Fitness flux in SARS-CoV-2 and influenza H3N2

Trevor Bedford

Fred Hutchinson Cancer Center / Howard Hughes Medical Institute
3 Mar 2026
VRC Tuesday Seminar
NIH Vaccine Research Center
Slides at: bedford.io/talks

Genetic relationships of SARS-CoV-2 from 2020 to present

Rapid displacement of existing diversity by emerging variants

Mutations in S1 domain of spike protein driving displacement

SARS-CoV-2 evolution fast relative to previous endemic viruses

This talk

Frequency dynamics
Fitness flux
Mutational fitness effects

Frequency dynamics

Multinomial logistic regression (MLR)

Simple haploid population genetic model is equivalent to statistical multinomial logistic regression

The frequency $x_i(t)$ of variant $i$ at time $t$ is determined by its initial frequency $p_i$ along with its fitness $f_i$ following

$$x_i(t) = \frac{p_i \, \mathrm{exp}(f_i \, t)}{\sum_j p_j \, \mathrm{exp}(f_j \, t) }$$

Multinomial logistic regression fits variant frequencies well

Original VOC viruses had substantially increased transmissibility

Assessing MLR models for short-term frequency forecasting

Retrospective projections twice monthly during 2022

+30 day short-term forecasts across different countries

MLR models generate accurate short-term forecasts

30 days out, countries range from 5 to 15% mean absolute error

Correlates with data availability (median number of sequences available from the previous 30 days):

USA: ~45k sequences
Australia: ~4k sequences
South Africa: 170 sequences
Vietnam: 30 sequences

Clade and lineage forecasts continuously updated

BA.3 has been slowly growing, though does not yet have much of a toehold in the US

Fitness flux

Fitness flux is the rate of change of mean population fitness

With variant frequency $x_i(t)$ and constant variant fitness $f_i$

Mean population fitness $\bar{f}(t) = \sum_i x_i(t) \, f_i$ Fitness flux $\phi(t) = \Delta \bar{f}(t) / \Delta t$

Clade-level frequency dynamics and MLR fits in sliding windows

Constant clade fitness within each window, USA data only, ignores within-clade fitness variation

Charting fitness of SARS-CoV-2 variants through time

Initially doubled in fitness every year, but has slowed since 2024
Line thickness is proportional to variant frequency, 44 total variants

Analogous frequency dynamics and MLR fits for H3N2

Constant clade fitness within each window, USA data only, ignores within-clade fitness variation

H3N2 roughly doubled in fitness every 10 years

Line thickness is proportional to variant frequency, 32 total variants

Dramatically faster fitness flux of SARS-CoV-2

Traveling fitness waves

Multistrain models produce traveling waves in antigenic space

Many mutations of small effect create traveling fitness waves

Richard Neher and others have analytically characterized these waves

Diffusion constant $D = \mu \, \langle \delta^2 \rangle/2$, where the average $\langle \ldots \rangle$ is over the distribution of mutational effects $K(\delta)$

Using empirical frequencies and MLR fitness to characterize fitness wave in SARS-CoV-2

SARS-CoV-2 fitness variance correlates well with fitness flux

H3N2 fitness variance also correlates well with fitness flux

This is a specific example of Fisher's fundamental theorem

"The rate of increase in fitness of any organism at any time is equal to
its genetic variance in fitness at that time," ie $$\frac{d\bar{f}}{dt} = Var(f)$$

Mutational fitness effects

Analyze MLR fitness between parent/child lineages

Expand to 367 Pango lineages with at least 1000 sequence counts in the US from 2020 to 2025

Similar concept to Obermeyer et al

Most Pango branches have 0-1 spike mutations and change log fitness by ±0.1

Spike mutations tend to increase fitness

Non-spike mutations do not impact fitness on average

Looking across the genome shows that spike is the focus for positive selection, but accessory genes have some signal

Some attenuation of fitness effects over time

Predicting fitness effects

Simple linear model to combine predictors into a fitness estimate

In this case, a very simple model of mutation counts

Framework to compare predictors of fitness

EvEscape combines a variational autoencoder for mutation effect + antibody accessibility + biochemical dissimilarity

EvEscape does no better than counting spike mutations

CoVFit uses spike protein embeddings from ESM-2 to predict MLR fitnesses

CoVFit performs poorly outside of training window

Note also the importance of properly assessing independent parent/child lineage deltas

Semanticity to predict immune escape via dissimilarity of embeddings

Re-implemented semanticity metric in ESM-2 via CLS token embedding

Semantic dissimilarity does no better than counting spike mutations

High-throughput experimental measurements of ACE2 binding and immune escape

But even these DMS measurements have short time horizons

Even with excellent out-of-sample fitness prediction, we still need approaches that explicitly model mutations and emergence of novel lineages

Acknowledgements

Seasonal influenza and SARS-CoV-2 genomics: Data producers from all over the world, GISAID

Nextstrain: Richard Neher, Ivan Aksamentov, John SJ Anderson, Kim Andrews, Jennifer Chang, James Hadfield, Emma Hodcroft, John Huddleston, Jover Lee, Victor Lin, Cornelius Roemer, Thomas Sibley

MLR and fitness modeling: Marlin Figgins, Eslam Abousamra, Jover Lee, James Hadfield, John Huddleston, Philippa Steinberg, Jesse Bloom, Cornelius Roemer, Richard Neher

Bedford Lab: John Huddleston, James Hadfield, Katie Kistler, Jover Lee, Marlin Figgins, Victor Lin, Nashwa Ahmed, Cécile Tran Kiem, Philippa Steinberg, Jacob Dodds, Amin Bemanian, Carlos Avendano, Aayush Verma