The canalization model of Bedford, Rambaut and Pascual (2012) reproduces the paradox of human influenza A/H3N2 - rapid antigenic evolution with low standing diversity - by representing viral antigenic phenotypes as points in a Euclidean antigenic map and host protection as a function of antigenic distance to the closest phenotype previously encountered. It predicts a canalized, near-linear antigenic trajectory and a 1-2 year horizon of evolutionary repeatability, but rests on simplifications its authors explicitly flagged: immunity that ignores original antigenic sin and non-nearest-phenotype effects, antigenicity attributed to hemagglutinin (HA) alone, and phenotypic mutation parameters tuned rather than measured. Genotype-to-phenotype antigenic mapping and evolution-informed forecasting have since been built, substantially closing two of the five omissions the source flagged. The open problem is: how original-antigenic-sin-structured (order-dependent) immune histories and the joint antigenicity of HA and neuraminidase (NA), for which an antigenic map only became available in 2026, quantitatively alter canalization, cluster dynamics, and the predictability horizon in realistic models of A/H3N2 evolution - and how often canalization fails into a deep lineage bifurcation in the real H3N2 population, re-testing the source's model-versus-observation rate comparison once those simplifications are removed.

Background

Human influenza A/H3N2, circulating since 1968, continually evolves to escape population immunity. Most antibody-mediated escape ('antigenic drift') is driven by changes in epitopes of the hemagglutinin (HA) surface protein, with the neuraminidase (NA) protein providing the other major antibody target. Antigenic phenotype is measured by the hemagglutination inhibition (HI) assay, which quantifies the cross-reactivity of one virus against serum raised against another; results across many strain pairs can be projected onto a two-dimensional 'antigenic map' (a technique called antigenic cartography), on which distance reflects antigenic dissimilarity, with one unit corresponding roughly to a twofold dilution of antiserum. On this map, H3N2 traces a largely linear path with serial replacement of strains and no major bifurcations, mirrored by a spindly genealogy with a single predominant trunk lineage: rapid evolution but paradoxically low standing diversity, despite strong selection to diversify away from human immunity.

Bedford, Rambaut and Pascual (2012) proposed an individual-based explanation. Each virus carries an antigenic phenotype as a point in a two-dimensional Euclidean space; mutations displace the phenotype in a random direction by a random distance (phenotypic mutation rate 10^-4 per infection per day, effect sizes with mean 0.6 and standard deviation 0.4 antigenic units, chosen to reproduce the observed drift of about 1.2 antigenic units per year). Hosts - in simulations of roughly 90 million individuals across tropical and temperate regions with seasonal forcing - accumulate lifelong immune histories, and the risk of infection upon exposure grows with antigenic distance to the closest phenotype previously encountered. The model reproduces H3N2's epidemic sizes, punctuated turnover of antigenic clusters, trunk-like genealogy, and linear antigenic trajectory: selection to escape immunity canalizes the population along a single antigenic axis. 'Winding back the tape' - replaying replicate simulations from an identical viral population and immune state - shows that the evolutionary trajectory is repeatable for only 1-2 years, a predictability that derives from standing low-frequency antigenic variants. Deep bifurcations of the genealogy arise in 20 of 100 replicate simulations, roughly matching the historical frequency of major lineage splits across influenza types (about one per 195 years).

The authors themselves flagged what the model omits. (i) Host immune response is dictated by the closest phenotype in the host's history, whereas original antigenic sin - the immune system's bias toward responses against early-encountered influenza strains, also described as 'antigenic seniority' when subsequent infections elicit progressively weaker responses - makes protection depend on the order and identity of all prior infections. (ii) Only HA antigenicity is modeled, although NA undergoes comparable adaptive evolution and contributes to protection; the authors conjectured that NA antigenic change could make the HA map rougher while smoothing year-to-year incidence. (iii) The phenotypic mutation effect sizes were chosen in part to reproduce observed drift rather than measured from mutational data, although the phenotypic mutation rate itself was cross-checked against an independent estimate derived from synonymous substitution rates. (iv) The 1-2 year predictability window was not connected to operational forecasting of vaccine strain selection. (v) Deep bifurcations arose in 20 of 100 replicate simulations, translating to roughly one per 200 years and matching the historical estimate of about one major lineage split per 195 years; how often canalization actually fails into a deep bifurcation in the real H3N2 population - and whether that model-versus-observation rate consistency survives removal of the model's simplifications - was left open.

Subsequent work closed parts of this agenda. Substitution-level genotype-to-phenotype models integrate genetic and antigenic evolution (Bedford et al. 2014) and predict antigenicity from HA sequence alone (Neher et al. 2016), and evolution-informed forecasting systems quantify the skill of predicting H3N2 evolutionary and epidemic dynamics from surveillance data (Luksza and Lassig 2014; Du et al. 2017; Castro et al. 2020). On the immunological side, theoretical analyses show that original antigenic sin imposes a 'speed limit' on serial strain replacement (McGough and Cobey 2024), and transmission models with antigenic seniority reproduce long-term attack-rate trends (Eales et al. 2025). On the antigenic side, a 60-year antigenic map of the N2 neuraminidase, built from neuraminidase-inhibition assays that measure antibody blockade of NA enzymatic activity, reveals gradual NA antigenic evolution discordant with HA (Rosu et al. 2026), and joint HA/NA epitope distances improve prediction of epidemic dynamics (Perofsky et al. 2024). Traveling-wave theory - a statistical-mechanics description of adaptation as a population 'wave' moving through trait space - yields a phase diagram of persistence versus lineage splitting for multi-strain epidemiological models (Yan et al. 2019), and ecological coexistence theory has been adapted to predict pathogen strain co-circulation (Park et al. 2024).

What no combination of these works provides is an answer to the source paper's central question at its own level: a quantitative account, in models with the empirical ingredients now available, of how order-dependent immune histories and joint HA-NA antigenicity change canalization itself - the linear trajectory, cluster turnover, map roughness, and the 1-2 year repeatability horizon - and of the real-world frequency of deep bifurcations.

Problem Statement

The problem is: determine how canalized and predictable the antigenic evolution of human influenza A/H3N2 actually is, once the model's central simplifications are removed. (Two further omissions the source flagged - empirically grounded genotype-to-phenotype antigenic mapping and operational evolution-informed forecasting - have been substantially addressed by later work and are summarized in the Background.)

Specifically, three linked questions must be answered quantitatively:

  1. Immune-history structure. How do original-antigenic-sin-ordered immune responses (antigenic seniority) and contributions of non-nearest phenotypes in a host's infection history to protection alter the canalized evolutionary trajectory - the linearity of the antigenic path, standing antigenic and genealogical diversity, antigenic cluster turnover times, and the 1-2 year repeatability horizon measured by replaying replicate evolutionary histories from identical viral-population and immune states ('winding back the tape')?

  2. Joint HA-NA antigenicity. How does incorporating measured NA antigenicity, i.e. a joint HA-NA antigenic phenotype space, change the same canalization metrics and the year-to-year incidence pattern - in particular, does it, as the source conjectured, produce a rougher HA antigenic map together with smoother interannual incidence?

  3. Failure of canalization. At what rate do deep antigenic and genealogical bifurcations arise in the real H3N2 population, and does the baseline model's rate - a deep bifurcation in 20 of 100 replicate simulations, translating to roughly one per 200 years - remain consistent with the historical estimate of about one major lineage split per 195 years once the model's central simplifications are removed? A deep bifurcation is a split in which two viral lineages move in different antigenic directions and the split is evident in both the antigenic map and the genealogical tree; the operational criterion used to classify a split as deep must be stated explicitly.

Answers may be simulation-based, analytical, or data-driven, quantifying effects on the shared canalization metrics above relative to the baseline nearest-phenotype, HA-only model.

References

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