Fitness flux in SARS-CoV-2 and influenza H3N2

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?

Reviewer #2 (Public review):

Summary:

The author uses multinomial logistic regression to assign fitness values to SARS-CoV-2 and Influenza H3N2 clades. The mean population fitness, referred to as the cumulative fitness flux, is tracked throughout evolution to describe the rate of adaptation. The author shows a clear decrease in the rate of adaptation for SARS-CoV-2 after mid 2022, coinciding with the emergence of the Omicron clades; the rate of adaptation of H3N2 is much slower, but inferred to be constant in time. With this analysis, the author confirms Fisher's fundamental theorem of natural selection. Using a fine-grained clade definition scheme, the author attributes changes in fitness to substitutions in different genomic regions, highlighting the importance of the spike and, in particular, the RBD region of spike. A fitness model based on a multinomial regression is shown to perform better than EvEscape and protein-language-model semanticity to predict changes in fitness.

Strengths:

The author provides an interactive reading experience on the github.io hosted website, which has additional interactivity with figures and offers simple manipulation of what is shown. The methods are well explained and are easy to follow. The conclusions of the study- the decrease in the rate of adaptation of SARS-CoV-2, mutations in Spike S1 as the main driver of evolution, and the Spike S1 mutational count as predictor of fitness change - are clear to follow.

Weaknesses:

(1) The main conclusions that (i) the rate of adaptation of SARS-CoV-2 has decreased after Jun 2022 and is lower than in Influenza H3N2 and (ii) that mutations in Spike S1 are the main drivers of evolution are not novel.

(2) At the core, the multinomial logistic regression assumes a time-independent fitness value for each viral clade, while the clade fitness is not constant and depends on the population immunity, which will change over time. As a result, the fitness increase can be wrongly interpreted: The author observes a doubling of the mean fitness every 6 months from Jan 2021 to Jun 2022, and every 2.4 years from July 2022 to Dec 2025. We would then expect that the mean fitness in Dec 2025, \bar{f}_t, has increased more than 2 to the power 4, as compared to the mean fitness in Jan 2021, \bar{f}_0 (\bar{f}_t > 2^{4} \bar{f}_0). Is the mean viral fitness in Dec 2025 more than 16 times higher than in Jan 2021? Fitness differences between viral populations at different times cannot be meaningfully compared because the fitness landscape is time-dependent. The increase in fitness, without accounting for the change in population immunity, is in part an artifact of the multinomial regression.

(3) The multinomial regression treats the fitness landscape on which the virus evolves as static. However the fitness landscape is actually time-dependent, as population immunity changes. For a static fitness landscape, the cumulative fitness flux is the mean population fitness. However, for a dynamic fitness landscape, this is no longer the case: the (mean population) fitness changes both because of adaptation, and because changes of changes in the fitness landscape, i.e., an increase in population immunity will decrease fitness non-uniformly, also affecting individual selection coefficients s_i(t). This leads to cases where the cumulative fitness flux between t_0 and t_n can be positive, but the fitness remains the same. This study neglects the time-dependence of the fitness landscape and therefore incorrectly calculate the fitness flux, leading to an overestimation of the rate of adaptation.

Reviewer #3 (Public review):

Summary:

Bedford considers how the fitness of SARS-CoV-2 and influenza H3N2 variants have changed over time. The fitness of viral variants are estimated from trajectories of variant frequencies using multinomial logistic regression (MLR). The MLR approach was previously developed and is well-validated. Changes in mean population fitness (i.e. fitness flux) is then derived from changes in the fitness of circulating variants through time.

Strengths:

The manuscript makes some noteworthy observations. For one, it is reassuring to know that fitness variation well predicts the rate of fitness change in viral populations, as expected under Fisher's fundamental theorem. Similarly, it is interesting that simple counts of mutations perform as well as much more sophisticated protein language models in predicting variant fitness.

Weaknesses:

My two main concerns both relate to the interpretation of fitness flux and how confident we should be that it is quantifying changes in absolute fitness as opposed to environmentally-dependent changes in fitness through time.

(1) Interpretation of fitness flux:

I'm not entirely convinced that mean population fitness can be meaningfully compared through time, at least not as a measure of fitness change on an absolute scale. Here, mean population fitness is defined as the weighted sum of the relative fitness of each variant, so changes in mean pop fitness necessarily reflect changes in relative fitness. To obtain a fitness value of each variant that is comparable across time, a "scaffolding approach" is used to estimate window-specific effect and the global fitness (f_i) of each variant. The major assumption here is that by accounting for the window-specific effects, the global fitness of each variant becomes directly comparable. This assumption seems somewhat suspect. It seems impossible to know whether the window-specific effect is capturing the full environmentally-dependent component of fitness in a given window. There could also be a high degree of temporal autocorrelation in window-specific effects between neighboring windows due to similarities in environment that would decay over time.

To put this in another way, say we directly competed a 2020 SARS-CoV-2 variant with a 2025 variant in the distant future after all host-immunity to these strains had waned. Would we really be confident in estimating the fitness advantage of the 2025 variant over the 2020 variant? Or would this estimates of relative strain fitness still reflect the environments in which they were measured in, including the NPIs that were in effect in 2020 and the complex immune structure of the host population in 2025?

(2) Inability to separate different components of fitness:

Earlier work, like Meijers et al. for SARS-Cov-2 (Cell, 2023), decomposed overall changes in fitness into different components of fitness such as changes in intrinsic fitness (transmission potential) and immune escape. While the current model is simpler, in some ways this earlier work was more elegant and more powerful in its ability to explain what components of fitness drove the overall change in population-level fitness.