent across locations [24]. Where vaccine was introduced, accessory gene frequencies were perturbed by the removal of vaccine types but trended back toward their pre-vaccine frequencies over time [21,24,31]. Negative frequency-dependent selection (NFDS) was proposed as the mechanism by which the frequencies of loci were restored after vaccine introduction [24]. NFDS is a type of balancing selection, which maintains diversity by favoring variants when rare but exacting a cost when they become common, such that the frequency of the variant stabilizes at intermediate values or, in some instances, result in frequency oscillations [9]. Examples of mechanisms produced by NFDS include host immunity and bacteriophage predation, and as such, balancing selection is recognized as a key contributor to population composition and diversity [32,33]. Among pneumococci, similar processes have been proposed to explain the coexistence of multiple serotypes [34] and vaccine-induced metabolic shifts [35].

Here, we present flexible, easily computable statistics that estimate the fitness of any strain using the contents of its accessory genome as a proxy for how it will be affected by NFDS, dependent on the frequencies of other strains in the population and specifically, of the accessory genes they carry. Even though we do not know the specific loci under selection or the mechanism involved, we are able to make predictions about the composition of a population as well as predict the fitness of any strain in any population, whether or not it has yet appeared in that population. Overall, this predictive model offers a way to study population processes and the response to interventions.

Results

In the sample of 937 pneumococcal isolates composed of 35 strains from the Southwest US, we observed a sharp decline in PCV7-VT strains following vaccination (Fig 1 and S1 Fig). VT strains were subsequently replaced by NVT strains, including 2 emergent NVT strains that had not been observed pre-vaccine, although they were present during the same time period in a carriage dataset from Massachusetts [21,28]. We first show that there was considerable deviation from the null expectation that NVT strains would increase in prevalence pro rata to their pre-vaccine frequency; the most common NVT strains before vaccination were not necessarily the most prevalent 12 years after the introduction of the vaccine (Fig 1A). In particular, we find 13 of 35 strains deviated significantly from the prevalence expected under a null pro rata model; 9 were more common than expected, and 4 were less common (annotated with plus and minus signs, respectively, in Fig 1B). The impact of vaccination on individual NVT strains was, hence, not easily predictable. Consequently, public health authorities and vaccine manufacturers have had to rely on surveillance after the introduction of PCV7 to estimate the next epidemiologically important lineage and determine subsequent vaccine formulations. At best, this uncertainty reduces the population impact of vaccination; at worst, it could unintentionally increase the prevalence of virulent or antibiotic resistant lineages [36].

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Fig 1. Strain’s prevalence.

A. Pre-vaccine to post-vaccine SCs. Strains are ordered from highest to lowest pre-vaccine prevalence. Raw data used in this figure are included in S1 Table. Observed prevalence change calculated as post-vaccine frequencies minus pre-vaccine frequencies. Changes in prevalence are compared with that expected under a pro rata null model (i.e., not using the predictive methods in this paper). Observed changes in prevalence are represented by points colored by the serotype composition of the strain: NVT only, PCV7 VT only, and VT-NVT. The point and whiskers show the prevalence change expected if all VT strains were removed and NVT increased proportional to their pre-vaccine prevalence—i.e., in a null model of pro rata increase in which only the VT strains were removed and all NVT strains increased equally in proportion to their pre-vaccine prevalence. The dot is the median, and the whiskers give the 2.5% and 97.5% quantiles of predicted changes under the null model using 10,000 bootstraps from pre-vaccine samples. Significant differences between the changes in prevalence from the pro rata model and the observed data are denoted with plus and minus signs specifying strains that were significantly more (n = 9) or less (n = 4) common, respectively. Among the most successful were strains that contained both VT and NVT isolates (SC-22 and SC-23) whose NVT component included serotypes 6C, 15C, and 35B, as well as SC-24 and SC-25, which were dominated by the NVT serotypes 23A and 15C, respectively. SC-27 is polyphyletic, composed of an aggregate of strains that are at low frequency in the overall population. Compared with strains composed of solely NVT isolates, those with mixed NVT-VT had marginally higher risk differences, indicating greater success than expected under the null model (β = 0.03, SE = 0.015, F(1,29) = 3.67, p = 0.06). Two strains that emerged during the study period (SC-10 and SC-24) were not included in this analysis as they were not present at the first time point. See S1 Data and S1 Code for details. NVT, nonvaccine serotype; SC, sequence cluster; SE, standard error; VT, vaccine serotype; VT-NVT, mixed VT and NVT.

https://doi.org/10.1371/journal.pbio.3000878.g001

Having documented that there were strains that increased significantly more or less than their pre-vaccine frequency would indicate, we sought to define a parsimonious predictive algorithm based on NFDS that could account for these changes. We hypothesized that evolutionary dynamics could be predicted on the premise that after perturbation by vaccine, strains characterized by accessory genomes that could best restore the pre-perturbation accessory gene frequency equilibrium would have the highest fitness and therefore increase in prevalence disproportionately. To this end, we implemented a deterministic model using the replicator equation to calculate the fitness of a strain based on its accessory genome, using vaccination as an example of perturbation [37–39] (Eq 1).

(1)

Under this formulation, x_i denotes the frequency of strain i (i = {1, …, n}) after the vaccine introduction, n is the total number of strains, ω_i denotes the fitness of strain i (adapted from Ref. [24]), and φ is the average population fitness. The difference (ω − φ) is a standardized predicted fitness. The fitness vector ω is defined as the product of 2 elements (Eq 2), matrix K and the vector (e − f). The element k_i,l of matrix K is a value between 0 and 1 and refers to the frequency of accessory gene l in strain i. The element l^th of the vector (e − f) corresponds to the difference between accessory gene l’s pre-vaccine frequency and its post-vaccine frequency. Here, f_l is defined as the frequency of gene l among the isolates that are nonvaccine types. Intuitively, this vector represents the gap that vaccination produces in the population in terms of the accessory loci it removes, and ω_i quantifies the ability of strain i to fill that gap. In contrast with previous work [24], we do not define carrying capacity or migration rates, requiring only knowledge of the accessory gene frequencies at equilibrium and which strains they are associated with; these quantities can be estimated from a population survey prior to the perturbation of interest. We assume that the impact of recombination on the accessory genome is negligible over the time period we study here.

(2)

Using simulated data, we first assessed the ability of a strain’s standardized predicted fitness (ω − φ) (for brevity, we drop the modifier “standardized” hereafter) to predict the direction of its change in frequency, based on its ability to resolve the vaccine-induced perturbation (Fig 2). Note that this predicted fitness uses only data available before vaccine rollout. Using this model, we show that in simulated datasets, the predicted fitness is consistent with the direction of a simulated strain’s adjusted prevalence change (i.e., changes in prevalence minus what would be expected if all NVT strains increased by the same proportion from their pre-vaccine prevalence) 92.8% of cases (Fig 2B).

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Fig 2. Simulations.

A. Conceptual diagram for simulations. Descriptive representation of the strain prevalence at different stages relative to vaccine introduction: pre-vaccine equilibrium, vaccine introduction, and post-vaccine equilibrium. We modeled a population of VT and NVT strains (represented as unique genotypes with alleles 1 or 0 at a locus, denoting the presence or absence of a single accessory locus) and simulated the removal of VT genotypes, following the post-vaccine population to equilibrium (details in methods). In this illustrative figure, 8 strains are shown, with their prevalence in the population evolving over time. The system is allowed to evolve until it reaches a steady state (“pre-vaccine equilibrium”). Three strains were then targeted to mimic a vaccine introduction, which removes them from the system. The predicted fitness was then estimated from the period just after the vaccine introduction, when the population has been depleted of VT but relative prevalence of NVT has not changed—a quantity that can be calculated from pre-vaccine data alone. Finally, the system reaches a second steady state (“post-vaccine equilibrium”). Different shades of blue represent the rank of the strain frequencies in the post-vaccine equilibrium. B. Predicted fitness. Comparison of the direction of prevalence change of strains from pre- to post-vaccine using simulated data and predicted fitness from these simulated data. For these 10 replicate simulations, 2,371 accessory loci and 35 randomly chosen strains were simulated, including 3 VT genotypes. For each replicate, the pre-vaccine equilibrium frequencies of the 2,371 accessory loci were varied. Final prevalence of strains was obtained by quadratic programing, and prevalence change for each NVT strain was calculated as post-vaccine prevalence minus pre-vaccine prevalence, in both cases with all NVT strains summing to 100%. Each column in the decreased and increased category represents the results from 1 simulation (i.e., the first column in the decreased category corresponds to the first column in the increased category, and the dots sum to 32). The predicted fitness of the strain accurately predicts the direction of the prevalence change in 92.8% of cases (teal dots). Gray dots represent instances in which the direction of the prevalence change was not predicted correctly in the simulation. See S1 Data and S1 Code for details. NVT, nonvaccine serotype; VT, vaccine serotype.

https://doi.org/10.1371/journal.pbio.3000878.g002

Next, we asked whether this approach could predict the post-vaccine composition of an actual pneumococcal population and specifically, the relative contribution of each strain to serotype replacement. For each strain present before vaccine introduction, we used the accessory genome to calculate the strain’s fitness following the removal of vaccine types. We identified 2,371 genes that were present in between 5% and 95% of isolates. In this dataset, we found the predicted fitness value was significantly and positively correlated with the observed prevalence change (Adjusted R² = 0.41, p << 0.001, Fig 3A). Further, the trajectory following vaccination, whether increasing or decreasing in frequency, was accurately predicted for 28 of the 31 tested strains identified in the sample, as indicated by the upper right and lower left quadrants of Fig 3A. Strains with a positive prevalence change had substantially higher predicted fitness than those with a negative one (mean fitness of strains that increased versus decreased 6.4 versus −2.4; 95% CI 5.0–12.5, p < 0.001).

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Fig 3. Predicted fitness and predicted prevalence.

A, Relationship between predicted fitness and observed prevalence change from pre- to post-vaccine among 31 strains, in each case summing to 100%. Prevalence change was calculated as post-vaccine frequencies minus pre-vaccine frequencies. Predicted fitness was calculated using data solely from the pre-vaccine sample (n = 27), with the exceptions of strains for which there were no NVT isolates present in the sample before the introduction of PCV7 (n = 4). For those strains, data were imputed from the time point during which they were first observed. Four strains were excluded either because they were polyphyletic (SC-27) or had no NVT isolates present pre- or post-vaccine, and therefore could not be imputed (SC-04C, SC-12, and SC-17). The points are colored by serotype composition of strains: nonvaccine types in blue and mixed VT and NVT types in yellow. The shaded quadrants indicate regions of accurate prediction of the prevalence change direction (increased post-vaccine versus decreased) given the predicted fitness value. Three outlier strains are annotated for which the predicted direction of their prevalence change differed from that which was observed (i.e., they were predicted to increase based on their fitness when their prevalence from pre- to post-vaccine decreased, or vice versa). B, Scatterplot of observed versus predicted prevalence of 27 strains at post-vaccine equilibrium based on quadratic programming. These 27 strains contained at least 1 NVT strain pre-vaccine. Points are colored based on serotype composition as described in panel A. Perfect predictions would lie on the dotted line of equality (1:1 line). The shaded gray region shows the CI from the linear regression model used to test for deviation of the observed versus predicted values compared with the 1:1 line. Two outliers are annotated for which the difference between their predicted and observed prevalence was >1.5 times the interquartile range of the distribution of predicted and observed prevalence differences. As a note, the predictions remained significant if SC-09 (the extreme strain at 10% prevalence in B) was removed (slope, 95% CI 0.021–1.05; intercept, 95% CI −0.003 to 0.03; p = 0.19, chi-squared = 3.5). C-D, Comparison of the predicted prevalence change from quadratic programming analysis using accessory genes and naive pro rata model as shown in Fig 1B but applied to just these 27 strains. The dotted line of equality (1:1 line) and CI (gray) are shown as in panel B. Goodness-of-fit statistics including SSE, RMSE, and degrees of freedom Adj. R² are given for each model. The lower SSE and RMSE indicate a better model fit. See S1 Data and S1 Code for details. Adj. R², adjusted R-squared; NFDS, negative frequency-dependent selection; NVT, nonvaccine serotype; PCV7, 7-valent pneumococcal conjugate vaccine; RMSE, root mean squared error; SC, sequence cluster; SSE, sum of squared errors; VT, vaccine serotype.

https://doi.org/10.1371/journal.pbio.3000878.g003

Although the predicted fitness estimates how successful each strain will be immediately following vaccination, the long-term post-vaccine prevalence or change in prevalence of each strain is of more direct interest for evolution and public health. Thus, we posited that over time post-vaccine, accessory gene frequencies would evolve to match as closely as possible to match those present pre-vaccine, and we used an optimization technique, quadratic programming, to calculate the NVT strain composition that produced these gene frequencies closest to those observed in the pre-vaccine population. Here, we specifically focused on only the 27 strains that were observed pre-vaccine in the Southwest US sample, allowing a projection with only data that were available at the time of vaccine introduction. This approach predicted the strain composition of the population following vaccination well, characterized by a 95% CI of the observed versus predicted post-vaccine strain frequencies that includes the line of equality (1:1 line), which denotes a perfect prediction, and by an intercept and slope that does not differ significantly from zero and one, respectively (p = 0.24; intercept 95% CI −0.005 to 0.030; slope 95% CI 0.257–1.075, Fig 3B). Similar results were obtained when comparing predicted and observed change in prevalence (Fig 3C), where again the dotted line of equality fell within the 95% CI of the regression of observed versus predicted change in prevalence (p = 0.75; intercept 95% CI −0.02 to 0.01; slope 95% CI 0.23–1.36). In comparison, a naive pro rata estimate based solely on pre-vaccine prevalence performed poorly in predicting the prevalence change (Fig 3D, p = 0.001; intercept 95% CI −0.05 to −0.008; slope 95% CI −1.43 to 0.35).

In the Southwest US, the 13-valent PCV13 vaccine was introduced during the second half of our post-vaccine sampling [21]. Despite this, the prevalence of PCV13 vaccine serotypes remained largely unchanged, suggesting little impact of this vaccine over the period of our study. To test the potential effect on our current analysis, we partitioned the post-vaccine sample into pre- and peri-PCV13 (i.e., around the time that PCV13 was initially introduced but before a significant proportion of the population was immunized), and the results are provided in Table 1, which demonstrate that our predictions were robust to subsampling. Finally, we tested the predictive value of different genomic elements, which are linked to accessory genes, finding that core genome loci (n_loci = 17,101) and metabolic loci (n_loci = 5,853) were also capable of predicting the impact of vaccine, though not as accurately as the accessory genome based on goodness-of-fit statistics (Table 1). This finding must be considered in the context of recombination, selection, and the evolutionary timescale impacting the pneumococcal genome, which may impact the varying magnitude of NFDS signal across sets of loci. Despite moderate levels of bacterial recombination among pneumococci, there remains appreciable linkage disequilibrium between loci nearby as well as genome-wide [8], which makes it difficult to discern the relative selective importance of any particular locus. Exactly which genomic elements are responsible for the predictive ability we document here is unknown but is obviously of interest and should be a focus for future work.

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Table 1. Comparison of pre- to post-vaccine prevalence change predictions using multiple models.

https://doi.org/10.1371/journal.pbio.3000878.t001

To further support our findings, we examined a previously published carriage dataset of pneumococci colonizing children in Massachusetts. This dataset is imperfect in several respects. First, it was smaller (N = 616), particularly the initial sample from the population, which had only 131 isolates and came in the first year of vaccine introduction rather than before it. Also making this dataset less ideal, the last sample was obtained only 6 years after the first sample, giving less time for evolution to occur than in our Southwest US dataset. Changes in strain frequencies are shown in S2A and S2B Fig. Despite the limitations of the dataset, applying the same quadratic programming approach, we could predict the post-vaccine equilibrium prevalence of the 9 strains used in the analysis (p = 0.65; intercept 95% CI −0.05 to 0.09; slope 95% CI 0.25–1.33) better than the pro rata model (S2C–S2E Fig).

Last, by combining the Massachusetts and Southwest US datasets [28,40], we assessed the capacity for migration and emergence of the 2 strains that were first observed in the Southwest US sample after the introduction of the PCV7 vaccine, shown as SC-10 (serotype 19A; ST320) and SC-24 (serotypes 15A, 23A/B; ST338) in Fig 1 and S1 Fig. These 2 strains were present at the initial time point in the Massachusetts dataset (2001–2004) and also increased in prevalence thereafter. We found that they have a predicted fitness of 8.6 and 7.2, for SC-10 and SC-24 respectively, higher than any of the other potential migrant strains that were not present in our Southwest US sample before vaccination, indicating that their accessory gene frequencies were well adapted to offset the PCV7 perturbation in the Southwest US population. Indeed, only 2 of the strains present before vaccination in the Southwest US (SC-23 and SC-9) had a higher predicted fitness, suggesting that this approach can be used to quantify which strains are most likely to successfully invade a population.

Discussion

We show that by estimating the fitness of strains using an NFDS-based model and the frequencies of accessory genes, we are able to predict the direction of prevalence change following vaccination and more broadly, the post-vaccine population composition. The ability of this type of balancing selection to determine the strain composition of a population is consistent with findings from environmental microbiology on multiple bacterial species [33]. Among pneumococci, changes in population dynamics after the introduction of vaccine have been explained by selection on many different aspects of the organism, including metabolic types, antibiotic resistance, carriage duration, recombination rates, and serotype competition, all of which are likely to be relevant contributors alongside, or components of, the accessory genome [35,36,41,42]. We provide a simple and effective approach for estimating the fitness of any strain in a population evolving under NFDS acting on accessory loci. All that is required is knowledge of the strain composition of the population and the accessory loci associated with each strain, as this approach does not depend on NFDS acting on particular known biological functions to predict the consequences of vaccination. It is quite conceivable that a minority of loci are involved, including even SNPs in the core genome, which also show a correlation (see Table 1 and [24]). We do not wish to imply that the sorts of selection discussed here act alone. Our previous work suggests the interplay between host immunity and polymorphic protein antigens may play a significant role [43], and other work suggests an important role for metabolic loci in the core genome [35]. Phage predation and defense as well as antibiotic resistance all likely contribute to the observed signal [27].

The pneumococcus is well known for being naturally transformable and indeed, exhibits high rates of homologous and nonhomologous recombination, which can vary quite markedly among strains [27,44]. Recombination plays a significant role in the movement and therefore distribution of accessory loci as well as the evolution of new strains, which, together with mutation, dictates population structure. However, the timescale over which recombination results in measurable changes to a population is unclear. In some instances, dramatic changes may occur rapidly, such as capsular switches that lead to the emergence of new strains [45]. In others, such as the movement of large mobile elements, the process may occur much slowly, as those elements have been found to be relatively stable within strains [27]. Of note, the strains included in the present study are estimated to have emerged, on average, 90 years ago, with the youngest strain (SC10) emerging around the introduction of PCV7 in the US (2010) [21]. Despite this seemingly long duration, the distribution of accessory loci within a strain is relatively uniform. Further, although recombination makes conventional phylogenetic analysis problematic, the methods we use to define strains [46] are not phylogenetic in nature, and we are not concerned with the details of the relationships between or within the strains, merely the definition of strains as a lineage of closely related bacteria that share characteristics of their core and accessory genomes.

There are 2 primary ways in which NVT strains can fill the gap left in the population by vaccination, depending on their genomic relatedness to the removed PCV7 VT strains. First, NVT taxa that are closely related to VT strains in core and accessory genomes are opportune replacements and are therefore expected to be more successful than average following vaccination. There are 2 strains in our dataset that are examples of this, which both increased after vaccination (see SC-09 and SC-23 in Fig 1 and S1 Fig). We therefore expect that for any strain that contains both VT and NVT representatives, the NVT fraction will increase post-vaccine, especially because these NVT taxa are sometimes similar to their VT counterparts in terms of serotype properties such as capsule thickness and charge, which are independently correlated with prevalence [47,48]. A good example of this is the serotype 15B/C component of strain SC-26 of the Southwest US sample, which we now predict to be successful following the more recent introduction of a vaccine incorporating 6 additional serotypes (PCV13) and which has indeed been noted to be increasing in certain locations [49–51]. Second, where such close relatives are not available, the pre-vaccine frequencies of accessory genes can be restored by other NVT that are divergent in core genomes but similar in accessory genomes. This association likely often results from the movement of mobile genetic elements (MGEs) in the population (e.g., phages and transposons) or nonhomologous recombination, which can make distantly related strains more similar in terms of genome content. As illustrated by the pairwise comparison of core/accessory genome divergence and absolute fitness difference of each strain (S3 Fig), there is an appreciable range of differences in fitness for strains that are equidistant in core and accessory genome divergence.

Certainly, as shown by outliers to predictions in Fig 3, we acknowledge that the model does not currently capture all population dynamics. Variation among loci in the strength of NFDS could account for some of these discrepancies, as indicated by retrospective model fitting. Other explanations include differences in the distribution of antibiotic resistance genes or possible vaccine cross-reactivity. For example, SC-18, containing serotype 6C, declined despite a positive predicted fitness; however, cross-reactivity between the PCV7 6B vaccine component and 6C may in part explain this observation [52]. Last, as components of the accessory genome may be redundant, meaning they encode similar functions or represent a single mobile element, our predictive power may be limited. Nevertheless, given the many potential pressures, mostly not directly observable, that we might expect to structure the pneumococcal population, it is notable how effectively this approach can predict the impact of this perturbation. Overall, we find a significant relationship between predicted fitness and the adjusted prevalence change of a strain. By optimizing the prevalence of each strain conditional on the gene frequencies before vaccination, we can estimate the equilibrium population after vaccination, using both the predicted fitness and numerical approximations of the post-vaccine equilibrium.

Predicting evolution is a central goal of population genomics especially when related to pathogens and human health. Although evolutionary theory provides an understanding of bacterial population processes including the relative success of lineages, distribution of phenotypes, and ecological niche adaption, these analyses are often conducted retrospectively. Here, we demonstrate a method for predicting the impact of perturbing the pneumococcal population that may be useful to predict the outcomes of future interventions including vaccines. An example application is the ability to predict the increase in strains 10 and 26, which are largely composed of serotype 19A and are significant for their antibiotic resistance and virulence [18]. The observed increase in invasive disease caused by serotype 19A after the introduction of PCV7 led to its later inclusion in PCV13. In principle, predicting the increase of 19A prior to PCV7 development would have guided decisions on serotype composition of the vaccine. Further, by incorporating information on invasive capacity based on serotype and epidemiological data, these predictions could be extended to inform changes in invasive disease rates [53]. Overall, these dynamics suggest novel vaccine strategies in which one could target those strains whose removal would result in a predicted re-equilibration that favors the least virulent or most drug-susceptible lineages [54].

Our findings suggest numerous potential directions for future work, among them identifying the specific accessory loci or other genomic elements that are responsible for what we observe. Expanding the model to include immigration of other strains and disentangling the relative contribution of selection on various loci is likely to be a fruitful area for future research. One area worth exploring is the degree to which recombination acts to maintain gene frequencies on the timescale of population-level shifts in lineage composition. The emergence of new strains, characterized by novel combinations of accessory loci, is expected to be limited by the other strains present in the population in ways that are currently not well understood. The pervasive finding of accessory genomes in most bacterial species is usually explained by specialization of lineages to specific niches; however, it could also reflect widespread NFDS, and so future work should seek for evidence of similar signal in the core and accessory genome of other bacteria [55].

Methods

Supporting information

Acknowledgments

The ideas in this paper and the collaborative relationships underlying them are owed in significant part to the Permafrost Conference on Microbial Genomics, of Blessed Memory.