1. Evolutionary Biology
  2. Microbiology and Infectious Disease
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Integrating genotypes and phenotypes improves long-term forecasts of seasonal influenza A/H3N2 evolution

  1. John Huddleston  Is a corresponding author
  2. John R Barnes
  3. Thomas Rowe
  4. Xiyan Xu
  5. Rebecca Kondor
  6. David E Wentworth
  7. Lynne Whittaker
  8. Burcu Ermetal
  9. Rodney Stuart Daniels
  10. John W McCauley
  11. Seiichiro Fujisaki
  12. Kazuya Nakamura
  13. Noriko Kishida
  14. Shinji Watanabe
  15. Hideki Hasegawa
  16. Ian Barr
  17. Kanta Subbarao
  18. Pierre Barrat-Charlaix
  19. Richard A Neher
  20. Trevor Bedford  Is a corresponding author
  1. Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, United States
  2. Molecular and Cell Biology Program, University of Washington, United States
  3. Virology Surveillance and Diagnosis Branch, Influenza Division, National Center for Immunization and Respiratory Diseases (NCIRD), Centers for Disease Control and Prevention (CDC), United States
  4. WHO Collaborating Centre for Reference and Research on Influenza, Crick Worldwide Influenza Centre, The Francis Crick Institute, United Kingdom
  5. Influenza Virus Research Center, National Institute of Infectious Diseases, Japan
  6. The WHO Collaborating Centre for Reference and Research on Influenza, The Peter Doherty Institute for Infection and Immunity, Department of Microbiology and Immunology, The University of Melbourne, The Peter Doherty Institute for Infection and Immunity, Australia
  7. Biozentrum, University of Basel, Switzerland
  8. Swiss Institute of Bioinformatics, Switzerland
Research Article
Cite this article as: eLife 2020;9:e60067 doi: 10.7554/eLife.60067
16 figures, 6 tables and 2 additional files

Figures

Schematic representation of the fitness model for simulated H3N2-like populations wherein the fitness of strains at timepoint t determines the estimated frequency of strains with similar sequences one year in the future at timepoint u.

Strains are colored by their amino acid sequence composition such that genetically similar strains have similar colors (Materials and methods). (A) Strains at timepoint t, 𝐱(t), are shown in their phylogenetic context and sized by their frequency at that timepoint. The estimated future population at timepoint u, 𝐱^(u), is projected to the right with strains scaled in size by their projected frequency based on the known fitness of each simulated strain. (B) The frequency trajectories of strains at timepoint t to u represent the predicted the growth of the dark blue strains to the detriment of the pink strains. (C) Strains at timepoint u, 𝐱(u), are shown in the corresponding phylogeny for that timepoint and scaled by their frequency at that time. (D) The observed frequency trajectories of strains at timepoint u broadly recapitulate the model’s forecasts while also revealing increased diversity of sequences at the future timepoint that the model could not anticipate, e.g. the emergence of the light blue cluster from within the successful dark blue cluster. Model coefficients minimize the earth mover’s distance between amino acid sequences in the observed, 𝐱(u), and estimated, 𝐱^(u), future populations across all training windows.

Time-series cross-validation scheme for simulated populations.

Models were trained in six-year sliding windows (gray lines) and validated on out-of-sample data from validation timepoints (filled circles). Validation results from 30 years of data were used to iteratively tune model hyperparameters. After fixing hyperparameters, model coefficients were fixed at the mean values across all training windows. Fixed coefficients were applied to 9 years of new out-of-sample test data (open circles) to estimate true forecast errors.

Phylogeny of H3N2-like HA sequences sampled between the 24th and 30th years of simulated evolution.

The phylogenetic structure and rate of accumulated epitope and non-epitope mutations match patterns observed in phylogenies of natural sequences. Sample dates were annotated as the generation in the simulation divided by 200 and added to 2000, to acquire realistic date ranges that were compatible with our modeling machinery.

Simulated population model coefficients and distances between projected and observed future populations as measured in amino acids (AAs).

(A) Coefficients are shown per validation timepoint (solid circles, N = 33) with the mean ± standard deviation in the top-left corner. For model testing, coefficients were fixed to their mean values from training/validation and applied to out-of-sample test data (open circles, N = 18). (B) Distances between projected and observed populations are shown per validation timepoint (solid black circles) or test timepoint (open black circles). The mean ± standard deviation of distances per validation timepoint are shown in the top-left of each panel. Corresponding values per test timepoint are in the top-right. The naive model’s distances to the future for validation and test timepoints (light gray) were 8.97 ± 1.35 AAs and 9.07 ± 1.70 AAs, respectively. The corresponding lower bounds on the estimated distance to the future (dark gray) were 4.57 ± 0.61 AAs and 4.85 ± 0.82 AAs. Source data are in Table 4—source data 1 and 2.

Figure 5 with 1 supplement
Simulated population model coefficients and distances to the future for individual biologically-informed fitness metrics and the best composite model.

(A) Coefficients and (B) distances are shown per validation and test timepoint as in Figure 4. Source data are in Table 4—source data 1 and 2.

Figure 5—figure supplement 1
Composite model coefficients and distances to the future for models fit to simulated populations.

(A) Coefficients and (B) distances are shown per validation timepoint and test timepoint as in Figure 4. Source data are in Table 4—source data 1 and 2.

Figure 6 with 3 supplements
Test of best model for simulated populations (true fitness) using 9 years (18 timepoints) of previously unobserved test data and fixed model coefficients.

These timepoints correspond to the open circles in Figure 2. (A) The correlation of log estimated clade frequency fold change, log10x^(t+Δt)x(t), and log observed clade frequency fold change, log10x(t+Δt)x(t), shows the model’s ability to capture clade-level dynamics without explicitly optimizing for clade frequency targets. (B) The rank of the estimated closest strain based on its distance to the future in the best model was in the top 20th percentile for 89% of 18 timepoints, confirming that the model makes a good choice when forced to select a single representative strain for the future population. (C) Absolute forecast error for clades shown in A by their initial frequency with a mean LOESS fit (solid black line) and 95% confidence intervals (gray shading) based on 100 bootstraps. (D) The correlation of all strains at all timepoints by the percentile rank of their observed and estimated distances to the future. The corresponding results for the naive model are shown in Figure 6—figure supplement 3.

Figure 6—figure supplement 1
Validation of best model for simulated populations of H3N2-like viruses.

Validation of best model for simulated populations of H3N2-like viruses for 33 timepoints. These timepoints correspond to the closed circles in Figure 2. (A) The correlation of estimated and observed clade frequency fold changes shows the model’s ability to capture clade-level dynamics without explicitly optimizing for clade frequency targets. (B) The rank of the estimated closest strain based on its distance to the future for 33 timepoints. The estimated closest strain was in the top 20th percentile of observed closest strains for 100% of timepoints, confirming that the model makes a good choice when forced to select a single representative strain for the future population. (C) Absolute forecast error for clades shown in A by their initial frequency with a mean LOESS fit (solid black line) and 95% confidence intervals (gray shading) based on 100 bootstraps. (D) The correlation of all strains at all timepoints by the percentile rank of their observed and estimated distances to the future. The corresponding results for the naive model are shown in Figure 6—figure supplement 2.

Figure 6—figure supplement 2
Validation of naive model for simulated populations of H3N2-like viruses.

Validation of naive model for simulated populations of H3N2-like viruses for 33 timepoints. These timepoints correspond to the closed circles in Figure 2. Note that the naive model sets future frequencies to current frequencies such that there is no estimated fold change in frequencies for the first panel.

Figure 6—figure supplement 3
Test of naive model for simulated populations of H3N2-like viruses.

Test of naive model for simulated populations of H3N2-like viruses for 18 timepoints. These timepoints correspond to the open circles in Figure 2. Note that the naive model sets future frequencies to current frequencies such that there is no estimated fold change in frequencies for the first panel.

Time-series cross-validation scheme for natural populations.

Models were trained in six-year sliding windows (gray lines) and validated on out-of-sample data from validation timepoints (filled circles). Validation results from 25 years of data were used to iteratively tune model hyperparameters. After fixing hyperparameters, model coefficients were fixed at the mean values across all training windows. Fixed coefficients were applied to four years of new out-of-sample test data (open circles) to estimate true forecast errors.

Figure 8 with 1 supplement
Natural population model coefficients and distances to the future for individual biologically-informed fitness metrics.

(A) Coefficients and (B) distances are shown per validation timepoint (N = 23) and test timepoint (N = 8) as in Figure 4. The naive model’s distance to the future (light gray) was 6.40 ± 1.36 AAs for validation timepoints and 6.82 ± 1.74 AAs for test timepoints. The corresponding lower bounds on the estimated distance to the future (dark gray) were 2.60 ± 0.89 AAs and 2.28 ± 0.61 AAs. Source data are in Table 6—source data 1 and 2.

Figure 8—figure supplement 1
Comparison of epitope-based models with knowledge of the future.

Model coefficients and distances to the future for antigenic novelty models fit to natural populations. (A) Coefficients and (B) distances are shown per validation timepoint and test timepoint as in Figure 4. The epitope antigenic novelty model relies on previously published epitope sites (Luksza and Lässig, 2014). The ‘oracle’ antigenic novelty model relies on sites of beneficial mutations that were manually identified from the entire training and validation time period (Methods). The improved performance of the ‘oracle’ model indicates that the sequence-based antigenic novelty metric can be effective when sites of beneficial mutations are known prior to forecasting. Source data are in Table 6—source data 1 and 2.

Figure 9 with 1 supplement
Natural population model coefficients and distances to the future for composite fitness metrics.

(A) Coefficients and (B) distances are shown per validation timepoint (N = 23) and test timepoint (N = 8) as in Figure 4. Source data are in Table 6—source data 1 and 2.

Figure 9—figure supplement 1
Composite models fit to most recent data from natural populations.

Model coefficients and distances to the future for best composite models and a FRA-based composite fit to recent data from natural populations as in Figure 4. (A) Coefficients and (B) distances are shown per test timepoint (N = 8). In contrast to the results for these models based on fixed coefficients from training/validation, these coefficients were learned for each six-year window prior to the corresponding test timepoint. The corresponding distances reflect the model’s performance with updated coefficients on what is effectively new validation data. The naive model’s distance to the future was 6.82 ± 1.74 AAs for these timepoints.

Figure 10 with 3 supplements
Test of best model for natural populations of H3N2 viruses, the composite model of HI antigenic novelty and mutational load, across eight timepoints.

These timepoints correspond to the open circles in Figure 7. (A) The correlation of estimated and observed clade frequency fold changes shows the model’s ability to capture clade-level dynamics without explicitly optimizing for clade frequency targets. (B) The rank of the estimated closest strain based on its distance to the future for eight timepoints. The estimated closest strain was in the top 20th percentile of observed closest strains for 100% of timepoints. (C) Absolute forecast error for clades shown in A by their initial frequency with a mean LOESS fit (solid black line) and 95% confidence intervals (gray shading) based on 100 bootstraps. (D) The correlation of all strains at all timepoints by the percentile rank of their observed and estimated distances to the future. The corresponding results for the naive model are shown in Figure 10—figure supplement 3.

Figure 10—figure supplement 1
Validation of best model for natural populations of H3N2 viruses.

Validation of best model for natural populations of H3N2 viruses for 23 timepoints using the composite model of mutational load and LBI. These timepoints correspond to the closed circles in Figure 7. (A) The correlation of estimated and observed clade frequency fold changes shows the model’s ability to capture clade-level dynamics without explicitly optimizing for clade frequency targets. (B) The rank of the estimated closest strain based on its distance to the future for 23 timepoints. The estimated closest strain was in the top 20th percentile of observed closest strains for 87% of timepoints, confirming that the model makes a good choice when forced to select a single representative strain for the future population. (C) Absolute forecast error for clades shown in A by their initial frequency with a mean LOESS fit (solid black line) and 95% confidence intervals (gray shading) based on 100 bootstraps. (D) The correlation of all strains at all timepoints by the percentile rank of their observed and estimated distances to the future. The corresponding results for the naive model are shown in Figure 10—figure supplement 2.

Figure 10—figure supplement 2
Validation of naive model for natural populations of H3N2 viruses.

Validation of naive model for natural populations of H3N2 viruses for 23 timepoints. These timepoints correspond to the closed circles in Figure 7. Note that the naive model sets future frequencies to current frequencies such that there is no estimated fold change in frequencies for the first panel.

Figure 10—figure supplement 3
Test of naive model for natural populations of H3N2 viruses.

Test of naive model for natural populations of H3N2 viruses for eight timepoints. These timepoints correspond to the open circles in Figure 7. Note that the naive model sets future frequencies to current frequencies such that there is no estimated fold change in frequencies for the first panel.

Figure 11 with 1 supplement
Observed distance to natural H3N2 populations one year into the future for each vaccine strain (green) and the observed (blue) and estimated closest strains to the future by the mutational load and LBI model (orange), the HI antigenic novelty and mutational load model (purple), and the naive model (black).

Vaccine strains were assigned to the validation or test timepoint closest to the date they were selected by the WHO. The weighted distance to the future for each strain was calculated from their amino acid sequences and the frequencies and sequences of the corresponding population one year in the future. Vaccine strain names are abbreviated from A/Fujian/411/2002, A/Wellington/1/2004, A/California/7/2004, A/Wisconsin/67/2005, A/Brisbane/10/2007, A/Perth/16/2009, A/Victoria/361/2011, A/Texas/50/2012, A/Switzerland/9715293/2013, A/HongKong/4801/2014, A/Singapore/Infimh-16-0019/2016, and A/Switzerland/8060/2017. Source data are available in Figure 11—source data 1.

Figure 11—source data 1

Weighted distances to the future per strain by strain type and timepoint.

https://cdn.elifesciences.org/articles/60067/elife-60067-fig11-data1-v2.csv
Figure 11—figure supplement 1
Relative improvement of model selections over vaccine strains.

Relative distance to future H3N2 populations between vaccine strains and corresponding observed and estimated closest strains at each timepoint as in Figure 11. Strains with relative distances greater than zero were farther from the future than the selected vaccine strain, while strains below zero were closer to the future. Source data are available in Figure 11—source data 1.

Snapshot of live forecasts on nextstrain.org from our best model (HI antigenic novelty and mutational load) for April 1, 2021.

The observed frequency trajectories for currently circulating clades are shown up to April 1, 2020. Our model forecasts growth of the clades 3c3.A and A1b/94N and decline of all other major clades.

Snapshot of the last two years of seasonal influenza H3N2 evolution on nextstrain.org showing the estimated distance per strain to the future population.

Distance to the future is calculated for each strain as the Hamming distance of HA amino acid sequences to all other circulating strains weighted by the other strain’s projected frequencies under the best fitness model (HI antigenic novelty and mutational load).

Bootstrap distributions of the mean difference of distances to the future between biologically-informed and naive models for simulated populations.

Empirical differences in distances to the future were sampled with replacement and mean values for each bootstrap sample were calculated across n = 10,000 bootstrap iterations. The horizontal gray line indicates a difference of zero between a given model and its corresponding naive model. Each model is annotated by the mean ± the standard deviation of the bootstrap distribution. Models are also annotated by the p-value representing the proportion of bootstrap samples with values less than zero (see Methods).

Bootstrap distributions of the mean difference of distances to the future between biologically-informed and naive models for natural populations.

Empirical differences in distances to the future were sampled with replacement and mean values for each bootstrap sample were calculated across n = 10,000 bootstrap iterations. The horizontal gray line indicates a difference of zero between a given model and its corresponding naive model. Each model is annotated by the mean ± the standard deviation of the bootstrap distribution. Models are also annotated by the p-value representing the proportion of bootstrap samples with values less than zero (see Materials and methods).

Author response image 1
Distribution of distances to the future by Hemisphere for the best natural model (HI antigenic novelty and mutational load) subtracted from the corresponding distance to the future for the naive model at the same timepoint.

Tables

Table 1
Summary of models used with simulated and natural populations.

Models are labeled by the type of population they were applied to, the type of data they were based on, and the component of influenza fitness they represent.

ModelPopulationsData typeFitness categoryOriginally implemented by
true fitnesssimulatedsimulated populationspositive controlthis study
naivesimulated, naturalHA sequencesnegative controlthis study
epitope antigenic noveltysimulated, naturalHA sequencesantigenic driftLuksza and Lässig, 2014
epitope ancestorsimulated, naturalHA sequencesantigenic driftLuksza and Lässig, 2014
HI antigenic noveltynaturalserological assaysantigenic driftthis study
mutational loadsimulated, naturalHA sequencesfunctional constraintLuksza and Lässig, 2014
deep mutational scanning (DMS) mutational effectsnaturalDMS assaysfunctional constraintLee et al., 2018
local branching index (LBI)simulated, naturalHA sequencesclade growthNeher et al., 2014
delta frequencysimulated, naturalHA sequencesclade growththis study
Table 2
Number of epitope and non-epitope mutations per branch by trunk or side branch status for simulated populations.

Epitope sites were defined previously described (Luksza and Lässig, 2014). Annotation of trunk and side branch was performed as previously described (Bedford et al., 2015). Mutations were calculated for the full validation tree for simulated sequences samples between October of years 10 and 40.

branch typeepitope mutationsnon-epitope mutationsepitope-to-non-epitope ratio
side branch59013270.44
trunk23121.92
Table 3
Number of epitope and non-epitope mutations per branch by trunk or side branch status for natural populations.

Epitope sites were defined previously described (Luksza and Lässig, 2014). Annotation of trunk and side branch was performed as previously described (Bedford et al., 2015). Mutations were calculated for the full validation tree for natural sequences samples between 1990 and 2015.

branch typeepitope mutationsnon-epitope mutationsepitope-to-non-epitope ratio
side branch48511770.41
trunk50321.56
Table 4
Simulated population model coefficients and performance on validation and test data ordered from best to worst by distance to the future in the validation analysis.

Coefficients are the mean ± standard deviation for each metric in a given model across 33 training windows. Distance to the future (mean ± standard deviation) measures the distance in amino acids between estimated and observed future populations. Distances annotated with asterisks (*) were significantly closer to the future than the naive model as measured by bootstrap tests (see Methods and Figure 14). The number of times (and percentage of total times) each model outperformed the naive model measures the benefit of each model over a model than estimates no change between current and future populations. Test results are based on 18 timepoints not observed during model training and validation. Source data are in Table 4—source data 1 and 2.

Distance to future (AAs)Model > naive
ModelCoefficientsValidationTestValidationTest
true fitness9.37 +/− 0.926.82 +/− 1.52*7.38 +/− 1.89*32 (97%)16 (89%)
LBI1.31 +/− 0.337.24 +/− 1.66*7.10 +/− 1.19*32 (97%)18 (100%)
 + mutational load−1.77 +/− 0.49
LBI2.26 +/− 1.067.57 +/− 1.85*7.51 +/− 1.20*29 (88%)17 (94%)
delta frequency1.46 +/− 0.448.13 +/− 1.44*8.65 +/− 1.99*26 (79%)13 (72%)
epitope ancestor0.35 +/− 0.078.20 +/− 1.39*8.17 +/− 1.52*29 (88%)17 (94%)
 + mutational load−1.57 +/− 0.13
mutational load−1.49 +/− 0.128.27 +/− 1.35*8.20 +/− 1.50*29 (88%)17 (94%)
epitope antigenic novelty0.03 +/− 0.198.33 +/− 1.35*8.22 +/− 1.51*28 (85%)17 (94%)
 + mutational load−1.38 +/− 0.39
epitope ancestor0.14 +/− 0.118.96 +/− 1.359.03 +/− 1.68*20 (61%)13 (72%)
naive0.00 +/− 0.008.97 +/− 1.359.07 +/− 1.700 (0%)0 (0%)
epitope antigenic novelty−0.03 +/− 0.199.03 +/− 1.379.07 +/− 1.6914 (42%)7 (39%)
Table 4—source data 1

Coefficients for models fit to simulated populations.

https://cdn.elifesciences.org/articles/60067/elife-60067-table4-data1-v2.csv
Table 4—source data 2

Distances to the future for models fit to simulated populations.

https://cdn.elifesciences.org/articles/60067/elife-60067-table4-data2-v2.csv
Table 5
Comparison of composite and individual model distances to the future by bootstrap test (see Materials and methods).

The effect size of differences between models in amino acids is given by the mean and standard deviation of the bootstrap distributions. The p values represent the proportion of n = 10,000 bootstrap samples where the mean difference was greater than or equal to zero.

sampleerror typeindividual modelcomposite modelbootstrap meanbootstrap stdp value
simulatedvalidationtrue fitnessmutational load + LBI0.420.230.9644
simulatedvalidationmutational loadmutational load + LBI−1.030.21<0.0001
simulatedvalidationLBImutational load + LBI−0.330.140.0091
simulatedtesttrue fitnessmutational load + LBI−0.280.260.1392
simulatedtestmutational loadmutational load + LBI−1.110.25<0.0001
simulatedtestLBImutational load + LBI−0.420.160.0001
naturalvalidationmutational loadmutational load + LBI−0.690.280.0036
naturalvalidationLBImutational load + LBI−0.230.090.0025
naturalvalidationmutational loadmutational load + HI antigenic novelty−0.310.180.0417
naturalvalidationHI antigenic noveltymutational load + HI antigenic novelty−0.180.110.0513
naturaltestmutational loadmutational load + LBI1.190.790.9432
naturaltestLBImutational load + LBI−0.700.24<0.0001
naturaltestmutational loadmutational load + HI antigenic novelty−0.560.330.0133
naturaltestHI antigenic noveltymutational load + HI antigenic novelty−0.240.180.0999
Table 6
All model coefficients and performance on validation and test data for natural populations ordered from best to worst by distance to the future, as in Table 4.

Distances annotated with asterisks (*) were significantly closer to the future than the naive model as measured by bootstrap tests (see Materials and methods and Figure 15). Distances annotated with carets (∧) were not tested for significance relative to the naive model. Validation results are based on 23 timepoints. Test results are based on eight timepoints not observed during model training and validation. Model results for additional variants of fitness metrics including those based on epitope mutations and DMS preferences are included for reference. Source data are in Table 6—source data 1 and 2.

Distance to future (AAs)Model > naive
ModelCoefficientsValidationTestValidationTest
mutational load−0.68 +/− 0.345.44 +/− 1.80*7.70 +/− 3.5318 (78%)4 (50%)
 + LBI1.03 +/− 0.40
LBI1.12 +/− 0.515.68 +/− 1.91*8.40 +/− 3.9717 (74%)2 (25%)
oracle antigenic novelty0.80 +/− 0.215.71 +/− 1.27^8.06 +/− 2.49^18 (78%)2 (25%)
HI antigenic novelty0.89 +/− 0.235.82 +/− 1.50*5.97 +/− 1.47*17 (74%)6 (75%)
 + mutational load−1.01 +/− 0.42
HI antigenic novelty0.90 +/− 0.235.84 +/− 1.51*5.99 +/− 1.46*16 (70%)6 (75%)
 + mutational load−1.00 +/− 0.44
 + LBI−0.04 +/− 0.09
HI antigenic novelty0.83 +/− 0.206.01 +/− 1.50*6.21 +/− 1.44*16 (70%)7 (88%)
delta frequency0.79 +/− 0.476.13 +/− 1.71*6.90 +/− 2.3016 (70%)5 (62%)
mutational load−0.99 +/− 0.306.14 +/− 1.37*6.53 +/− 1.3917 (74%)6 (75%)
Koel epitope antigenic novelty0.28 +/− 0.366.22 +/− 1.26^6.72 +/− 1.51^18 (78%)4 (50%)
naive0.00 +/− 0.006.40 +/− 1.366.82 +/− 1.740 (0%)0 (0%)
DMS entropy−0.03 +/− 0.106.40 +/− 1.36^6.81 +/− 1.73^9 (39%)6 (75%)
DMS mutational load−0.02 +/− 0.136.45 +/− 1.42^6.82 +/− 1.73^7 (30%)5 (62%)
epitope ancestor0.53 +/− 0.526.60 +/− 1.346.53 +/− 1.5112 (52%)4 (50%)
 + mutational load−0.77 +/− 0.32
DMS mutational effects1.25 +/− 0.846.75 +/− 1.957.80 +/− 2.9711 (48%)4 (50%)
Wolf epitope antigenic novelty0.31 +/− 0.516.83 +/− 1.30^6.97 +/− 1.41^4 (17%)3 (38%)
epitope ancestor0.23 +/− 0.516.89 +/− 1.39^6.82 +/− 1.67^8 (35%)4 (50%)
epitope antigenic novelty0.57 +/− 0.776.89 +/− 1.426.46 +/− 1.317 (30%)4 (50%)
 + mutational load−0.77 +/− 0.27
epitope antigenic novelty0.52 +/− 0.737.13 +/− 1.476.70 +/− 1.517 (30%)5 (62%)
Table 6—source data 1

Coefficients for models fit to natural populations.

https://cdn.elifesciences.org/articles/60067/elife-60067-table6-data1-v2.csv
Table 6—source data 2

Distances to the future for models fit to natural populations.

Clustering of amino acid sequences for visualization.

https://cdn.elifesciences.org/articles/60067/elife-60067-table6-data2-v2.csv

Additional files

Supplementary file 1

GISAID accessions and metadata including originating and submitting labs for natural strains used across all timepoints.

https://cdn.elifesciences.org/articles/60067/elife-60067-supp1-v2.xlsx
Transparent reporting form
https://cdn.elifesciences.org/articles/60067/elife-60067-transrepform-v2.docx

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