Reviewer #1 (Public review):

Summary:

This manuscript calculates a measure of fitness flux for influenza and SARS-CoV-2 viruses, normalising by a generation time go generate comparable measures of viral adaptation over time. Potential correlates with gain in fitness flux, such as the number of mutations in different regions of the virus, are evaluated in terms of their correlation with the measured gain. A count of mutations in the S1 subunit of Spike performs slightly better in explaining observed fitness changes than previous deep-learning models describing SARS-CoV-2 evolution.

Strengths:

I enjoyed reading this manuscript. I liked the characterisation of fitness effects in a way that makes influenza and SARS-CoV-2 directly comparable. This is a neat new result.

I thought the retrospective regression against numbers of variants was a simple and interesting analysis. There is some precedent for examining correlates of fitness in key viral sites, for example in Bush et al., 1999 and Luksza and Lassig 2014: This carried on a useful tradition.

This paper is clearly written and well-constructed. The figures are well produced. There is an absence of hype in presenting results in a simple and straightforward manner.

After posing the question, I came to the conclusion that the comparison between S1 mutations and EVEscape was a fair one. The question here is that the details of the relationship between S1 mutations and fitness is derived in retrospect, from a large quantity of data, whereas PLM-based scores are advertised as having utility on the basis of only a single genome sequence. However, comparison was made with a fine-tuned model, which in some ways levels the playing field. Maybe further discussion could have been added around this point?

Weaknesses:

(1) I wasn't clear about whether the comparison with Fisher's fundamental theorem was a useful check on the analysis, or simply an inevitable consequence of any estimate of fitness scores. The fitness of a strain is measured in relative terms, as the difference in a fitness score relative to the mean of that score for the whole population. More rapid adaptation occurs when the relative difference to the mean is large, which may necessarily correlate with an increased overall variance in the fitness of strains.

(2) I would have valued more discussion on the potential implications of the findings of this manuscript. Two questions I was left with:

a) Thinking about application to a potential future emergent pathogen, to what extent is prior knowledge being leveraged in these methods? While a comparison is made of fitness gain versus statistics of multiple genes, in one sense we 'know' that the more accessible parts of the viral glycoprotein are going to be of higher relevance for viral fitness and evolution, simply from an understanding of the necessary geometry of antibody-viral interactions. Similar knowledge is leveraged in the Luksza and Lassig 2014 study: Characterising fitness by a number of epitope substitutions in that case rests on biological knowledge of which are the important epitope sites. The EVE family of methods use a similar approach where factors such as residue accessibility are combined with outputs from protein language models. But does this work have implications for how we evaluate emerging variants of existing viruses, notably SARS-CoV-2 or influenza? The H3N2/K substrain of influenza makes me want to ask this question: In that case a large number of non-synonymous changes in HA was not accompanied by a noticeable increase in the severity of seasonal influenza.

(b) What is the implication of this work for the use of PLM-based models for understanding virus evolution? One analysis that was not done is evaluating the performance of combined models, encompassing both mutation counts and PLM data. Models such as EVEscape already utilise multiple metrics alongside PLMs. Do PLMs contribute addition knowledge to a 'number of mutations on the outside of the glycoprotein' count?

Figures and data

Relative frequencies of SARS-CoV-2 clades through time.

Relative frequencies of H3N2 clades through time.

Cumulative SARS-CoV-2 fitness flux.

Cumulative H3N2 fitness flux.

Frequency vs fitness phase portrait for SARS-CoV-2 clades.

Fitness variance and fitness flux in SARS-CoV-2.

Fitness variance and fitness flux in H3N2.

Distributions of mutation and fitness change across SARS-CoV-2 lineage branches.

Lineage-specific amino acid change versus lineage-specific fitness change across regions of the SARS-CoV-2 genome.

Strength of the mutation–fitness relationship through time.

Multiple regression of fitness change on non-overlapping genome regions.

Lineage-specific predictors versus lineage-specific fitness change.