Trevor Bedford^1,2

1. Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Center, Seattle, WA, USA
2. Howard Hughes Medical Institute, Seattle, WA, USA

The tempo of viral adaptation is usually read indirectly from the composition of mutations, through measures such as dN/dS. Here we measure it directly from the dynamics of variant frequencies, where we use multinomial logistic regression to estimate a fitness for each co-circulating variant. We aggregate these estimates to derive the rate of change of mean population fitness, referred to as fitness flux. Tracing SARS-CoV-2 from 2020 to 2026 and comparing against seasonal influenza A/H3N2, we find that SARS-CoV-2 adapted rapidly with a 6.7-fold increase in fitness from 2020 to 2023, before slowing to a 2.2-fold increase from 2023 to 2026. Influenza H3N2 sustains a slower, steadier pace roughly threefold below recent SARS-CoV-2. In both, the rate of fitness gain closely tracks the variance in fitness, matching the 1:1 expectation of Fisher's fundamental theorem. Phylogenetic contrasts between parent and child lineages localize most fitness gain to spike, and within spike to the receptor-binding domain, where a simple count of spike S1 substitutions predicts lineage fitness about as well as deep-learning escape and protein-language-model scores. Measuring fitness directly thus offers a transparent, frequency-based alternative to mutational proxies for tracking and anticipating viral adaptation.

The recommended way to run the workflow is through the Nextstrain CLI with its Docker runtime, which provides every tool the pipeline needs (snakemake, evofr, aws, zstd, xz, tsv-select, …) without any local setup. Install the Nextstrain CLI and run the Docker setup once:

nextstrain setup --set-default docker

Then run any workflow target with nextstrain build --docker . <target> (examples below). The examples below drop the --docker flag for brevity; keep it (or set the default runtime with nextstrain setup --set-default docker) when using the Docker runtime.

Alternatively, run the workflow with snakemake <target> in a local environment. Install the Python dependencies with

pip install -r requirements.txt

Provisioning the input metadata additionally requires aws, zstd, xz, and tsv-select on PATH.

Data used to generate sequence counts is fetched from Nextstrain's S3 buckets. SARS-CoV-2 uses the public nextstrain-data bucket and is fetched unsigned (--no-sign-request), so no AWS credentials are required. A fresh clone can run the whole SARS-CoV-2 pipeline out of the box with nextstrain build . sarscov2. H3N2 reads the private nextstrain-data-private bucket, so the h3n2 target and the full build require AWS credentials with access to it.

Run the entire workflow with

nextstrain build .

The default target builds the full pipeline: sequence counts, variant relationships, MLR estimates, the fitness-flux analysis, and the lineage-deltas analysis. The individual stages can also be run on their own, as described below.

To build a single pathogen end-to-end, use the per-virus targets:

nextstrain build . sarscov2   # full SARS-CoV-2 pipeline (public data, no AWS credentials)
nextstrain build . h3n2       # full H3N2 pipeline (private data, needs AWS credentials)

sarscov2 builds the SARS-CoV-2 clade and lineage fitness-flux analyses plus the lineage-deltas analysis; h3n2 builds the H3N2 clade fitness-flux analysis. Because SARS-CoV-2 metadata is fetched unsigned from a public bucket, sarscov2 runs from a fresh clone with no credentials.

Input metadata is provisioned by the workflow itself (rule provision_metadata): it streams the per-virus Nextstrain metadata from S3, subsets to the columns the analysis uses, and writes data/{virus}_subset_metadata.tsv.zst. Provision both viruses with

nextstrain build . all_provision_metadata

or just run the full build — provisioning runs automatically as an upstream dependency whenever the metadata files are missing. The source URLs and column sets live under provision: in defaults/config.yaml. The files are provisioned once and not re-downloaded automatically; refresh with nextstrain build . --forcerun provision_metadata all_provision_metadata or by deleting data/*_subset_metadata.tsv.zst.

Daily clade and Pango-lineage sequence counts are provisioned to the sequence-counts/ directory, with rare clades collapsed into "other" and rare lineages rolled up into their parents. Run

nextstrain build . all_sequence_counts all_variant_relationships

to produce, for each dataset, the collapsed counts and the lineage parent–child relationships

sequence-counts/sarscov2_clades_2020/collapsed_seq_counts.tsv
sequence-counts/sarscov2_lineages_2020/variant_relationships.tsv

Fit multinomial logistic regression (MLR) with the evofr package on 1-year sliding windows for SARS-CoV-2 and 2-year windows for H3N2:

nextstrain build . all_mlr_estimates

to produce the MLR output JSON files

mlr-estimates/sarscov2_clades_2020/mlr_results.json

Within each window MLR measures fitness only relative to an arbitrary pivot. The all_fitness_flux target scaffolds the per-window estimates onto a single per-variant scale (rule fitness_flux_scaffold_fitness), then computes mean population fitness, fitness variance, and fitness flux through time:

nextstrain build . all_fitness_flux

This writes the analysis tables under fitness-flux-analysis/results/ together with the per-figure data consumed by the interactive components in viz/

fitness-flux-analysis/results/sarscov2_clades_scaffolded_fitness.tsv
viz/time-vs-fitness/data/sarscov2_clades.json

The all_lineage_deltas target counts amino-acid substitutions per Pango lineage (rule lineage_mut_counts), forms parent-to-child branches, and contrasts each branch's change in substitution count against its change in fitness — also comparing against the EvEscape and ESM-2 mutational-fitness predictors:

nextstrain build . all_lineage_deltas

producing the per-branch deltas and predictor correlations under lineage-deltas-analysis/results/

lineage-deltas-analysis/results/branch_deltas.tsv
lineage-deltas-analysis/results/predictor_correlations.tsv

nextstrain build . clean removes everything the workflow generates (the sequence-counts/, mlr-estimates/, logs, analysis results/, and generated viz data) so the repo can be rerun from scratch, leaving the provisioned raw metadata in place. nextstrain build . clean_analysis removes only the fitness-flux and lineage-deltas intermediates, leaving the upstream sequence counts and MLR estimates intact.

• manuscript/ — paper source (fitness-flux.md, fitness_flux.bib, figures), built with press.
• Snakefile, rules/ — workflow definition; each rules/*.smk file covers one pipeline stage.
• scripts/ — sequence-count preparation and MLR scripts (run-mlr-model.py, collapse-lineage-counts.py, prepare-pango-relationships.py, …).
• defaults/config.yaml — datasets and per-dataset parameters (windows, collapse thresholds, model settings).
• data/, sequence-counts/, mlr-estimates/ — provisioned metadata and generated workflow outputs (gitignored).
• fitness-flux-analysis/ — scaffolding plus the fitness-flux and fitness-variance analysis, figures, and viz source data.
• lineage-deltas-analysis/ — per-branch mutation-to-fitness contrasts and the EvEscape / ESM-2 predictor source data.
• mutation-counts/ — per-lineage substitution counts by genome region.
• inclusion-thresholds/ — collapse-threshold sweep and the rationale behind the chosen cutoffs.
• viz/ — interactive figure components (HTML/JS) fed by the viz/*/data/ tables the workflow generates.

The manuscript is released under semantic versioning: each release is a git tag vX.Y.Z with a matching GitHub Release, and the current version is shown in the manuscript header. The bump reflects the size of the scientific change:

v0.x.0 marks pre-submission drafts; v1.0.0 is the first preprint/submission.

To cut a release:

1. Bump version.name, version.url, and date in the manuscript/fitness-flux.md front-matter.
2. git commit -m "Release vX.Y.Z"
3. git tag -a vX.Y.Z -m "vX.Y.Z — <one-line summary>"
4. git push origin main --follow-tags
5. gh release create vX.Y.Z --title vX.Y.Z --notes "<what changed>"
6. ./manuscript/publish.sh to rebuild and redeploy the page.

Review changes between versions with GitHub's vA...vB compare view or git diff vA vB -- manuscript/fitness-flux.md.

Bedford T. 2026. Fitness flux in SARS-CoV-2 and influenza H3N2. bioRxiv: 2026.07.05.736619.