A population-genetic analysis of influenza A/H3N2 hemagglutinin sequences established that the virus adapts by clonal interference: beneficial epitope mutations arise in abundance and compete with one another, so adaptation is limited by the competition between clones rather than by the supply of beneficial mutations. That analysis rested on a minimal model with additive, stochastically flipping sitewise selection, calibrated to reproduce sequence diversity and epitope/non-epitope substitution rates. The open problem is to replace this phenomenological description with a mechanistic, data-calibrated theory: an explicit model of host–pathogen immune dynamics (susceptible–infected–recovered-type population structure with cross-immunity) that quantitatively generates both ingredients of interference — a steady supply of beneficial epitope mutations and residual competition between coexisting strains — and reproduces the observed genome-level interference statistics, including the frequency-propagator ratios used to infer interference.

Background

Seasonal influenza A/H3N2 is a rapidly evolving RNA virus that circulates in the human population. Its major surface protein, hemagglutinin (HA), binds host cells and is the primary target of antibodies; short segments of the protein recognized by antibodies are called antigenic epitopes. Point mutations in these epitopes reduce recognition by immunity acquired in previous infections, so the virus undergoes continuing antigenic drift — the gradual accumulation of immune-escape substitutions — while most of the rest of the genome evolves under purifying selection (the steady removal of deleterious mutations). Because influenza genomes within a host population reproduce largely asexually, mutations on the same genome segment are genetically linked and cannot be freely recombined; a beneficial mutation therefore drags along whatever else is linked to it (hitchhiking) and competes with other beneficial mutations arising elsewhere in the population.

When beneficial mutations are supplied faster than they fix, several beneficial clones coexist and compete: most beneficial mutations are lost not to drift but to superior competitors. This regime is called clonal interference. Strelkowa and Lässig (2012) showed that seasonal influenza A/H3N2 HA evolution is in this regime. Their inference used polymorphism time series from a sample of 1971 strains collected between 1969 and 2007: for a class of mutations (for example, nonsynonymous changes in epitopes), the frequency propagator G(x)G(x) is the probability that a newly arising allele ever exceeds frequency xx; the propagator ratio g(x)g(x) compares G(x)G(x) with the same quantity for synonymous (putatively neutral) mutations, and the loss propagator ratio h(x)h(x) similarly compares the probability of exceeding frequency xx and later being lost. Values g(x)>1g(x)>1 together with h(x)>1h(x)>1 at intermediate frequencies signal adaptive substitutions (fixations) occurring while other beneficial alleles of the same class are wasted in competition — the joint signature of positive selection and interference. The data show this signature clearly, and a minimal simulation model reproduces it when calibrated so that selection is strong compared to genetic drift — the product of the average selection coefficient and the effective population size (the equivalent ideal-population size that produces the observed strength of genetic drift) is of order 100 — and dynamic (the preferred allele at an epitope codon flips about every 30 years, i.e., rate γ≈3.3×10−2\gamma\approx3.3\times10^{-2} per year).

Crucially, that minimal model is phenomenological: fitness is additive over sites, and immune-driven selection enters only as stochastic flips of the preferred allele per site. Biologically, however, epitope fitness effects are generated by epidemiological dynamics. In a standard susceptible–infected–recovered (SIR) epidemiological model, each viral strain depletes its own pool of susceptible hosts, so a strain's growth rate (its fitness) decreases as specific immunity builds up in the host population; a strain carrying an epitope mutation that reduces cross-immunity (the partial protection against related strains left by prior infection) enjoys a transient growth advantage and can displace the older strain. The source paper argues that host–pathogen interactions must both (a) generate a steady supply of beneficial epitope mutations and (b) maintain residual competition among all coexisting strains — the second being needed to keep the pool of susceptible hosts bounded and to prevent influenza from splitting into independent lineages — and that clonal interference constrains any candidate immune model to produce a high enough rate of beneficial epitope mutations. But the paper does not derive its genome-level statistics from any explicit epidemiological model, nor does it explain mechanistically how the two ingredients arise. Establishing this link between influenza's epidemiology and its genome evolution had been flagged as an important challenge (Holmes and Grenfell 2009, cited therein), and the specific population genetics of the SIR fitness landscape was explicitly left for future work, as was the inference of epistatic interactions between epitope sites (non-additive joint fitness effects of mutations), which is confounded by genetic linkage and interference. Subsequent work has built parts of the bridge: predictive additive fitness models for HA that forecast next-year strain frequencies (Łuksza and Lässig 2014; Lou et al. 2024), sequence-based models of antigenicity (the immune-recognition phenotype of a strain) and of neutralization (Ito et al. 2025; Kikawa et al. 2026), theories mapping multi-strain SIR dynamics onto adapting-population traveling waves, that is, the coherent forward motion of a population's fitness distribution under continuing selection in large asexual populations (Yan, Neher and Shraiman 2019; Marchi et al. 2021; Barrat-Charlaix and Neher 2024), and inference methods that resolve genetic linkage when estimating selection (Sohail et al. 2021; Abdullah et al. 2026).

Problem Statement

The problem is to turn the phenomenological, additive description of clonal interference in seasonal influenza A/H3N2 into a mechanistic, predictive theory that derives the virus's genome-level adaptive dynamics from host–pathogen immune interactions, in the sense demanded by Strelkowa and Lässig (2012). Specifically, one must construct and validate an explicit, data-calibrated model of influenza's immune epidemiology — susceptible–infected–recovered-type population structure with strain cross-immunity and whatever additional biology is needed (host heterogeneity, waning immunity, reassortment — the exchange of whole genome segments between co-infecting strains — and seasonality) — that quantitatively generates both ingredients of interference: (a) a steady supply of beneficial epitope mutations in hemagglutinin, and (b) residual competition among coexisting strains keeping the susceptible-host pool bounded; and that reproduces, from these mechanisms, the observed genome-level statistics of clonal interference, namely the frequency-propagator ratios g(x)>1g(x)>1 and h(x)>1h(x)>1 for nonsynonymous epitope mutations, the clustering of nucleotide fixations in recurrent selective sweeps (rapid fixations of beneficial mutations), and the non-Poissonian distribution of yearly fixation numbers. The fitness landscape generated by the immune model should be allowed to be epistatic (non-additive across epitope sites). The source separately discusses, as further future directions rather than as parts of this core objective, the inference of epistatic interactions between epitope sites — which must carefully discount the confounding effects of genetic linkage — and the inference of more specific characteristics of influenza SIR dynamics from genomic data on larger and less geographically biased strain samples.

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