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Variable rates of SARS-CoV-2 evolution in chronic infections [1]

['Ewan W. Smith', 'Mrc-University Of Glasgow Centre For Virus Research', 'Glasgow', 'United Kingdom', 'William L. Hamilton', 'Department Of Medicine', 'University Of Cambridge', 'Cambridge', 'Cambridge University Hospitals Nhs Foundation Trust', 'Wellcome Sanger Institute']

Date: 2025-05 

Abstract An important feature of the evolution of the SARS-CoV-2 virus has been the emergence of highly mutated novel variants, which are characterised by the gain of multiple mutations relative to viruses circulating in the general global population. Cases of chronic viral infection have been suggested as an explanation for this phenomenon, whereby an extended period of infection, with an increased rate of evolution, creates viruses with substantial genetic novelty. However, measuring a rate of evolution during chronic infection is made more difficult by the potential existence of compartmentalisation in the viral population, whereby the viruses in a host form distinct subpopulations. We here describe and apply a novel statistical method to study within-host virus evolution, identifying the minimum number of subpopulations required to explain sequence data observed from cases of chronic infection, and inferring rates for within-host viral evolution. Across nine cases of chronic SARS-CoV-2 infection in hospitalised patients we find that non-trivial population structure is relatively common, with five cases showing evidence of more than one viral population evolving independently within the host. The detection of non-trivial population structure was more common in severely immunocompromised individuals (p = 0.04, Fisher’s Exact Test). We find cases of within-host evolution proceeding significantly faster, and significantly slower, than that of the global SARS-CoV-2 population, and of cases in which viral subpopulations in the same host have statistically distinguishable rates of evolution. Non-trivial population structure was associated with high rates of within-host evolution that were systematically underestimated by a more standard inference method.

Author summary Novel SARS-CoV-2 variants such as Alpha and Omicron were characterised by the presence of multiple genetic changes not found in other SARS-CoV-2 viruses at the time. One hypothesis is that these variants arose from cases of chronic SARS-CoV-2 infection, with the virus gaining variants during long-term infection before emerging back into the global viral population. A key parameter in assessing this hypothesis is the within-host rate of virus evolution. Measuring the within-host rate of evolution is made more complex if the virus is compartmentalised. If there are two or more independent viral populations within the host these may potentially evolve at different rates from one another. We here present the results of a novel statistical method to infer the presence or absence of independent viral populations in a host alongside their rates of evolution. Applied to nine cases of chronic SARS-CoV-2 infection, we find evidence for more than one independent viral population in five of the cases. Accounting for compartmentalisation leads us to infer more rapid viral evolution during chronic infection, supporting the hypothesis that chronic infections have an important role in global virus evolution.

Citation: Smith EW, Hamilton WL, Warne B, Walker ER, Jahun AS, Hosmillo M, et al. (2025) Variable rates of SARS-CoV-2 evolution in chronic infections. PLoS Pathog 21(4): e1013109. https://doi.org/10.1371/journal.ppat.1013109 Editor: Katia Koelle, Emory University, UNITED STATES OF AMERICA Received: June 5, 2024; Accepted: April 8, 2025; Published: April 28, 2025 Copyright: © 2025 Smith et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: The software package Blanche can be downloaded from the repository https://github.com/cjri/Blanche. IVY can be downloaded from the repository https://github.com/cjri/IVY. The latter repository includes anonymised data used in this project. Funding: This work was supported by funding from the UK Medical Research Council (MC_UU_00034/1 and MC_UU_00034/6 and MC_ST_00034) provided to CI and ES and from the Wellcome Trust (207498/Z/17/Z and 206298/Z/17/Z) provided to IG. Data and Material provision was supported by grants from: the National Institute for Health Research (NIHR; award CO-CIN-01), the Medical Research Council (MRC; grant MC_PC_19059), and by the NIHR Health Protection Research Unit (HPRU) in Emerging and Zoonotic Infections at University of Liverpool in partnership with Public Health England (PHE), (award 200907), NIHR HPRU in Respiratory Infections at Imperial College London with PHE (award 200927), Liverpool Experimental Cancer Medicine Centre (grant C18616/A25153), NIHR Biomedical Research Centre at Imperial College London (award IS-BRC-1215-20013), and NIHR Clinical Research Network providing infrastructure support. The views expressed in this report are those of the authors and not necessarily those of ISARIC4C, NIHR, MRC, or PHE. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript Competing interests: The authors have declared that no competing interests exist

Introduction The evolution of the SARS-CoV-2 virus during the early phases of the pandemic has been characterised by two apparently distinct processes [1]. In the first process, the viral population gained in diversity via the gradual accumulation of mutations. Mutations acquired in this process included those which conferred a fitness advantage upon the virus. For example, the D614G mutation in Spike protein was associated with higher viral load, and was observed at an increasing frequency over the course of 2020 within the UK [2]. The accumulation of mutations provided a distinct genetic signal, with the genetic distance of a virus from the original Wuhan strain increasing roughly linearly with time. In the second process, viral genomes were sometimes observed that differed by multiple mutations from anything else observed in the viral population. Notable examples of this were the Alpha and Omicron variants of concern [3,4]. These two processes have been understood as the combined result of within-host and between-host virus evolution. For example a viral population acquiring genetic substitutions during the course of a chronic case of infection might remain unobserved for a substantial period of time before spilling into the general population via a transmission event [5,6]. Multiple individual cases of chronic SARS-CoV-2 infection have been described in the literature [7–9]. In one example, the Δ69–70 deletion in the Spike protein, characteristic of the Alpha variant, was observed prior to the emergence of that variant during a case of chronic infection [10]. The hypothesis that chronic infection with SARS-CoV-2 lay behind the emergence of both the Alpha and Omicron strains imposes two demands upon the relevant cases of chronic infection. Firstly, to produce highly mutated viruses, evolution must proceed faster during the period of chronic infection than it would in a pattern of regular cases of infection and transmission, generating and fixing multiple substitutions in the viral genome. Secondly, having acquired these mutations, the virus must transmit back into the regular population, maintaining sufficient fitness to compete with viruses that had not passed through a chronically infected host. Positive selection, either for immune escape or to evade antiviral therapy, provides one mechanism via which rapid within-host evolution could occur. A study of multiple cases of SARS-CoV-2 evolution in immunocompromised hosts identified an increased proportion of substitutions in the Spike protein compared to the global viral population, supporting the hypothesis of positive selection [11]. Other analyses have identified increased burdens of mutation in viral populations from immunocompromised hosts [12,13], incidences of transmission of SARS-CoV-2 from cases of chronic infection [14], the emergence in immunocompromised hosts of variants conferring immune evasion [15], and the early emergence of variants yet to be found in the global viral population [16]. Although the existence of positive selection during SARS-CoV-2 infection is clear, the presence of selection does not imply an increased rate of virus evolution. Sequence data from selected cases of chronic SARS-CoV-2 infection have been used to identify more rapid rates of evolution during within-host infection than in the global population [8,17]. However, the overall picture is complex. An analysis of more than 100 cases of SARS-CoV-2 infection in hospitals did not find a generally increased rate of within-host evolution [18]. A recent overview of several hundred cases of chronic infection found examples of both apparently low and apparently high rates of within-host evolution [19]. Estimating within-host rates of virus evolution is a complex task, with multiple factors potentially confounding the calculation. Methods for phylogenetic analysis, used for evolutionary rate estimation in global RNA viral populations [20], assume that the sequences which make up the tree describe the genomes of individuals in a population [21]. When applied to a set of consensus sequences from a within-host viral population, this assumption is not correct. Phylogenetic methods usually do not account for errors in sequencing, which can increase terminal branch lengths [22]. Perhaps most significantly, efforts to infer within-host evolutionary rates rarely include a formal consideration of within-host population structure. Population structure has been hypothesised as contributing factor to the persistence of SARS-CoV-2 infection [23], with subpopulations potentially existing deep within the lungs [24] or elsewhere in the body [25]. For the purposes of rate estimation this complicates matters, in so far as distinct within-host populations might evolve at different rates [26]. A single rate of evolution, however inferred, may not reflect biological reality. Here we use two novel approaches to gain an insight into within-host SARS-CoV-2 evolution. A first approach conducts sequence-based cartography, mapping consensus sequences, and therefore patterns of within-host evolution, in a simple visual manner. While only semi-quantitative in nature, this approach highlights potentially complex patterns of virus evolution, including potential substructure in the population, in cases of virus infection. A second approach performs a statistical calculation to infer the number of distinct viral populations within a host from what are assumed to be error-prone data, estimating rates of evolution for each population identified. Examining a set of 9 cases of chronic SARS-CoV-2 infection, we find evidence that within-host population structure, involving independently-evolving viral populations, is a common feature of infection. Subpopulations within the same host are found to evolve at significantly distinct rates, with a complex relationship pertaining between selection, viral phenotype, and the within-host rate of evolution.

Discussion Within-host SARS-CoV-2 evolution may be more complex, and more varied, than has to date been appreciated. We have here applied a novel approach to study data from nine cases of chronic SARS-CoV-2 infection. Our method allows for a formal discrimination to be made between simple and complex population structures, inferring the presence of one or more independent viral subpopulations during a case of infection. Here, evidence for more than one subpopulation was found in five out of nine cases. We identified subpopulations evolving significantly faster, and significantly slower, than an estimated rate of evolution for the global SARS-CoV-2 population. However, rates of evolution were not linked in a simple manner to viral phenotype. For example, phenotypically validated mutations identified in patient H and associated with escape from convalescent plasma therapy did not arise in a subpopulation with a higher inferred rate of evolution. Considered from a clinical perspective, we found a significant association between an individual being severely immunocompromised, and the identification of more complex within-host structure. Multiple potential explanations underlie this result. One possibility is that more severely immunocompromised individuals provide an environment that enhances the proliferation of multiple populations, through the colonisation by viruses of more regions within the airway. A second possibility is that the absence of host factors which would typically restrict the initiation of infection leads to higher transmission bottlenecks, with a more diverse viral population existing from the onset of infection. A third possibility is that our result has indirect cause. A longer period of infection in an immunocompromised host, or greater level of clinical monitoring of such an individual, could bias towards the collection of a greater number of samples, biasing our result towards the detection of complex structure even in the absence of a difference in structure itself. Our study is not the first to identify subpopulations during within-host SARS-CoV-2 evolution, though our method has novelty in doing this in a formal statistical manner. In identifying distinct subpopulations, our method provides an advantage over simple linear-regression-based models. Distance metrics have in the past been used to identify sequences that may be associated with faster-evolving subpopulations [10]. Against these approaches, our method can identify different populations even where their rates of evolution cannot be distinguished. Indirect evidence, such as the partial onset of drug resistance, or a limited extent of interaction between distinct viruses in a host, has also been used to highlight potential within-host structure. While indicative, such data does not constitute formal statistical evidence [32,33]. Direct sampling from different anatomical locations in an infected individual provides the best evidence of spatial separation [34,35]. Viral proteins and RNA have been identified in multiple other organs within individuals, creating the potential for sequence diversity going beyond what was accessible to our study [36]. However, there are practical limitations in obtaining such samples in routine clinical care. In common with other methods for inferring rates of evolution, our method is built around assumptions. For example, linear regression assumes that viruses in a host comprise a coherent population that evolves at a coherent rate. Our method relaxes the assumption of a single population but maintains that each population evolves at a constant underlying rate. In some cases, this assumption could affect the inference of the number of within-host populations. For example, in Patient E, sequences on days 12 and 21 equal to that on day 0 is followed by a sequence on day 31 containing five new mutations. In Patient F, something similar is observed, with sequences on days 20 and 22 differing by seven new mutations. In each of these cases, the assumption of a constant rate of evolution pushed the model towards a conclusion of emissions from differing populations, as opposed to a sudden gain of multiple variants. In particular, where antiviral drugs have the potential to accelerate evolutionary processes [37], a model of variable evolutionary rate may be appropriate. Models of time-dependent evolutionary processes have been used to study within-host evolution [38]. However, the limited nature of the data in this case mandated a cautious approach towards more complex evolutionary models. Among the individuals in our study, Patient H was repeatedly treated with convalescent plasma [10], suggesting that, while the division into subpopulations is strongly supported, a variable rate of evolution in each population might be considered. Within our data, conclusions in favour of distinct subpopulations are clearest where multiple samples contain shared, and distinct, variants. Inferred rates of evolution should be understood as mean values estimated over time. The timing of cases in our cohort, hospitalised in early-to-mid-2020, means that specific antiviral treatment was rare. Other assumptions of our method may also influence the results. For example, the assumption that subpopulations are founded at the time of infection by a virus or viruses which share a common sequence reflects limited within-host sequence diversity during SARS-CoV-2 infection and a tight population bottleneck at the time of infection [39]. In the absence of higher numbers of samples it is difficult to distinguish subpopulations initiated by genetically distinct viruses from independently evolving populations founded by identical viruses. To the extent that our data show variants accumulating in populations over time, they support the hypothesis of virus evolution, as opposed to mere genetic diversity, present from the foundation of each infection. Next, our approach models fluctuations in the consensus sequences as occurring via a regular Poisson process. In this sense we do not explicitly account for cases in which individual sequences include large numbers of sequence errors. A different model of fluctuations could change the interpretation of data from Patients E and F. Thirdly, our model assumed that the detection of virus in quantities sufficient to produce sequence data implies the existence of a replicating viral population. If this assumption were not correct, the presence of residual viral genetic material could potentially explain apparently slower rates of evolution in some cases. We note that, if later samples from individuals are merely emissions from a dead virus population, the rates of evolution we report underestimate those for replicating virus populations. Finally, we assumed that each consensus sequence could be assigned uniquely to a single subpopulation. This assumption is supported by some past data describing population structure in respiratory virus infection [10,26]. However, not all viruses follow this pattern, and it remains an assumption [40]. As we note for Patient H, some minor variants seemed to be shared between samples from distinct subpopulations, reflecting that our model, which is based upon consensus sequences, does not capture the full information provided by short-read data. Additional work is required to better understand the extent to which viral material collected via respiratory samples describes the viral population in a host. Our results provide a novel perspective upon the impact of chronic infection upon the global SARS-CoV-2 viral population. Non-trivial population structure was associated with at least one subpopulation having an inferred rate of evolution substantially greater than that of the global population. Our detection of rapidly-evolving subpopulations within chronically infected hosts highlights the potential contribution of chronic cases to the evolution of the global SARS-CoV-2 population. The increased rates of evolution inferred by our method, arising from the account made for population structure, suggest that this potential may previously have been underestimated. Our study was unable to evaluate which of the variants generated during infection, if any, were transmitted to other individuals. However, it is interesting that the highest rates of evolution that we infer within-host (max. likelihood 3.9 x 10-3 substitutions per site per year, upper bound 7.9 x 10-3) are comparable with those inferred for branches leading to the emergence of novel SARS-CoV-2 variants (Beta 2.8 x 10-3 per site per year; Alpha 8.5 x 10-3 [41]). The rapid evolutionary processes generating novel variants may have occurred in compartmentalised populations. Further work is required to combine methods for studying within-host rates of evolution with larger and more descriptive datasets, to better understand the role of vaccination and antiviral therapies upon within-host evolution, and more broadly to understand the existence and consequences of virus compartmentalisation in immunocompromised hosts.

Methods Ethics statement This study was conducted as part of surveillance for COVID-19 infections under the auspices of Section 251 of the NHS Act 2006. As such, the collection of viral genome sequences and sample dates for this study did not require individual patient consent. The ISARIC/WHO Clinical Characterisation Protocol UK (ISARIC CCP-UK) was approved by the Oxford C Research Ethics Committee (reference: 13/SC/0149) and by the Scotland A Research Ethics Committee (reference 20/SS/0028). Symptom onset data provided by ISARIC CCP-UK was obtained by written consent. The COG-UK study protocol was approved by the Public Health England Research Ethics Governance Group (reference: R&D NR0195). Sequence data. Our data comprised samples collected from nine patients who were treated for SARS-CoV-2 infection at Addenbrookes Hospital in Cambridge, UK. Identified positive samples were collected as part of a broader effort to investigate suspected hospital-acquired cases of infection [42]. In investigating suspected cases a multiplex PCR-based approach was used according to the modified ARTIC version 2 protocol with version 3 primer set, and amplicon libraries sequenced using MinION flow cells version 9.4.1 (Oxford Nanopore Technologies, Oxford, UK). Patients were selected from a dataset of cases of infection with samples collected prior to the end of October 2020, for whom i) at least four high-quality genome sequences were available and ii) the time interval between the collection of samples for the first and the last sequences was at least 21 days. Date of symptom onset was derived from the ISARIC study [43] for eight patients. Consensus level sequence data generated via nanopore sequencing were available for all nine patients [42]. Viral genome sequence coverage is shown in S9 Fig. To supplement these data we reanalysed short-read sequence data describing in more detail one of the nine cases of infection; a previous analysis of these data was published elsewhere [10]. Samples were collected via swab, sputum sample, or via aspirate. Diagnostics were carried out either using qPCR or using the Hologic Panther Fusion approach [44]. CT values for patients, where these were available, are shown in S10 Fig. Phylogenetic trees. Phylogenetic trees were created for the purpose of visually illustrating relationships between viral genome sequences. Trees were conducted with iQTree2 [45] under default parameters. In each case the best fitting rate model was identified using the ModelFinder software package [46], which uses the Bayesian information criterion to fit a model of nucleotide substitution rates. Trees produced by this method were visualised using iToL [47]. Our method for identifying rates of evolution differs substantially from phylogenetic analysis: Where phylogenetics typically assumes that consensus sequences represent individuals drawn from an underlying population, we consider sequences as stochastic entities, representing noisy consensus samples from an underlying population (or one of multiple populations) in a host. Basic inference of subpopulations and rates of evolution. Our inference method is based upon a framework of biological assumptions. Viral infection is founded in a host by a population of genetically similar viruses [26]. Viruses causing infection may comprise either a single coherent population of viruses, or more than one population, with populations being spatially segregated in the respiratory system, such that mixing between segregated populations is negligible [32], and each population evolves within a host in an independent manner. To the extent that selection acts upon viral populations, parallel adaptation, in the sense of specific mutations fixing in more than one independent populations, is rare [48]. We note that the majority of cases in this study were not treated with specific antiviral therapies, due to their occurrence early in the pandemic. We inferred rates of evolution using models of viral populations which included successively higher numbers of distinct subpopulations, denoted I, V, Y, and X. We used model selection (i.e., the Bayesian Information Criterion [49]) to identify the model which best explained the data. Conversion of sequence data to binary code. Variant positions in consensus viral sequences were identified. Assuming no more than two alleles per site, the aligned consensus sequences were converted into binary code, with a 0 representing the first observed allele at a site in the genome and a 1 representing the variant allele. Ambiguous nucleotides were marked as an N, while non-variant sites were removed from consideration. To these data we added an initial consensus sequence at time zero, by default equal to the sequence of the first sample observed within the patient. Further calculations were conducted using these binary data (Fig 7A and 7B). PPT PowerPoint slide

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TIFF original image Download: Fig 7. Processing of sequence data. A. Viral genome sequences were reduced to the set of loci at which variants were found. Ambiguous nucleotides are represented by an N. Data shown are from Patient G. B. This alignment was converted into binary code, representing consensus and variant alleles. The sequence 0C represents the consensus. Variants in the genome are labelled by position, from 0 to 7. C. Sequences were split into subpopulations, each with the same consensus. One example splitting is shown, representing the optimal split for these data. Multiple alternative splittings are possible. D. Non-variant sites were removed for each subpopulation. Fixations were identified for each subpopulation, being shown via a 1 in the ‘Fix’ row below the sequence data. Timings of each fixation are shown as the interval in which they occurred (red text). For each sample after the proposed consensus, the numbers of fixations and fluctuations in that sample are shown. Fixation and fluctuation numbers, and the respective days of their observation, were used to infer rates of evolution for each subpopulation. Fixation numbers for events occurring in the final time-point are starred; these were modelled as potentially describing either fixations or fluctuations in the sequence, calculating all possible likelihoods according to Equation 4. https://doi.org/10.1371/journal.ppat.1013109.g007 Allocation of samples to subpopulations. Samples were divided into subpopulations, with each sample uniquely ascribed to one of between one and four subpopulations (Fig 7C). Each population shared the initial consensus sequence. Constraints were placed upon the division of samples. Firstly, at least one subpopulation had to be represented by three or more samples. Next, we made the assumption that different subpopulations within the host evolve independently from one another. Noting the large size of the genome relative to the number of variant sites, we then favoured explanations in which variants did not arise multiple times in independent populations. Where a variant was observed in more than one subpopulation we applied a penalty of log v/L to the model likelihood for each such occurrence, where v was the number of variant sites, and L was the total length of the viral genome. Further, we excluded any division of samples whereby two sequences in different populations shared two or more variants. This exclusion had a pragmatic purpose, greatly reducing the number of ways of dividing samples between subpopulations, and facilitating more rapid calculations. Fixation sites. Having defined subpopulations, variant positions were re-calculated, identifying ‘fixation’ sites for each subpopulation (Fig 7D), representing sites in the genome for which the modelled underlying consensus sequence underwent a permanent change. Across the samples representing a subpopulation, we calculated the Hamming distance between the binary vector representing the presence or absence of a variant at each locus to two sets of vectors. The set V 0 comprised two vectors, one consisting of all zeros, and the other consisting of all ones. The set V 1 comprised the set of ‘fixation’ vectors, with a string of zeros followed by a string of ones (S11 Fig). Where the minimum Hamming distance to a vector in set V 1 was smaller than the minimum Hamming distance between to a vector in set V 0 , a variant position was classified as a fixation. Fixation times. Times of fixations were inferred as the interval between the first observation of a 1 in at a variant site, and the previous observation from that subpopulation (Fig 7D). For any given time interval between samples, we calculated the number of fixations occurring in that interval. The number of fluctuations in a sample was defined as the number of observations of a 1 that were not at fixation sites, plus the number of observations of a 0 at fixation sites after the time of a fixation event. Likelihood calculation. Fixation and fluctuation numbers were used to calculate the maximum likelihood rate of evolution for each population. We specified a rate of evolution λ, measured in units of number of fixations per day, and an ‘error’ parameter ε, measured in units of the number of variants per sequence. The likelihood of these two rates was described by (1) Where is the number of fixations in the time period between the collection of sample i and the previous time-point, is the time in days between the collection of sample i and the previous time-point, is the number of fluctuations in sample i, and (2) Fluctuations in the first time point (i = 1, above) were not considered, as this was defined by the initial consensus. We note that fluctuations in the consensus sequence could be caused by multiple factors, including formal errors in sequencing, but also clonal competition between variants. We retain the ‘error’ terminology used in a previous publication [18] while remaining ambiguous to the true cause of sequence fluctuations. The log likelihood of a model was calculated as the sum of the log likelihoods L(λ,ε) across all subpopulations. An improvement in the Bayesian Information Criterion of 10 units was required for the acceptance of a more complex model, representing a conservative cutoff for the acceptance of additional subpopulations. In our model we inferred independent values of λ for each subpopulation. The value of ε was fixed to a constant value of 0.207 nucleotide errors per sequence, using a value inferred from a large set of sequences from 136 patients at Addenbrookes Hospital, sequenced using the same protocol [18]. Investigation of those data did not identify a strong effect of CT value upon the number of nucleotide errors in a sequence [18]. Initial and final status of subpopulations. Our model presumes that each subpopulation has a common initial consensus sequence, and evolves to some final state in sequence space. Defining the initial and final states of the system involved further calculations. Final state of each subpopulation. In the model described, the observation of novel variants in the final sequence from a subpopulation creates some ambiguity, as these variants could represent either fixations in the population or simply fluctuations arising from clonal competition or sequencing error. These events were treated in a flexible manner. If for a population there were fixations in the final time interval, we considered the ensemble of cases for which there were s fixations, and -s additional fluctuations observed in the final time point, for different integer values of s between 0 and . The maximum likelihood model was then defined as the maximum likelihood calculated for any case within this ensemble. (3) Defining the initial consensus. Our approach assumed that any subpopulations within a host were founded from a common initial consensus sequence, rather than by viruses with distinct sequences. The initial consensus sequence was defined in a model-specific way, summarised in S12 Fig, as follows: Initial consensus: Model I: One subpopulation. Where data were available, the time of symptom onset for a patient was denoted as day zero; in the absence of data the first collected sample was denoted as day zero. If the first available sample was collected on day zero of infection, this sample was used as the initial consensus; evolution was modelled from this point forwards. If the first sample was not collected on day zero, the potential exists for substitutions to have occurred in the viral population prior to the collection of the first sample. We denote by n pre the number of fixations prior to the collection of the first sample, and optimised over this parameter. (4) Initial consensus: Model V: Two subpopulations. Model V describes the evolution of two distinct viral populations, which are separated at the moment of initiating infection. Within this model we have two subpopulations, each of which has a first-collected sequence; these two sequences may differ by some number of variants. An ensemble of models were generated in which the consensus sequence was one of the set of possible sequences including the two first-observed sequences and any possible sequence intermediate to the two (S12 Fig). The maximum likelihood was then calculated, considering all possible consensus sequences in turn. Initial consensus: Models Y and X: Three or four subpopulations. Models Y and X describe the evolution of three and four populations respectively, with a common initial consensus. In constructing a consensus, where the first sample from only one population described a variant, that variant was assumed to have arisen in that population. However, sites for which the first samples from more than one population contain a variant are ambiguous. An ensemble of models were generated in which the consensus sequence was one of the set of possible sequences with a 0 at every site for which a variant was seen in the first samples from zero or one populations, and either a 0 or a 1 at every site for which a variant was seen in the first samples from two or more populations. The maximum likelihood was then calculated, considering all possible consensus sequences in turn. Likelihood calculations and fixation probabilities. Maximum likelihood values of rate parameters were calculated using a simple optimisation routine, considering all possible assignments of samples to subpopulations. Upper (and lower) bounds for single rate parameters were conducted using a ratcheting process whereby a parameter was fixed to only increase (or decrease) while other parameters were free to change, subject to the likelihood being within two units of the maximum likelihood. Where different initial sequences or values of the parameter s led to likelihoods within two units of the maximum likelihood, calculations were repeated across all such initial sequences and values, finding extreme values subject to the likelihood constraint. The identification of plausible combinations of rate parameters, used to generate Fig 2B, was conducted on a grid, altering parameters by units of 0.002, identifying parameter combinations that produced likelihoods within 2 units of the maximum. In our model the fixation of a variant can occur in some, but not in all, scenarios. We used the likelihood of each scenario to calculate a probability of fixation, equal to the weighted sum over all parameter choices of a binary value denoting fixation, weighted by the respective scenario likelihoods. (5) where the sum was calculated over all possible assignments of samples to populations a, all possible starting sequences, c, and all possible decisions about fixations in the last time point s. The value 1 fix here equals one if the variant fixed given s, a, and c, and zero otherwise. Rates of substitutions at synonymous and non-synonymous sites were calculated in terms of the number of fixation events at each type of site per day of evolution. Suppose that P(fix) i,j,k denotes the probability that variant k fixes in subpopulation j in patient i. Then the rate of non-synonymous evolution for this population was calculated, in units of substitutions per nucleotide per day, as (6) Where o denotes the number of sites in the genome that would provide non-synonymous mutations, and T i is the length of time over which samples were collected from population j in individual i. The rate of evolution at synonymous sites was calculated in a similar manner. Mapping consensus viral sequences. We developed the Blanche software package to perform sequence-based cartography, inspired by the use of similar methods for plotting genetic and antigenic data [50,51]. Blanche carries out a simple dimension reduction calculation to facilitate the plotting of viral genome sequence data collected from individual patients. Given a set of viral sequences, we first calculated a matrix DH of Hamming distances between sequences. Ambiguous nucleotides in the data were represented in our calculation by their expected value. Where a sequence contained an ambiguous nucleotide (e.g., N) at a variant site in the population, this nucleotide was set to the expected value given the composition of other sequences from the same individual. For example, if at a site there were three unambiguous observations of an allele A, and two observations of an allele C, an ambiguous nucleotide would be defined as (0.6 A, 0.4C). The distance from this nucleotide to an A would then be equal to 0.4, while the distance from this nucleotide to a C would be 0.6. Given values for the matrix DH, we then used a simple optimisation process to identify a set of points in two-dimensional Euclidean space, with matrix of Euclidean distances between points DE, so as to minimise the sum of the squared distances between matrix elements (7) In this calculation two-dimensional Euclidean space was chosen to provide a simple representation of points on a page or screen. We note that for many datasets the minimum value of D was non-zero: Our representations provide an approximate picture of the relationships between genome sequences. Simulated data. We generated simulations describing the accumulation of mutations in simple and mixed populations. Simulations were analysed using IVY, making use of the GNU parallel software package [52]. In a simple population, evolution was modelled as occurring via a simple process of the gain of mutations. The initial sequence of the population was specified, somewhat arbitrarily, as the Wuhan Hu-1 strain of the SARS-CoV-2 virus. The population was then modelled in terms of a consensus sequence. Sequences were sampled from our population at regular times, spaced at intervals Δt. At each sampling point, the viral sequence gained a number of consensus mutations defined as the outcome of a Poisson process with rate λ. Specifically, the number of changes to the sequence was calculated as (8) Changes in the sequence were modelled to occur at uniformly randomly sampled positions within the sequence. No distinction was made between changes that caused synonymous, non-synonymous, or nonsense mutations. Further to the changes in the viral population, we modelled errors as arising in the sequence at rate μ, independent of time, so that the observed sequence contained n e errors, where (9) Errors also occurred at uniform random positions in the sequence. By default we collected samples at seven time points, with the first sample collected at time zero, and Δt = 5 days. Simulations were calculated for values of λ in {0.1, 0.2, 0.3} day-1 and with μ = 0.206845. Mixed populations were generated in a similar manner to simple populations, but with two or three underlying viral populations that shared an initial consensus sequence. Each population evolved independently of the other, with an independent rate of evolution, again in {0.1, 0.2, 0.3} day-1. At each sampling point the consensus sequence of one of the underlying populations was recorded, subject to error. The schedule of which population a consensus was collected from at each sampling point was randomly chosen to have an equal probability of sampling either population at a given time point, but with the restriction that over time, a total of at least two samples were collected from each population. Samples from simulations involving three underlying populations were collected at ten five-day intervals, with the final sample collected on day 45.

Acknowledgments We thank Iain Barrass for research computing support. This work uses Data/ Material provided by patients and collected by the NHS as part of their care and support #DataSavesLives. The Data/ Material used for this research were obtained from ISARIC4C. The COVID-19 Clinical Information Network (CO-CIN) data was collated by ISARIC4C Investigators.

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