Seasonal influenza viruses create a persistent global disease burden by evolving to escape immunity induced by prior infections and vaccinations. New antigenic variants have a substantial selective advantage at the population level, but these variants are rarely selected within-host, even in previously immune individuals. Using a mathematical model, we show that the temporal asynchrony between within-host virus exponential growth and antibody-mediated selection could limit within-host antigenic evolution. If selection for new antigenic variants acts principally at the point of initial virus inoculation, where small virus populations encounter well-matched mucosal antibodies in previously-infected individuals, there can exist protection against reinfection that does not regularly produce observable new antigenic variants within individual infected hosts. Our results provide a theoretical explanation for how virus antigenic evolution can be highly selective at the global level but nearly neutral within-host. They also suggest new avenues for improving influenza control.
Antibody-mediated immunity exerts evolutionary selection pressure on the antigenic phenotype of seasonal influenza viruses (
New antigenic variants like those that result in antigenic cluster transitions (
In the absence of antibody-mediated selection pressure, de novo generated antigenic variants should constitute a tiny minority of the total within-host virus population. Such minority variants are unlikely to be transmitted onward or detected with current next-generation sequencing (NGS) methods. But selection pressure imposed by the antibody-mediated immune response in previously exposed individuals could promote these variants to sufficiently high frequencies to make them easily transmissible and NGS detectable. The potential for antibody-mediated antigenic selection can be readily observed in infections of vaccinated mice (
Surprisingly, new antigenic variants are rarely observed in human seasonal influenza virus infections, even in recently infected or vaccinated hosts (
(
We hypothesized that influenza virus antigenic evolution is limited by asynchrony between virus diversity and antibody-mediated selection pressure. Antibody immunity at the point of transmission in previously-infected or vaccinated individuals should reduce the initial probability of reinfection (
We used a mathematical model to investigate our hypothesis that realistically-timed antibody-mediated immune dynamics slow within-host antigenic evolution. We found three modeling results: (1) antibody neutralization at the point of inoculation can protect experienced hosts against reinfection and explain new antigenic variants’ population-level selective advantage. (2) If successful reinfection occurs, the delay between the start of virus replication and the mounting of a recall antibody response renders within-host antigenic evolution nearly neutral, even in experienced hosts. (3) It is therefore reasonable that substantial population immunity may need to accumulate before new antigenic variants are likely to observed in large numbers at the population level, whereas effective within-host selection would predict that they should be readily observable even before they proliferate.
Our modeling results suggest a plausible mechanism that can explain otherwise poorly-reconciled empirical patterns, and should motivate further experimental investigation of the mechanisms of immune protection and natural selection on influenza virus antigenic phenotypes at the point of transmission.
Our model reflects the following biological realities: (1) Seasonal influenza virus infections of otherwise healthy individuals typically last 5–7 days (
Our model can be parameterized to reflect different hypothesized immune mechanisms, different host immune statuses, and different durations of infection. In the model, virions
The model can accommodate
To assess the importance of transmission bottlenecks, initial virus diversity, and sIgA antibody neutralization in virus evolution, we model the point of transmission as a series of stochastic events which may ultimately lead to one of more virions invading cells and initiating an infection. The recipient host is inoculated with a random sample of within-host virus diversity from the transmitting host. In experienced hosts, this inoculum is probabilistically thinned by host antibodies. The founding population that initiates the infection is then randomly sampled from among any remaining virions.
Mathematically, we model the number of inoculated virions as Poisson-distributed with a mean
The model is continuous-time and stochastic: cell infection, virion production, virus mutation, and virion decay are stochastic events that occur at rates governed by the current state of the system, with exponentially distributed (memoryless) waiting times. The system is approximately well-mixed: we track counts of virions and cells without an explicit account of space within the upper respiratory tract. We treat infected and dead or removed cells implicitly.
Parameterized as in
Parameter | Meaning | Units | Value | Source or justification |
---|---|---|---|---|
time post-infection of antibody response in experienced hosts | days | 2 | literature (see review in Appendix Section A2) | |
time post-infection of a novel immune response to the old antigenic variant | days | 6 | literature (see review in Appendix Section A2) | |
per-capita growth rate of target cells at low density | 0 | ignored on the timescale of a single infection | ||
maximum number of target cells | cells | 4 × 108 | standard in the modeling literature ( | |
within-host basic reproduction number for the virus | unitless | 5 | empirical fits of target cell models ( | |
average number of infectious virions produced by a cell infected with old antigenic variant virus | virions | 100 | literature ( | |
average number of infectious virions produced by a cell infected with new antigenic variant virus | virions | 100 | no within-host deleteriousness for new antigenic variants | |
probability of mutation from old variant to new variant | unitless | 0.33 × 10–5 | literature ( | |
probability of mutation from new variant to old variant | unitless | 0 | back-mutation neglected | |
rate of infectious contact between virions and target cells per cell per virion | calculated | from | ||
number of target cells lost per infectious contact | cells | 1 | one cell lost per cell infection | |
exponential decay rate of infectious virions | 4 | empirical fits of target cell models ( | ||
additional per-virion neutralization rate in the presence of a well-matched antibody response | 6 | varied to test hypotheses | ||
fractional cross reactivity during viral replication between host antibodies and the old antigenic variant | unitless | 0 or 1 | naive or homotypically reinfected hosts | |
fractional cross reactivity during viral replication between host antibodies and the new antigenic variant | unitless | 0 | full escape variant | |
probability that an individual old antigenic variant virion inoculated into an experienced host is neutralized in the respiratory tract mucosa | unitless | set from | calculated from | |
probability that an individual new antigenic variant virion inoculated into an experienced host is neutralized in the respiratory tract mucosa | unitless | reduced relative to | ||
fractional cross immunity at the sIgA bottleneck between old antigenic variant and new antigenic variant | unitless | 0 | full escape variant | |
number of virions encountering sIgA | virions | 10 × | ||
size of final/cell infection bottleneck | virions | 1 | NGS studies ( | |
viral load at which there is a fifty percent transmission probability | virions | 108 | chosen to give realistic transmission window ( | |
transmission threshold for threshold model | virions | 107 | chosen to be consistent with |
We give a full mathematical description of the model in the Materials and methods.
In addition to analyzing this within-host model, we explored the between-host and population-level implications of these within-host dynamics using a simple transmission chain model and an SIR-like population-level model, which we describe in the Materials and methods.
In our model, sufficiently strong antibody neutralization during the virus exponential growth period can potentially stop replication and block onward transmission, but this mechanism of protection results in detectable new antigenic variants in each observable homotypic reinfection, since the infection is terminated rapidly unless it generates a new antigenic variant that substantially escapes antibody neutralization (
If there is antibody neutralization throughout virus exponential growth and it is not sufficiently strong to control the infection, this facilitates the establishment of new antigenic variants: variants can be generated de novo and then selected to detectable and easily transmissible frequencies (
Adding a realistic delay to antibody production of two days post-infection (
We find that replication selection of antigenic novelty to detectable levels becomes likely only if infections are prolonged, and virus antigenic diversity and antibody selection pressure therefore coincide (
Adding antibody neutralization of virions at the point of inoculation (e.g. by mucosal sIgA) to our model produces realistic levels of protection against reinfection, and when reinfections do occur, they are overwhelmingly old antigenic variant reinfections. New antigenic variants that arise during these reinfections remain undetectably rare, reproducing observations from natural human infections (
(
Regardless of host immune status, an antigenic variant that has been generated de novo within a host must survive a series of population bottlenecks if it is to infect other individuals. To found a new infection, virions must be expelled from a currently infected host (excretion bottleneck), must enter another host (inter-host bottleneck), must escape mucus on the surface of the airway epithelium (mucus bottleneck), must avoid neutralization by sIgA antibodies on mucosal surfaces (sIgA bottleneck), and must infect a cell early enough to form a detectable fraction of the resultant infection (cell infection bottleneck) (
We find that because antigenic variants appear at very low within-host frequencies when generated de novo and undergo minimal or no replication selection, new antigenic variants most commonly reach detectable levels within hosts through founder effects at the point of inter-host transmission: a low-frequency antigenic variant generated in one host survives the net bottleneck to found the infection of a second host (
Given that influenza bottlenecks are thought to be on the order of a single virion (
In our model, new antigenic variants therefore survive the transmission bottleneck upon inoculation into a naive host with a probability approximately equal to the donor-host variant frequency
But if different virions have different chances of being neutralized at the point of transmission, the founding process may be selective. Among the virions that encounter antibodies, those that are less likely to be neutralized have a higher than average chance of undergoing stochastic promotion to consensus while those that are more likely to be neutralized have a lower than average chance. A new antigenic variant may then be disproportionately likely to survive the net bottleneck (
There is some suggestive evidence of differential survival of particular (not necessarily antigenic) influenza genetic variants at the point of transmission from experiments in ferrets (
The strength of inoculation selection depends on the ratio of the number of virions that compete to found an infection in the absence of well-matched sIgA antibodies (the mucus bottleneck size
When new antigenic variant immune escape is incomplete due to partial cross-reactivity with previous antigenic variants, increased antibody neutralization is a double-edged sword for new antigenic variant virions. Competition to found the infection from old antigenic variant virions is reduced, but the new antigenic variant is itself at greater risk of being neutralized. The impact of inoculation selection therefore depends on the degree of similarity between previously encountered viruses and the new antigenic variant. An experienced recipient host could facilitate the survival of large-effect antigenic variants (like those seen at antigenic cluster transitions [
Inoculation selection is limited by the low frequency
Onward transmission of new variants can be facilitated by natural selection—replication selection, inoculation selection, or both. The degree of facilitation depends principally on four quantities: (1)
When
Calculated according to
At realistic parameter values and assuming all individuals develop well-matched antibodies to previously encountered antigenic variants, only ∼1 to 2 in 104 inoculations of an experienced host results in a new antigenic variant surviving the bottleneck (
To investigate the between-host consequences of adaptation given weak replication selection, tight bottlenecks, and possible inoculation selection, we simulated transmission chains according to our within-host model, allowing the virus to evolve in a 1-dimensional antigenic space (
Distribution of antigenic changes along 1000 simulated transmission chains (
In particular, we note that whereas an immediate recall response would predict strong near-constant directed evolution of virus antigenic phenotypes away from existing immunity (
We used an epidemic-level model to study the consequences of individual-level inoculation selection for population-level antigenic selection. If inoculation selection is efficient, an intermediate initial fraction of immune hosts maximizes the probability that a new antigenic variant infection is created during an epidemic (
Analytical model results (see Materials and methods) for population-level inoculation selection, using parameters in
Any explanation of influenza virus antigenic evolution—and why it is not even faster—must explain why population-level antigenic selection is strong, as evidenced by the typically rapid sequential population-level replacement of old antigenic variants upon the emergence of a major new antigenic variant, but within-host antigenic evolution is rarely observed.
We hypothesized that antibodies present in the respiratory tract mucosa at the time of virus exposure can effectively block transmission, but have only a small effect on viral replication once cells become productively infected. Antigenic selection after successful infection therefore begins with the mounting of a recall response 48–72 hr post infection. In this case, selection pressure can be strong at the point of transmission, but subsequently weak until after the period of virus exponential growth. This mechanistic paradigm reconciles strong but not perfect sterilizing homotypic immunity with rare observations of new antigenic variants in successfully reinfected experienced hosts.
We consider several possible explanations for the observed phenomenon that new antigenic variants are rare within experienced infected hosts and at the population level prior to cluster transitions. But among these candidate hypotheses, only the mechanism of small inocula, transmission-blocking mucosal antibodies, and a slow-to-mount recall adaptive immune response can explain all the aforementioned empirical observations simultaneously.
Alternative possibilities include strong immune protection through antibody neutralization during early viral replication (an immediate recall response), heterogeneous neutralization rates during early viral replication, new antigenic variants that are deleterious in the absence of antibody selection, and the need for new variants to emerge against a favorable genetic background.
As shown above, protection through antibody neutralization early in replication can result in rare within-host observation of new antigenic variants, but it contradicts understanding of antibody kinetics and makes other empirical predictions that are unrealistic. It implies that homotypic challenge has a binary outcome: either it results in an undetectable infection that is rapidly cleared or it results in a visible infection dominated by an escape mutant (
Antibody neutralization during early replication could avoid binary outcomes if individual hosts are heterogeneous in the strength of their neutralizing response, so some individuals clear the infection rapidly while others barely exert antibody selection upon it. But while heterogeneity in immunity exists (
New antigenic variants could be replication-competent, but weakly deleterious within-host in the absence of immune selection and/or compensatory substitutions. Two studies (
Finally, it has been hypothesized that antigenic mutants can only proliferate at the population level if they arise against a favorable genetic background (
We discuss these alternative explanations in more depth in the Appendix (Section A7.4).
Previous literature on influenza virus transmission mentions a ‘selective bottleneck’ (
To our knowledge, however, ours is the first study to undertake a mechanistic, model-based comparison between the role of antigenic selection at the point of transmission and that of antigenic selection during replication, to show that immunologically plausible mechanisms could make the former more salient than the latter, and to connect that finding to the rarity of observable new antigenic variants in homotypically reinfected human hosts. We discuss the relationship between this paradigm and those put forward in previous modeling studies at further length in Appendix Section A7.
The study presented here nonetheless has important limitations that suggest opportunities for future investigation. This is a modeling study, and a mainly theoretical one. That is out of necessity. Quality experiments of the kind that are necessary to observe selection at the point of transmission directly and measure its strength have not been published, and we were unable to find any experimental measurements of within-host competition between known antigenic variants. For additional discussion of unmodeled biological realities and mechanistic uncertainties, see Appendix Sections A2 and A5.
Our within-host model is a simple target cell-limited model, but the decrease in infectible cells as the infection proceeds can be qualitatively interpreted as any and all antigenicity-agnostic limiting factors that come into play as the virion and infected cell populations grow. This could include the action of innate immunity, which acts in part by killing infected cells and by rendering healthy cells difficult to infect via inflammation (see immunological review in Appendix Section A2). The key mechanistic role played by the target cells in our model is to introduce a non-antigenic limiting factor on infections. This prevents an infection from repeatedly evolving out from under successive well-matched antibody responses, as occurs in HIV and in influenza patients with compromised immune systems (
Similarly, the antibody response we introduce at 48 hours is qualitative—it is modeled simply as an increase in the virion decay rate for antibody-matching virions. This response could represent IgA targeted at HA, but other antigenicity-specific modes of virus control could also be subsumed under the increased virion decay rate, for instance IgG antibodies, antibody dependent cellular cytotoxicity (ADCC), antibodies against the neuraminidase protein, or others. The key point we establish is that none of these mechanisms efficiently replication select because they all emerge once non-antigenic limiting factors have come into play. They speed clearance, but should not substantially alter virus evolution. A corollary to this point is that there are many mechanisms—and interventions—that could reduce the severity of influenza infections without substantially speeding up antigenic evolution, including universal vaccines.
A key proposal of our study is that population-level antigenic selection and homotypic protection are mediated by antibody neutralization (likely sIgA) at the point of transmission. Currently, empirical evidence for antibody protection at the point of transmission is mostly indirect. Most of this evidence comes from human and animal challenge studies (
Another limitation of our study is that, while we put forward mucosal sIgA as a biologically-documented potential mechanism of immune protection at the point of inoculation that would not lead to strong selection during early viral replication, no modeling study can establish such a mechanism without empirical investigation. Our study reveals that such an empirical investigation would be of substantial scientific value.
We model neutralization at the point of transmission as a binomial process. Each virion is independently neutralized with a probability
Moreover, individual variation in immune system properties and complex effects of host immune history (
Finally, while we believe neutralization at the point of transmission is a crucial mechanism of protection against detectable reinfection for influenza, this may not be true for all RNA viruses. Some, such as measles and varicella, have long incubation periods even in naive hosts and induce reliable, long-lasting immune protection against detectable reinfection. This may be because they replicate slowly enough that they cannot ‘outrun’ the adaptive response as influenza can. Neither shows influenza virus-like patterns of clocklike immune escape, suggesting that (1) escape mutants may be less available and (2) the adaptive response acts on a small population and is forceful.
We parameterized our models based on estimates from previous studies, but there are not good estimates for several important quantities. There are no high quality estimates of the rate of antibody-mediated neutralization in the presence of a homotypic antibody response or of how much this rate is reduced by particular antigenic substitutions, and there may be substantial inter-individual variation (
We also do not have a clear sense of exactly how neutralization probability in the respiratory tract mucosa (parameter
How readily a particular individual host or host population helps new antigenic variants reach within-host consensus depends upon several unknown quantities: (1) how host susceptibility changes with extent of antigenic dissimilarity, (2) the ratio of virions that encounter sIgA to virions that found the infection (
Our study has a number of implications for the study and control of influenza viruses.
Experienced hosts are undoubtedly heterogeneous in their immunity to a given influenza variant (
Prior modeling has suggested that despite repeated tight bottlenecks at the point of transmission, evolution of influenza viruses should resemble evolution in idealized large populations (
Seasonal influenza antigenic evolution does not resemble idealized large population evolution. Within an antigenic cluster, influenza viruses acquire substitutions that change the antigenic phenotype by small amounts. Given the large influenza virus populations within individual hosts, we might expect a quasi-continuous directional pattern of evolution away from prior population immunity. Between clusters, evolution is indeed strongly directional: only ‘forward’ cluster transitions are observed. These are jumps—large antigenic changes. But incremental within-cluster evolution is
This noisy jump pattern is easy to explain in light of the weakness of replication selection and the importance of antigenic founder effects. Selection acts on the small sub-sample of donor-host diversity that passes through the excretion, inter-host, and mucus bottlenecks to encounter the sIgA bottleneck. Evolution via inoculation selection is therefore slower and more affected by stochasticity than evolution via replication selection (
Local influenza virus lineages rarely persist between epidemics (
Our work suggests a simple mechanism by which accumulating immunity to an antigenic variant could produce punctuated population-level antigenic evolution. Population-level modeling has shown that influenza virus global epidemiological and phylogenetic patterns can be reproduced if new antigenic variants emerge at the population level with increasing frequency the longer an old antigenic variant circulates (
If immunity to the old variant only gives new variants a population-level transmission advantage (population-level selection), we anticipate a constant rate of population-level antigenic diversification, with selective sweeps once a new variant has a sufficient population-level advantage over the old variant. If population immunity also helps new variants become the dominant within-host variant through inoculation selection, increasing population immunity to an old variant can produce increasing rates of new variant emergence (
Potential synergy between brief antigenic replication selection late in infection and subsequent inoculation selection (
One suggestive population-level pattern is that new antigenic variants frequently are observed quasi-simultaneously on multiple branches of the influenza virus phylogeny shortly prior to sweeping (see Appendix Section A6). This suggests that emergence rate and population-level selection pressure do increase together. That said, alternative explanations are possible, such as reduced rates of stochastic loss of new variants at higher scales (e.g. the epidemic scale) with increased population immunity.
Regardless of the strength of these effects, however, our prediction is that new antigenic variant infection foundation events should constitute a rare but non-negligible fraction of transmission events: on the order of 1 in 105 or 1 in 104. This parsimoniously explains why new antigenic variants lineages are hard to observe prior to undergoing positive population-level selection but are readily available to be selected upon (see Appendix Section A6) once that population-level selection pressure has become sufficiently strong. Before that point, they could be rendered unobservable by population-level neutralizing dynamics or by clonal interference from non-antigenic weakly adaptive mutants (
The slow rate of antigenic evolution of A/H3N2 viruses in swine lends further support to this argument. A/H3N2 viruses accumulate genetic mutations at a similar pace in swine and humans, but antigenic evolution is much slower in swine (
The population-level emergence of new antigenic variants, in other words, tracks the accumulation of immunity in the population, not the accumulation of genetic diversity. This suggests that A/H3N2 evolution is indeed selection-limited, not diversity-limited. But much generated antigenic diversity is invisible to surveillance: in the absence of positive selection, it is likely to be lost at bottlenecks.
The inoculation and replication selection paradigm has implications for the understanding and management of other pathogens. For example, HIV does not readily evolve resistance to contemporary pre-exposure prophylaxis (PrEP) antiviral drugs, but it can do so when these antivirals are taken by an individual who is already infected with HIV (
The asynchrony between within-host virus diversity and antigenic selection pressure provides a simple mechanistic explanation for the phenomenon of weak within-host selection but strong population-level selection in seasonal influenza virus antigenic evolution. Measuring or even observing antibody selection in natural influenza virus infections is likely to be difficult because it is inefficient and consequently rare. Theoretical studies are therefore essential for understanding these phenomena and for determining which measurable quantities will facilitate influenza virus control. Our study highlights a critical need for new insights into sIgA neutralization and IgA responses to natural influenza virus infection and vaccination. Cross-scale dynamics can decouple selection and diversity, introducing randomness into otherwise strongly adaptive evolution.
In all model descriptions,
The within-host model is a target cell-limited model of within-host influenza virus infection with three classes of state variables:
New virions are produced through infections of target cells by existing virions, at a rate
Virions have a natural per-capita decay rate
We use a parameter
We assume that an antibody immune response is raised whenever the host has experienced a prior infection with a partially cross-reactive strain. For notational ease, we define the host’s strongest cross-reactivity against strain
So a recall antibody response is raised during an infection with strains
For this study, we consider a two-antigenic variant model with an ancestral ‘old antigenic variant’ virions
These events occur at the following rates:
For simplicity, the equations are symmetric between old antigenic variant and new antigenic variant viruses, except that we neglect back mutation, which is expected to be rare during a single infection, particularly before mutants achieve large populations. The parameters
We characterize a virus variant
When parametrizing our model, we fixed the within-host basic reproduction number
Another useful quantity is the within-host effective reproduction number
Note that
We denote the frequency of new variant virions at time
The distribution of virions that encounter sIgA antibody neutralization depends on the mean mucosal bottleneck size
Note that since
We then model the sIgA bottleneck—neutralization of virions by mucosal sIgA antibodies. Each virion of variant
Since each virion of strain
By Poisson thinning, this is equivalent to:
At this point, the remaining virions are sampled without replacement to determine what passes through the cell infection bottleneck,
If
When there is mucosal antibody neutralization, the variant’s survival probability can be reduced below this (inoculation pruning) or promoted above it (inoculation promotion), depending upon parameters. There can be inoculation pruning even when the new antigenic variant is more fit (neutralized with lower probability, positive inoculation selection) than the old antigenic variant (see
Default parameter values for the minimal model and sources for them are given in
In this section, we derive analytical expressions for the within-host frequency of the new variant over time in an infected host (
(
The within-host frequency of the new variant,
If the variant is neutral in the absence of antibodies, then
When additional mutations after the first cannot be neglected, we add a correction term to
And when
In our stochastic model, new variant lineages that survive stochastic extinction are produced by de novo mutation according to a continuous-time, variable-rate Poisson process. The cumulative distribution function for the time of the first successful mutation,
Surviving mutants therefore occur at a rate
We define the cumulative rate
It follows that the CDF of the first mutation time
This expression is exact for any given realization of the stochastic model if the realized values of the random variables
The resultant approximate solution for the CDF of new variant mutation times agrees well with simulations (
Black line shows analytically calculated CDF. Blue cumulative histogram shows distribution of new variant mutation times for 250,000 simulations from the stochastic within-host model with (
The slightly earlier simulated mutation times in the immediate recall response case (
By inverting the within-host replicator equation, we can also calculate the time
If
If
It may be that
Finally, it is worth noting that in the case of a complete escape mutant (
This is a linear function of
Given this and the new variant first mutation time CDF calculated in
This analytical model agrees well with simulations (
Probability of replication selection to one percent (left column) or consensus (right column) by
When
Finally, note that for
When
See Appendix Section A3.6 for a derivation.
In this section, we describe our model of the point of transmission, including how sIgA neutralization may impose selection pressure.
Given contact between an infected host and an uninfected host, we assume that a transmission attempt occurs with probability proportional to the current virus population size
The parameter
If there are
Summing
At low donor-host variant frequencies
At least one new antigenic variant survives the sIgA bottleneck with probability:
If
Summing over the possible
It follows that there is an approximate closed form for the probability that a new variant survives the final bottleneck:
We use this expression to calculate the analytical new variant survival probabilities shown in the main text, and to gain conceptual insight into the strength of inoculation selection relative to neutral processes (see Appendix Section A4.5).
A given per-virion sIgA neutralization probability
Some transmissions fail even without sIgA neutralization; this occurs with probability
The probability that there are no remaining virions of variant
This can be solved algebraically for
An infection occurs with probability
This yields the same expression for
For moderate to large
Note also that seeded infections can also go stochastically extinct; this occurs with approximate probability
Translating host immune histories into old antigenic variant and new antigenic variant neutralization probabilities for the analysis in
In the multiplicative model, the probability
In the sigmoid model:
With these analyses in hand, it is possible to combine the within-host and the point of transmission processes to calculate an overall probability that a new variant survives the transmission bottleneck.
To evaluate the relative probabilities of replication selection and inoculation selection for antigenic novelty and to check the validity of the analytical results, we simulated 106 transmissions from a naive host to a previously immune host. The transmitting host was simulated for 10 days, which given the selected model parameters is sufficient time for almost all infections to be cleared. Time of transmission was randomly drawn from that period, weighted by transmission probability, and an inoculum was drawn from the within-host virus population at that time. Variant counts in the inoculum were Poisson-distributed with probability equal to the variant frequency within the transmitting host at the time of transmission. We simulated the recipient host until the clearance of infection and found the maximum frequency of transmissible variant: that is, the variant frequencies when the transmission probability was greater than
To study evolution along transmission chains with mixed host immune statuses, we modeled the virus phenotype as existing in a 1-dimensional antigenic space. Host susceptibility
Within-host cross immunity
We then simulated a chain of infections as follows. For each inoculated host, we tracked two virus variants: an initial majority antigenic variant and an initial minority antigenic variant. If there were no minority antigenic variants in the inoculum, a new focal minority variant (representing the first antigenic variant to emerge de novo) was chosen from a Gaussian distribution with mean equal to the majority variant and a given variance, which determined the width of the mutation kernel (for results shown in
We founded each chain with an individual infected with all virions of phenotype 0, representing the current old antigenic variant.
We simulated contacts at a fixed, memoryless contact rate
We iterated this process until the first phenotypic change event—a generated or transmitted minority phenotype becoming the new majority phenotype. We simulated 1000 such events for each model and examined the observed distribution of phenotypic changes compared to the mutation kernel.
For the results shown in
To assess the causes of the observed behavior in our transmission chain model, we also studied analytically how replication and inoculation selection determine the distribution of observed fixed antigenic changes given the mutation kernel when a host with one immune history inoculates another host with a different immune history.
We fixed a transmission time
To evaluate the probability of variants being selected and proliferating during a local influenza virus epidemic, we first noted that the per-inoculation rate of new antigenic variant infections for a population with
We then considered a well-mixed population with frequency-dependent transmission, where infected individuals from all susceptibility classes are equally infectious if infected. Using an existing result from epidemic theory (
We assessed the sensitivity of our results to parameter choices by re-running our simulation models with randomly generated parameter sets chosen via Latin Hypercube Sampling from across a range of biologically plausible values.
We simulated 50,000 infections of experienced hosts (
We analyzed two cases: one in which the immune response is unrealistically early and one in which it is realistically timed. In the unrealistically early antibody response model,
Parameter | Minimum value | Maximum value |
---|---|---|
6 | 9 | |
108 | 109 | |
5 | 15 | |
10 | 500 | |
0.33 × 10−6 | 0.33 × 10−4 | |
2 | 8 | |
3 | 16 | |
0.5 | 1 | |
0.70 | 0.99 | |
0.5 | 0.9 | |
107 | 109 | |
1 | 50 |
Discussion of sensitivity analysis results can be found in Appendix Section A8.
We downloaded processed variant frequencies and subject metadata from the two NGS studies of immune-competent human subjects naturally infected with A/H3N2 with known vaccination status (
For within-host model stochastic simulations, we used the Poisson Random Corrections (PRC) tau-leaping algorithm (
We obtained numerical solutions of equations, including systems of differential equations and final size equations, in Python using solvers provided with SciPy (
All code, data, and other materials needed to reproduce the analysis in this paper are provided online on the project Github repository:
They are also available on OSF:
Output data generated by stochastic simulations, within-host NGS meta-analysis, and phylogenetic analyses are archived on OSF:
We thank Daniel B Cooney, Andrea L Graham, Joseph Gibson, Katelyn M Gostic, Alvin X Han, Chadi M Saad-Roy, and Edward C Schrom for helpful discussions. We thank Christopher J Illingworth, Daniel B Weissman, and an anonymous reviewer for helpful comments on prior versions of this manuscript.
We thank the GISAID Initiative and the influenza surveillance and research groups who openly shared the genetic sequence data used in this work (a table with accession numbers and associated labs is available online in the project materials and data repositories on Github and OSF, see above for links).
Reviewing editor,
No competing interests declared
Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing
Conceptualization, Investigation, Writing - original draft, Writing - review and editing
Formal analysis, Validation, Investigation, Writing - review and editing
Formal analysis, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing
Investigation, Writing - review and editing
Formal analysis, Investigation, Methodology, Writing - original draft, Writing - review and editing
Supervision, Investigation, Writing - review and editing
Conceptualization, Supervision, Funding acquisition, Investigation, Visualization, Methodology, Writing - original draft, Project administration, Writing - review and editing
All data used in this study are specifically listed in the appendix. No new primary data was generated in this study.
This appendix contains additional information for ‘Asynchrony between virus diversity and antibody selection limits influenza virus evolution’.
We provide a detailed review of virological and immunological evidence supporting our model of the interaction between influenza viruses and the (human) host immune system (Section A2). We give a more detailed mathematical analysis of our within-host model, deriving the approximate and exact analytical results that are used in the main text, and provide intuition to explain model behavior and limitations (Section A3). We do the same for our model of the point of transmission, and assess which hosts are most likely to act as inoculation selectors and which mutants are most likely to be inoculation selected (Section A4).
We next discuss parameter uncertainties and report the results of a sensitivity analysis for our within-host models (Section A5). We report an additional empirical analysis showing that new variants often emerge polyphyletically: they appear simultaneously on multiple branches of the influenza virus phylogeny. We discuss how this is more easily explained in light of our model than in light of previous models (Section A6).
We then review these prior studies and models of within-host influenza virus antigenic evolution and general pathogen immune escape in depth. We argue that they are insufficient to explain within-host influenza virus antigenic evolution and that inoculation selection accompanied by a realistically-timed antibody response is the most likely competing hypothesis (Section A7). We elaborate on the conclusions that can be drawn from our study and its implications for influenza virus control and for future basic research (Section A8). We conclude by providing complete step-by-step mathematical derivations of lemmas and approximations from elsewhere in the text (Section A9).
In this section, we review relevant immunology to establish the biological realities that we built our model to capture. We also discuss some unmodeled biological complexities, and why they are unlikely to change our qualitative conclusions.
The establishment of successful influenza virus infection requires access to respiratory epithelial cells covered by a mucosal layer, which acts as a protective barrier for virus entry. Sialic acid residues present in the mucus act as decoys for virions and the enzymatic activity of the influenza virus neuraminidase (NA) protein is essential for penetration of the mucosal layer (
Virions that successfully cross the mucosal barrier can infect epithelial cells in the respiratory tract. Upon initiation of replication in host cells, newly generated virions can be subjected to replication selection via virus-specific antibodies. Replication selection can take place only if influenza virus-specific antibodies are present in mucosa-associated lymphoid tissue (MALT) at the time of virus replication.
Influenza virus-specific antibodies in the MALT are secreted by local plasmablast populations, generated following activation of B naive cells or B memory cells. The exposure history of the host determines the timing and the immunological trajectory for the generation of influenza virus-specific antibodies. In individuals without previous exposure to influenza virus, newly generated virions are recognised by naive B cells which undergo rounds of affinity maturation and somatic hypermutation to produce highly-specific antibodies to the virus. This process typically occurs in germinal centers, requires T-cell help, and takes around 7 days for production of highly-specific antibodies (
In individuals with previous exposure history to influenza viruses, where the newly generated influenza virions are antigenically matched or have some degree of cross-reactivity to previously encountered variants, the generation of influenza virus-specific antibodies mainly results from B memory recall response. The activation of pre-existing memory pools enables the immune system to respond quicker to previously encountered antigens without the need to recruit naive B cell populations. The generation of antigen-specific antibodies from recalled B memory pools does not typically start until 3–5 days post infection (
The B naive and B memory cells generating serological responses to influenza viruses are referred to as B-2 cells. The activation of these cell types depends on the recognition of virus protein via the B-cell receptor and sufficient affinity of binding to trigger stimulatory signal. Depending on their specificity to the recognised virus antigen, the antibodies produced by these cell types have the potential to apply replication selection to any generated new antigenic variant viruses and to old variant viruses during the course of infection. Antibodies against influenza viruses can also be generated from the so-called B-1 cells, which do not require specific recognition of virus antigen and are activated by innate mechanisms (
B-1 cells produce natural IgM antibodies with low affinity which constitute the earliest humoral response generated in the first 48–72 hr of infection (
The peak of influenza virus replication occurs in the first 24–48 hr post infection (
The design of the inoculation selection model focuses on selection applied by the mucosal layer upon the entry of influenza virus in naïve or previously exposed hosts. We do not take into account the potential bottleneck applied during exit of viruses from the respiratory tract of an infected host. Selection of newly generated virions at the point of exit of an infected host is technically possible as the virions released from infected epithelial cells need to cross the mucosal barrier again to reach the lumen of the respiratory tract. Such selection upon virus exit would have the same directional effect as inoculation selection; it would provide a competitive advantage for mutant viruses with large antigenic effects. The potential strength of such selection depends heavily the how many sIgA antibodies in the transmitting host’s mucosa are free to neutralize the virions passing through; this quantity is unknown. Incorporating such mucosal selection upon virus exit thus requires better knowledge of the quantities of sIgA antibodies in given volume of mucus and what proportion of the available sIgA antibodies are engaged with antigen when an infected host transmits. Such data is not currently available and would require well-designed cellular culture models which take into account the role of mucosal layer in the process of virus infection and release of newly generated viruses.
According to our model, the strongest inoculation selection can take place in infection of previously exposed individuals and the highest probability of antigenic diversification occurs in populations with an intermediate proportion of immune hosts. In deriving this result, we have assumed homogeneous and static quantities of sIgA antibodies among previously exposed individuals. This is an oversimplification. There is substantial variation in level of sIgA antibodies across individuals depending on the nature of their previous exposures (through vaccination or natural infection). For example, intranasal inoculation with influenza virus via live attenuated influenza virus vaccines leads to generation of better mucosal immunity (
The model also does not account for waning of sIgA antibody titers in the months and years following each exposure. The waning of sIgA titers is likely to be substantial in absence of re-exposure but the waning process should only decrease the efficiency of inoculation selection and make the accumulation of population level selection pressure—and thus the appearance of observable new antigenic variants—rarer.
The dynamics of mucosal immunity with age are also likely to have impact on the selector phenotype of previously exposed hosts. In older individuals, multiple previous exposures will eventually lead to preferential activation of recall responses for antibody production to new variants as a result of original antigenic sin (
Even if the recall responses result in backboosting and higher levels of sIgA, these antibodies are unlikely to be well-matched to the new variant or succeeding variants, as continuous re-exposure favors responses to conserved epitopes (
As a result of the limited ability to generate novel immune responses and the phenomenon of antigenic seniority, an elderly individual who has been exposed multiple times in the past is likely to exert very weak inoculation selection to newly infecting viruses. By contrast, a young person recently exposed to influenza virus is more likely to act as a strong selector, due to the availability of mucosal sIgA antibodies and the more limited impact of original antigenic sin. However, due to the acute nature of influenza virus infection, very young children are likely to require more than one exposure before they begin to develop highly-specific antibody responses to influenza virus infection able to exert inoculation selection (
Most current efforts for characterizing humoral immunity to influenza virus infections are focused on antibody responses in the serum. However, there is limited understanding of the relationship between antibodies in the serum measured via HI and the levels of mucosal antibodies able to exert inoculation selection. Better characterization of the dynamics of mucosal immunity with age and across individuals is needed to understand the implications of inoculation selection to influenza virus evolution depending on the host population structure.
Here we analyze the within-host model in depth, and find expressions for within-host variant frequencies over time, the probability distribution for the time of first successful mutation to a new variant, and an approximate probability of replication selection to a given frequency by a given time.
In our minimal model, competition between new variant and old variant viruses obeys a simple replicator equation.
The within-host frequency of new variant virus is
If the new variant is neutral in the absence of antibody-mediated selection,
If the fitness difference
If
It is therefore straightforward to apply this expression to the within-host model with binary immunity by evaluating different immunity regimes piece-wise.
We consider the case of a host who is experienced to the old variant (
If first appears at a time
Thus far we have neglected mutation the first mutation of interest (i.e. the first that produces a new variant lineage that evades stochastic extinction). In fact, with symmetric mutation between the two types of interest, we have:
The rate of fitness-irrelevant mutation is assumed to be equal for the two types, and to preserve antigenic type (
It can be shown (see Section A9) that the equation for
When
When
In either case, we mainly study a situation in which
If
But if the first mutation to produce a new variant is sufficiently late and there is little or no positive selection, we do not necessarily have
With this approximation for
And when
We can also see this by inspecting the other two expressions for
These approximations break down once
We use the expression in
Ongoing mutation enhances possibilities for both replication and inoculation selection. It truncates the left tail of the distribution of
The consequence is that probabilities of replication selection and inoculation selection should both be somewhat higher than those estimated based on the time to the first non-extinct de novo mutant lineage, as in
For a fixed
For a given
The expected number of virus replications per lost target cell is given by
Fixing
A virus of a given
In other words, the relatively large infected cell productivity of influenza viruses—perhaps as large as hundreds or thousands of viable virions per cell (
One special case bears mentioning, because it corresponds to multiple existing models (
Each virion has a probability µ of being an escape mutant with
The approximations use the Poisson approximation to the binomial and the approximation
The unconditional probability of replication selection
Given
So we have
Note that
In our model, mucosal antibodies acting at the point of transmission provide a mechanism for population level selection pressure: some protection of experienced hosts against infection with old variant virus, and worse protection against infection with new variant virus. In particular, it provides a mechanism that produces selection pressure for new antigenic variants while predicting that reinfections with old variant viruses—without observable new variant viruses—should still be observed. Prior models (see Section A7) predict that in fully immune hosts, any observable reinfections will have new antigenic variant viruses at consensus.
Antibodies at the point of transmission appear to play a key role in population-level influenza virus evolution: they produce the selection pressure that allows new variants to spread more reliably and thus rapidly from host to host than old variants. But they may play a second role as well: promoting of new variants in frequency from the low frequencies at which they are typically generated to high frequencies at which they can be observed and reliably transmitted onward. This inoculation selection takes on the role of previously held by replication selection in explaining why inoculations of experienced hosts might produce new variant infections at a higher rate (per inoculation) than inoculations of naive hosts.
As noted in the main text, new variants can reach high within-host frequencies through founder effects. These events are both possible and rare due to influenza’s tight transmission bottleneck (
Whether this process is purely neutral or stochastically selective depends on whether the recipient host is naive, and if not how well they neutralize old variant versus new variant virions.
As mentioned in the Methods, in a fully naive host with large
When
As noted in the main text Materials and methods, mucosal antibody neutralization can reduce the new variant’s survival probability relative to this neutral case (inoculation pruning) or increase it (inoculation promotion), depending upon parameters.
There can be inoculation pruning even when the new variant is more fit than the old variant (i.e. neutralized with lower probability). But sufficient subsequent bottlenecking after sIgA neutralization can create an inoculation promotion effect.
Whether inoculation selection produces pruning or promotion depends on the ratio of
As shown in the Materials and methods, the probability that a new variant survives the cell infection bottleneck of size
Note that when
These probabilities have several intuitive and useful properties:
The correction term in
If
Since
It is sometimes useful to write this as:
For given values of the other parameters, larger
Consider
For realistically small
Then we have
Several intuitive results follow:
If we hold
Conversely, if we hold
Since
For a bottleneck of size
This is increasing in
In a host strongly immune to the old variant (large
This provides intuition for the effects seen in main text
Moreover, if we let
Our replicator equation implies that this ratio
Note that we did not integrate over the emergence times to obtain this ratio; instead, we derived principles that take the initial frequency as a given.
We also wish to know which hosts best promote antigenic novelty when inoculated, given a level of cross-immunity
We optimize
Consider the endpoint at
So
Since
In other words, if immune escape is incomplete for
When
In other words, with extremely small cell infection bottlenecks like those observed for influenza viruses, fully immune hosts are the best selectors provided that the number of virions
The intuition is that larger
Here we discuss parameter uncertainties in our models and how they affect our conclusions. We also conduct a simulation-based sensitivity analysis of the central within-host model.
A crucial parameter in our model is
Parameter estimates for antibody-mediated virion neutralization in the presence of substantial well-matched antibody correspond to values of
For
A
With large
A final reason why a high
Small
Indeed, it is unlikely that
As noted in the Discussion, the relationship between the mucosal antibody neutralization rate
One reason statistical independence may be violated is that antibody numbers are finite, and an antibody that binds to one virion cannot bind to another. Consider a focal virion. Given that another virion has been neutralized, there are fewer antibodies remaining to neutralize our focal virion. This is particularly important for mixed inocula. Old variant virions, which have higher affinity for the inoculated host’s sIgA antibodies, may indirectly protect the new variant by competing with it for antibody-binding. A new variant virion may have a higher individual chance of being neutralized by those same antibodies if it is part of a monomorphic inoculum composed of other, identical new variants. Such an interaction would strengthen inoculation selection relative to the independent neutralization we have modeled here.
Inoculation selection may improve mutant bottleneck survival relative to neutral drift (see
Evidence suggests that a non-antigenic bottleneck does occur after the sIgA bottleneck because bottlenecks measured in vaccinated and non-vaccinated hosts are of comparable size (indistinguishable from one), suggesting that founding virion population sizes are cut down to small numbers even in the absence of IgA antibodies, though this would also be consistent with the case of
An experimental evolution study of avian influenza virus adaptation in ferrets found that transmission bottlenecks in naive hosts became tighter that as the virus adapted (
One modeling study of influenza viruses proposes that infections should have a second peak after initial innate responses are overcome and some target cells are once again susceptible to infection (
That said, the empirical data suggesting double-peaked kinetics comes from experimental inoculation of naive horses with a large quantity of influenza virus: 106 50% egg infectious dose (
In human kinetics data (
Furthermore, for realistic (incomplete) degrees of antibody-binding escape, we expect both old and new antigenic variant population sizes to decline even due to
The upshot is that virus clearance should be rapid following the mounting of the adaptive response in the experienced hosts where we expect selection to take place, and thus in immune-competent hosts we should expect a limited window for antibody-mediated selection on transmissible virus populations.
In the simulation results shown in the main text (
Since influenza virus population sizes grow and shrink rapidly around the within-host peak, however, this model should be qualitatively similar to a threshold model in which transmission occurs with certainty if the total viral load is above a certain threshold
Probability shown as a function of probability of no old variant infection (
Threshold version of
(
As described in the Materials and methods, we further assessed sensitivity of the within-host model to variation in key parameters by studying random parameter sets chosen from biologically plausible parameter ranges.
We analyzed two cases: one in which the immune response is unrealistically early (
We found that with early immunity, regardless of particular parameter values, new variants are frequently seen when experienced hosts are detectably reinfected, and the overall probability of new variant infections is unrealistically high. These observable new variants are most often generated de novo and replication-selected (
When immunity is realistically-timed, the pattern of much rarer replication selection is robust to variation in parameters. New variant infections compose a realistically small fraction of all detectable reinfections (
Parameters randomly varied across the ranges given in
Parameters randomly varied across the ranges given in
Amino acid substitutions associated with antigenic “cluster transitions” have reached fixation in parallel—and near-synchronously in time—in genetically distinct co-circulating lineages. This has occurred both in A/H1N1 and in A/H3N2 seasonal influenza viruses.
Existing 'mutation-limited' or 'diversity-limited' model explanations of why observable influenza virus antigenic novelty is rare despite continuous genetic evolution are less convincing in light of this synchronous polyphyly (see Section A7). In particular, a number of models hypothesize that large effect antigenicity-altering substitutions can only emerge in specific genetic contexts (
Synchronous, polyphyletic cluster transitions cast doubt on these claims. If major antigenic changes appeared infrequently due to the rarity of 'jackpot' scenarios of a large-effect mutant in a favorable genetic background (
To show that large effect antigenic changes occur near-synchronously in multiple backgrounds, we assessed evolutionary relationships and built phylogenetic trees for known recent polyphyletic antigenicity-altering substitutions that have emerged in A/H1N1 and A/H3N2. Our analysis rules out reassortment as an explanation for the apparent polyphyly, thus verifying that the branches represent distinct, independent, but simultaneous de novo lineages.
We analyzed polyphyletic antigenic changes using hemagglutinin (HA) gene nucleotide sequences deposited in the GISAID EpiFlu database.
We downloaded all seasonal A/H1N1 HA sequences from the period 1999–2008, to center on the antigenic cluster transition from the New Caledonia/1999-like phenotype to the Solomon Islands/2006-like phenotype, excluding pandemic A/H1N1 viruses. We downloaded A/H3N2 virus HA sequences for two periods: 2008 to 2011, to center on cluster transition from Brisbane/07 to the Perth/2009-like and Victoria/2009-like phenotypic split, and 2012 to 2014, to capture the co-circulation of Clade 3C.2a and 3C.3a (
A/H1N1 1999–2008 | A/H3N2 2008–2011 | A/H3N2 2012–2014 | |||
---|---|---|---|---|---|
Pre-filter | Final dataset | Pre-filter | Final dataset | Pre-filter | Final dataset |
4882 | 3514 | 7050 | 5738 | 11970 | 10107 |
We aligned sequences using MAFFT v7.397 (
We mapped amino acid substitutions onto branches using custom Python scripts. All numbering complies with H1/H3 numbering scheme (
The HA K140E antigenicity-altering substitution first occurred in 2000 and was detected sporadically prior to its independent fixation in 2006–2007 in three phylogenetically distinct, geographically segregated lineages of A/H1N1 that diverged in 2004 (
The three lineages have distinct HA1 mutational trajectories away from their most recent common ancestor, as defined by the set of amino acid substitutions that accumulate along the predominant trunk lineages both prior to and following the fixation of the K140E substitution (
Lineage | Geographic composition in first year of co-circulation | Trunk substitutions from MRCA to K140E fixation | Trunk substitutions post- K140E fixation |
---|---|---|---|
1 | South Asia | Y94H, R188K, E273K | D35N, K145R*, A189T, G185V, N183S, G185S |
2 | East Asia | Y94H, S36N, A189T, R188M, T193K* | N244S, K82R*, I47K, E68G |
3 | South-East Asia | Y94H, K73R, V128A*, A128T* | P270S |
Branch tip color indicates the amino acid identity at position 140. Co-circulating lineages defined by the K140E fixation are highlighted. Scale bar indicates the number of nucleotide substitutions per site. Tree rooted to A/New Caledonia/20/1999.
In the period 2008-2011, the K158N substitution was only detected once in 2009 before fixing in combination with N189K in the same year in two distinct co-circulating A/H3N2 lineages. N189K was not detected before fixing as a K158N/N189K double substitution. The combination of the substitutions resulted in an antigenic phenotype switch from Wisconsin/2005-like to the Perth/2009-like and Victoria/2009-like phenotypes respectively. Residues 158 and 189 are both located in antigenic site B adjacent to the receptor binding site, with substitutions at both residues characterized as cluster-transition substitutions in multiple historic A/H3N2 cluster transitions (
Lineage | Trunk substitutions from MRCA to K158N/N189K fixation | Trunk substitutions post- K158N/N189K fixation |
---|---|---|
1 (Victoria / 2009-like) | T212A, S45N, T48A, K92R, Q57H, A198S, V223I, N312S, N278K,Q33R, N145S, G5E, E62V, D53N, E280A, I230V, Y94H, I192T, S199A | |
2 (Perth / 2009-like) | E62K | N144K, R261Q, I260M, P162S, E50K, V213A, N133D, T212A, R142G |
Branch tip color indicates the amino acid identity at position 158 and 189. Co-circulating lineages defined by the K158N/N189K fixation are highlighted. Scale bar indicates the number of nucleotide substitutions per site. Tree rooted to A/Brisbane/10/2007.
In 2014 two independent substitutions at position 159, F159S and F159Y, fixed in distinct A/H3N2 lineages co-circulating globally (
Residue 159 is located in antigenic site B. The S159Y substitution in combination with Y155H and K189R substitutions previously resulted in the transition of the A/H3N2 Bangkok/79-like antigenic phenotype to Sichuan/87-like phenotype (
The two lineages have independent mutational trajectories for their HA gene away from their most recent common ancestor, excluding both acquiring the N225D substitution prior to F159X-fixation, with acquired changes at the major antigenic epitopes (
Lineage | Trunk substitutions from MRCA to F159X fixation | Trunk substitutions post- F159X fixation |
---|---|---|
F159Y (lineage 1, Clade 3C.2a) | L3I, N225D, Q311H, N144S, K160T | R142K, R261L |
F159S (lineage 2, Clade 3C.3a) | R142G, T128A, A138S, N225D |
Branch tip color indicates the amino acid identity at position 159. Co-circulating lineages defined by the F159X fixation are highlighted. Scale bar indicates the number of nucleotide substitutions per site. Tree is rooted to A/Perth/16/2009.
In this section, we discuss how our work fits into the substantial existing theoretical literature on influenza virus evolutionary dynamics.
A number of theoretical studies over the last 20 years have addressed the tempo and structure of seasonal influenza virus antigenic evolution, but only two have addressed within-host influenza virus antigenic evolution (
Our model suggests revisions to the theoretical understanding of within-host and point-of-transmission evolutionary dynamics. The revised paradigm has implications for the population-level models—most notably, it suggests that the rate of population-level antigenic diversification may not be constant over time.
The two within-host studies both make two key assumptions: (1) immune selection pressure is strong from the moment of inoculation in experienced hosts and (2) influenza virus transmission bottlenecks are wide (1 × 105 virions [
Both within-host studies find that new antigenic variants are routinely generated de novo during an infection and undergo substantial positive selection during that same infection. NGS studies of natural human infections suggest that this is in fact uncommon (
The most crucial assumption in prior work on influenza virus immune escape within-hosts (
What is more, our models show that it protection via neutralization produces binary outcomes: either no reinfection, or detectable reinfection with exclusively mutant viruses. This binary outcome was previously considered a feature, not a bug, because the frequency of homotypic reinfection was not yet known.
A model of immune and therapeutic escape for a generic pathogen (
Similarly, the antimicrobial resistance literature makes a distinction between 'acquired' and 'transmitted' (or 'primary') drug resistance (
Two studies (
In our paradigm, non-variant-specific limiting factors such as target cell depletion play three roles. (1) Denying new variants the opportunity to rise in frequency once an antibody response has been mounted and fitness differences have become substantial. (2) Explaining why immune-compromised hosts, in whom these non-antigenic limiting factors are weaker, can select for antigenic mutants at the scale of a single infection. (3) Clearing infections of naive hosts well before an adaptive immune response can select an escape variant. Point (3) has been posited previously by [60], but to our knowledge (1) and (2) are novel.
Note that
For influenza viruses, the de novo mutation that creates a stable new variant lineage of interest typically precedes time of adaptive immune proliferation, so a distinct model is required.
Previous population-level studies have argued that non-antigenic fitness costs associated with antigenic substitutions (
There are empirical reasons to doubt that influenza viruses are in fact antigenic diversity-limited due to fitness costs. We find multiple instances of polyphyletic cluster transitions: a cluster- transition amino acid substitution arises and proliferates on two or more branches of the virus phylogeny at this same time (see Section A6). This is inconsistent with the hypothesis that antigenic variants are either intrinsically unfit (deleterious substitutions) or incidentally unfit (poor background) prior to the moment that they proliferate at the population level (
In the absence of meaningful replication selection, the population level rate of antigenic diversification is the average rate at which new variants survive all transmission bottlenecks to found or co-found infections. In an inoculation selection regime, that rate is unlikely to surpass 2 in 104 inoculations (
Prior to the accumulation of population immunity, infections dominated by new variants should be rare, and new variants should be nearly neutral relative to the old variant at the population level. This may be sufficient to explain the absence of diversification early in the circulation of a cluster without invoking non-antigenic fitness costs. That said, additional constraints on the virus, particularly those that reduce the within-host fitness of new antigenic variants, should further slow virus antigenic diversification by reducing variant frequencies in donor hosts and thereby reducing the probability that the variants survive transmission bottlenecks. Furthermore, in the absence of substantial population immunity, adaptive substitutions may be lost at the population level due to competition from lineages with non-antigenic adaptive substitutions. Our work is thus consistent with a role for clonal interference in population level influenza virus antigenic evolution (
In this section, we expand on the discussion of alternative hypotheses from the main text (see Alternative explanations for rare new antigenic variants).
Adaptive immune pressure could be strong enough that
As we note in the main text, this makes two predictions that do not match empirical reality: binary outcomes to homotypic challenge—no infection or infection with an antigenic mutant—and frequent evolution of antigenic mutants in infections of intermediately immune hosts.
Recent empirical work (
A model of influenza virus evolution
Intermediate-to-strong immunity to old variant viruses is likely to be common in the human population even at the beginning of a new antigenic cluster’s circulation (
Our proposed model of immune selection can explain why intermediately immune hosts may not reliably select for new antigenic variants. A realistically-timed recall response makes replication selection unlikely. Rates of inoculation selection are limited in all hosts due to low transmitting host mutant frequencies
One possibility is that adaptive immune pressure could be present from the start of replication, but vary substantially among individuals, even those with the same immune history. This heterogeneity could explain why some individuals (
While individual variation in immunity does exist (
Even if this unlikely hypothesis of bimodal early adaptive responses were true, there would remain a role for sampling effects at the point of transmission. If individuals either possess sterilizing-strength immunity that acts early in the timecourse of viral replication or possess sufficiently weak immunity that replication selection is unlikely, antigenic evolution would be dominated by cases in which mutants are inoculated into strongly immune hosts, as in simpler models with
Antigenic mutants could be replication-competent, but weakly deleterious within-host in the absence of immune selection and/or compensatory substitutions. Two studies (
Typically
We estimate
The effect could be particularly extreme in intermediately immune hosts if immunity drops superlinearly with antigenic distance. If the old variant is neutralized at a rate
In the absence of replication selection, even weak within-host deleteriousness should lead mutants to be rapidly purged (purifying selection should be efficient for phenotypes subject to replication selection) (
A final possibility is that antigenic mutants could be extremely deleterious in the absence of compensatory mutations:
In the absence of mucosal neutralization with small
On average,
Selection on inoculated diversity may be important in many host-pathogen systems, not just in influenza virus antigenic evolution. Some anti-microbial resistance in bacteria, for instance, is acquired through the uptake of preexisting plasmids, rather than through de novo mutation (
Population size, population level antigenic diversification ('mutation') rate, and degree of population structure all substantially impact the proliferation of new influenza virus antigenic variants at the population level. It has been hard for population-level models to distinguish plausible hypotheses regarding evolutionary constraints on the virus, because achieving simultaneous realism across in all these effects while retaining model tractability has proven extremely difficult.
For epidemiological models of influenza virus evolution overall population size matters: epidemics in larger populations involve more total inoculations, and therefore more opportunities for new variant survival at the point of transmission to occur. Large host populations with high transmission rates, strong population connectivities, and recurrent epidemics should promote antigenic evolution. This helps explain why influenza virus antigenic evolution appears to occur disproportionately in east and southeast Asia (
It also reveals an important consideration for interpreting results from individual-based simulation models of global influenza virus evolution. Due to computational constraints, many such models must use host population sizes that are orders of magnitude smaller than the true global human population (e.g.
The observation that immune escape can be reliably be selected for in egg (
The egg experiments (
The mouse passage experiments (
First, the mice were intranasally inoculated with 50
Second, inoculations were also carried out until a successful inoculation could be achieved. This further improves the chances of observing an escape mutant selected at the point of transmission. Finally, vaccinated mice in the passage chain were inoculated 10–21 days post-vaccination, meaning antibody levels could be higher than the memory baseline. This would be expected to strengthen inoculation selection and perhaps permit replication selection.
One detail in supplementary table 1 of the mouse passage study (
An example calculation illustrates this: if
And since
While it is difficult to compare fitness differences during replication to fitness differences in mucosal neutralization, a very small fitness difference of
When antigenic effect size of mutations approaches zero, the effects of stochastic loss and mistimed selection pressure dominate, and inoculation and replication selection become sufficiently weak that true drift dominates as a force for introducing new antigenic variants. In such a regime, we expect influenza viruses to evolve gradually, fail to cause large epidemics, and possibly diversify, not unlike influenza B viruses (
When antigenic jump size approaches the maximum size possible, such that all population immunity disappears each time there is an antigenic cluster transition (
'Preview' substitutions and polyphyletic cluster transitions also imply that the influenza virus is not typically mutation-limited at the population level—a substantial-effect escape mutant is usually accessible in sequence-space—but that the virus may nonetheless be highly constrained in its evolutionary trajectory. The virus repeatedly finds the same substitution as a solution to its antigenic evolutionary problem. This could occur either because only one escape mutant is available or because one of the available escape mutants provides substantially more immune escape (on average) than the others.
Without an explanation for why within-host dynamics do not more frequently promote antigenic mutants, it is difficult to explain the slow pace and noisy trajectory of influenza virus evolution. But such a within-host explanation, though likely necessary, may not be sufficient. It is conceivable that in a sufficiently large and well-connected global host population, population-level antigenic selection favoring mutants with higher
One important mechanism by which evolution might be also slowed at higher scales is analogous to the within-host dynamic of founder effects and inoculation selection: mutant lineages may be frequently lost (though perhaps selectively favored) at the bottleneck that occurs between distinct influenza virus epidemics.
Prior modeling work has found that population-level host competition between pathogen variants reduces the probability that a fit mutant variant causes a large epidemic in the population in which it first emerges (
We propose a previously unexplored consequence of this argument: successful establishment of a mutant lineage at the population level requires that the mutant lineage be exported to a new host subpopulation where susceptible hosts are common. This is rare but potentially selective sampling event.
When a new variant lineage emerges at the population level, it is likely to be surrounded by many propagating old variant lineages due to the generator-selector dynamic discussed in the main text (see main text
Many local influenza virus epidemics are likely to be evolutionary dead ends with no cases exported that establish chains of transmission in other locations. Because only a minority of the human population is likely to travel to or from the site of any particular epidemic, the majority of virus diversity generated within each epidemic is likely to be lost in between-epidemic bottlenecks. Conditional on being exported, new variant lineages could have competitive advantages over old variant lineages because they spread should spread more rapidly and go stochastically extinct less easily due to their higher
The rate of proliferation of mutants at the population level, then, may be limited by the rarity of early generation of mutant lineages during an epidemic (analogous to the rarity of very early within-host de novo generation of mutants) and by the rarity of successful mutant lineage exportation when generation is not early (analogous to the rarity of mutant virions surviving the transmission bottleneck between hosts).
We aim to explore this argument with a formal mathematical model in future work.
The derivation in this section establishes
We note that:
Dividing through by
With symmetric mutation at a rate µ, the replicator equation remains calculable.
Given symmetric mutation,
Substituting in to the previous derivation yields:
Note that if
To find the case with one-way mutation, we simply let all
This establishes the expression for the time
The frequency of the mutant at time
Neglecting ongoing forward mutation, the mutant must emerge at some frequency
Solving for
It follows that if
Taking the natural log of both sides and subtracting off
This establishes a value for
If
The expression from
To deal with this, we make the approximation:
This approximation is excellent unless the initial frequency
Letting
We find:
So when
Note that since we used an underestimate of
Finally, it may be that
Combining:
The derivation in this section establishes
We know that:
So substituting in:
This is exact when
Summing from
Adding that to the expression derived above completes the derivation.
This is most easily seen by rewriting
If
The last step uses the fact that the Poisson distribution is a proper probability distribution, and therefore sums to 1.
For
This is negative for
That
This can be rewritten in two useful ways:
This uses the fact that
We begin by showing that
When
Now we find
It follows that
This follows from the infinite sum expression for
This uses the fact that
For any
We follow an approach similar to A9.8, showing that
Similarly:
We have again used the fact that
Taking the difference of the approximate ratios:
That the expression is negative follows from the fact that all terms in the sum are negative, since
It follows that
If
And since
In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.
The manuscript presents a theoretical study that bridges the global and the within-host evolution of the influenza virus. The key finding is that the asynchrony between within-host viral growth and the delayed antibody response following an infection can explain the pattern of antigenic evolution for influenza, where selection for new variants is strong at the population level but not within individuals. This work is conceptually important and provides a theory-driven hypothesis to explain the observed antigenic evolution of influenza across scales.
[Editors’ note: the authors submitted for reconsideration following the decision after peer review. What follows is the decision letter after the first round of review.]
Thank you for submitting your work entitled "Asynchrony between virus diversity and antibody selection limits influenza virus evolution" for consideration by
Our decision has been reached after consultation between the reviewers. Based on these discussions and the individual reviews below, we regret to inform you that your work will not be considered further for publication in
This manuscript brings together a lot of good ideas and makes useful points about selection on influenza at transmission and a delayed within-host response. The reviewers agree that the proposed model is insightful and in principle could be used to understand the observed patterns of within-host viral diversity and the patterns of global influenza evolution. However, the reviewers also raised substantial concerns regarding the limited connection between the model and data and many of the speculations in the manuscript that are not fully supported by data. In addition, reviewers also suggest that paper should be rewritten in a sufficiently clear manner for a general audience to understand, and for this work to be of broad interest. Overall, the reviews propose a substantial re-writing and further analysis and inclusion of data, in order for the manuscript to be considered for publication in
This paper addresses the observation that, while global influenza populations are strongly influenced by selection for antigenic novelty, within-host populations. It describes a model in which within-host selection is active, but temporally delayed, while selection based on the immune history of an individual acts at the time of transmission, during the establishment of an infection.
1) I have two preliminary comments on the style in which this is written, as opposed to the content of the paper. Firstly, my experience reading this was that I found the main text difficult to follow until the point at which I had gained familiarity with the details of the model. For example, once I knew what \kappa_w, p_C, c, and k referred to I could understand the legend of Figure 3, though it took some time for me to get there. I suggest, if possible, rewriting the main text so as to be accessible in its own right to a casual reader. Secondly, I thought that the choice of data to be presented in figures was odd. The paper presents a model of viral evolution. As such, the interest (for me) was the extent to which the model replicates the observed behaviour of influenza virus in the real world. However, only Figure 1A and 1B describe any 'real world' data. Figure 4A is conceptual and useful, but the remainder of the figures exist in 'model space', showing how this or that parameter affects the behaviour of which part of the model. I'm not against model-to-model comparison (Figure 4E-H are useful though I'd personally keep only the top parts), but suggest removing anything from the main text which does not directly and clearly illustrate some key part of the model, or which does not show some direct comparison of the behaviours of different models as they relate directly to observations of the real-world system.
2) The claim is made that 'selection for new antigenic variants acts principally at the point of initial virus inoculation'. I have some questions and concerns around this claim.
- To what extent has antigenic selection during the establishment of infection been experimentally documented? The primary reference given here is that of Wang, 2017. However, while Wang is clear that antibodies in the mucus can be influenza-specific (as opposed to being specific to another virus) it did not seem so clear that these antibodies are strain-specific in the sense of identifying viruses that differed by a single mutation.
- With this in the background I was not clear about the first of the claimed key results, that 'sIgA antibody neutralisation protects experienced hosts against reinfection'. It is certainly true is that a model incorporating selection during the transmission process (plus delayed within-host selection) is consistent with a range of observed data describing influenza infection and evolution. However, this is not the same as what is claimed. The hypothesis of the importance of sIgA antibody neutralisation is shown to be more consistent with the data than other models, but that does not imply that the hypothesis is true.
- Given the modelling that has been done, it would seem straightforward to evaluate this claim further. Within-host selection is delayed, but not entirely absent. As such, the expected frequency of a novel antigenic variant at the time of transmission to a new host will in the mean be higher than it would otherwise be under pure neutrality. It should be possible compare this change in the expected variant frequency to that produced by the transmission process (illustrated in Figure 4E). Averaging over stochastic effects, what proportion of the selection is due to within-host processes and what is due to selection during transmission? In the manuscript, it is claimed without further details that within-host evolution is 'dominated' by inoculation selection. What does this really mean?
3) On the model of within-host viral load, this paper follows a commonly applied model of (roughly speaking) exponential growth followed by exponential decline. However, Pawelek et al. (2012) argue that a more bimodal pattern of behaviour is more realistic, a second peak arising from the re-emergence of susceptible cells that have been made refractory to infection by interferon. Would this increase the effect of within-host selection? Further, the work of Tsang et al. (2015) notes a proportion of transmission events occurring four or more days post the onset of symptoms; if within-host selection kicks in two days after infection it seems likely that within-host selection has a non-negligible effect even if events at transmission are the primary driver of selection.
4) I don't believe that the model presented is a good one for infection in immunocompromised individuals. To the best of my knowledge the oscillations shown in Figure 3B and C have not been observed in clinical cases. My suspicion is that the model ignores some of the complexities of within-host infection in a way that gives a reasonable picture of a typical infection, but that falls short when it comes to longer-term infections. The point being made here is that selection for antigenic variants can be effective during longer infections; I would accept this point fairly readily, but the data of Figure 3 did not make me particularly more convinced.
5) It is claimed that Figure 5 shows that proposed model of global influenza evolution better mimics empirical observations of the global population with regard to changes in the antigenic type of the virus. However, while it is clear from the figure that different models give different results, no indication of the observed behaviour of the global population is given in the Figure. The claim may be true. However, what is the observed distribution of changes in the global population to which Figure 5D provides a better match?
6) I was confused by Figure 7. Based on the methods I think that the term emergence describes the appearance of a variant in the population in such a way that it will not subsequently die out through genetic drift. Figure 7 then shows the distribution of emergence times under the case of an immediate recall response and a delayed recall response. My expectation would be that under an immediate recall response, positive selection would begin to apply to the variant earlier, making its emergence more likely to happen sooner, but the figure shows the opposite effect. I may have missed something in the explanation.
7) Appendix 6: To the best of my understanding, the idea that large effect antigenic changes can occur in multiple backgrounds is not contradicted by the work of Koelle and Rasmussen. In that work a distinction is made between 'good' and 'bad' genetic backgrounds, characterised by the extent of mutational load in a sequence, however, there can be multiple 'good' backgrounds or at least, multiple backgrounds good enough for a variant to appear multiple times in the global population before fixation. As another thought here, is the work of Strelkowa and Lassig, (2011) relevant as a proposed explanation for the pattern of global viral evolution, competition?
8) Appendix 7: The concept of selection acting both in the transmission process and during within-host replication is not entirely novel; Lumby et al. (2018) make this distinction in the context of influenza transmission and within-host growth (and further discuss the idea of a selective bottleneck). The idea that selection during the transmission process could play a role in the adaptation of global influenza populations has been raised very recently (Lumby et al., 2020) if not beforehand. This work therefore builds upon thinking about selection during viral transmission in the published literature.
Summary:
In this paper, the authors develop a model that reconciles the observed lack of antigenic evolution in influenza on the intra-patient scale with the strong evolutionary pressure observed on the global scale. Using this model, the authors infer a biological mechanism for this disparity. They claim that the asynchrony between peak viral loads and the adaptive immune response prevents selection during viral replication in a host. Instead, they propose that under a realistic set of infection and immune parameters, selection happening at the point of inoculation by matched sIgA antibodies would better explain intra-host and global evolutionary patterns.
Although others have similarly proposed that influenza evolution ordinarily takes place between hosts as opposed to within hosts, this paper models this idea in a much more systematic way than has been done before.
Essential revisions:
The paper is virtually all modeling except for a bit of deep sequencing data in Figure 1. Yet the authors strongly posit specific molecular mechanisms (such as secretory IgA) as driving the selection. While these mechanisms certainly seem plausible, the model is really just distinguishing between selection at transmission versus selection within-host after transmission. It would therefore be better to phrase more of the paper in those terms, and then perhaps in Introduction and Discussion section speculate about specific mechanisms that would drive different forms of selection.
Overall, I find these models informative and plausible. However, the comparison of the model predictions to real data is fairly limited and mostly qualitative.
Can the authors comment on the dynamics of infection in children? There is some evidence that infection times are longer in children than adults (Ng et al., 2016). Does this suggest that 'replication selection' could occur in children? If so, children make up a substantial proportion of the world population and would likely have a large impact on global transmission dynamics.
How would the model change in cases where influenza infects the lower respiratory tract? This would change the size of the target cell population substantially.
The authors should be clearer that when speaking about 'wild-type' and 'mutant' viruses, they refer to antigenicity and not the genotype. For example, in subsection “Model overview”, when the authors talk about 'within-host virus diversity' are they talking about the random accumulation of mutations or the random accumulation of antigenic variants? Also in the Results section, there would be a difference in the probability of a new variant infection and a new antigenic variant infection, so they should be clear about which they are referring to.
How does a cellular immune response affect viral titer? Do T-Cells help to mount an immune response? I think the authors are using adaptive immunity and antibody-mediated immunity interchangeably when they aren't fully interchangeable. In particular, vaccination and infection might elicit different levels of T-cell immunity.
How 'target-cell' limited is influenza really in practice? If it is, how would infections in immunocompromised individuals occur? I assume the rate of cellular replenishment is the same, and that rate of target cell depletion would also be the same.
This is an interesting manuscript that uses mathematical modeling to argue that the timing of within-host selection is crucial to understanding antigenic evolution in influenza. In particular, it argues that selection by antibodies on mucosal surfaces during initial infection is the key driver of adaptation. This seems important, although I had a hard time following the argument in places.
Essential revisions:
1) I would appreciate a clear, concise statement of which aspects of observed flu dynamics (e.g., reinfected hosts without escape mutants, global patterns of evolution, etc.) the model hits and which it doesn't, and which really distinguish it from what I understand to be the alternative model, that adaptation is driven by selection in partially immune hosts.
2) Related: I'm not sure I've understood what the point of the paper is. I thought from the Abstract that it was going to show that using a more realistic model of within-host evolution lets you get the right rate of global antigenic evolution, but after reading the paper I think that maybe that's not the case, and the authors are saying that there are also some interesting complications at the population level that would need to be taken into account. Putting it another way: I couldn't tell at times whether the point was that this was the first model of within-host evolution that included the known facts about immune dynamics, allowing it to say X about flu, or whether it was showing using influenza dynamics that a particular model of the immune system is correct.
3) As can be seen from Table 1, there is a lot going on in the model. The authors spend a lot of time giving intuition about the role of key features, but it would be nice if they could do even more, or even present a more stripped-down version of the model in the main text and save more details for the Appendix.
[Editors’ note: further revisions were suggested prior to acceptance, as described below.]
Thank you for submitting your article "Asynchrony between virus diversity and antibody selection limits influenza virus evolution" for consideration by
The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.
We would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). Specifically, we are asking editors to accept without delay manuscripts, like yours, that they judge can stand as
The manuscript presents a theoretical study that bridges the global and the within-host evolution of the influenza virus. The key finding of the manuscript is that the asynchrony between within-host viral growth and the delayed antibody response following an infection can explain the pattern of antigenic evolution for influenza, where selection for new variants is strong at the population level but not within individuals. The reviewers agree that this work is conceptually important and provides a theory-driven hypothesis, which could in principle be tested with data. However, there are still a few points that we would like to see addressed in the manuscript.
Essential revisions:
1) The manuscript is presenting a thorough analysis of a model with qualitative comparison to data that establishes the
2) The reviewers agreed that the comparison to data is limited, and they have a suggestion that could strengthen the paper. However, the authors could chose to ignore this suggestion and only discuss it as a potential test of the model:
Figure 5 shows that there is a clear and large difference between the outcomes of the models involving or not involving an immediate recall response, which would seem to give scope for a quantitative comparison of antigenic evolution rates. As you know, the maps of antigenic change, first shown in Smith et al., 2004, are displayed within a quantitative metric space, where one square on the map corresponds to a specific change in titre. Is it possible to convert the antigenic change of Figure 5 to an approximate change in HI titre (e.g. per year) that might be compared with the antigenic maps of Smith et al. or an alternative measurement of the rate of antigenic change?
3) Your original submission made a distinction between two paths:
i)"Transmission selection": This just means that a host with a variant-dominated infection will tend to transmit more, because they can transmit to hosts who are immune to an old variant.
ii) "Inoculation selection": This is when there is competition within a diverse inoculum and immunity favors the new variant by clearing out the old type.
One can expects that under inoculation selection, the absolute rate at which new antigenic-mutant infections arise increases as immunity to the old type increases, whereas under transmission selection they arise at a constant absolute rate. It would be good if the authors could add a discussion about the consequences of these selection paths to the manuscript and also discuss whether global patterns are consistent with one or the other.
[Editors’ note: the authors resubmitted a revised version of the paper for consideration. What follows is the authors’ response to the first round of review.]
Reviewer #1:
This paper addresses the observation that, while global influenza populations are strongly influenced by selection for antigenic novelty, within-host populations. It describes a model in which within-host selection is active, but temporally delayed, while selection based on the immune history of an individual acts at the time of transmission, during the establishment of an infection.
1) I have two preliminary comments on the style in which this is written, as opposed to the content of the paper. Firstly, my experience reading this was that I found the main text difficult to follow until the point at which I had gained familiarity with the details of the model. For example, once I knew what \kappa_w, p_C, c, and k referred to I could understand the legend of Figure 3, though it took some time for me to get there. I suggest, if possible, rewriting the main text so as to be accessible in its own right to a casual reader.
We agree with the reviewer that the model was insufficiently introduced prior to the presentation of modeling results. We have now expanded the subsection “Model overview” to give a more complete summary, including definitions, with motivating examples, of relevant parameters. We have also made other modifications throughout the text to improve readability.
Secondly, I thought that the choice of data to be presented in figures was odd. The paper presents a model of viral evolution. As such, the interest (for me) was the extent to which the model replicates the observed behaviour of influenza virus in the real world. However, only Figure 1A and 1B describe any 'real world' data. Figure 4A is conceptual and useful, but the remainder of the figures exist in 'model space', showing how this or that parameter affects the behaviour of which part of the model. I'm not against model-to-model comparison (Figure 4E-H are useful though I'd personally keep only the top parts), but suggest removing anything from the main text which does not directly and clearly illustrate some key part of the model, or which does not show some direct comparison of the behaviours of different models as they relate directly to observations of the real-world system.
A limitation of our study is that many of the needed measurements to compare our model to data do not yet exist. No one has attempted to observe antigenic selection at the point of transmission because the assumption has generally been that antigenic selection happens during replication. As we now say explicitly in the Discussion section, one of our key aims with this study is to provide theoretical motivation for relevant experiments.
As such, our figures are necessarily model exploration for the most part. That said, we have revised Figure 1A-B to provide additional information, and revised the text to highlight the need for appropriate animal model experiments.
2) The claim is made that 'selection for new antigenic variants acts principally at the point of initial virus inoculation'. I have some questions and concerns around this claim.
- To what extent has antigenic selection during the establishment of infection been experimentally documented? The primary reference given here is that of Wang, 2017. However, while Wang is clear that antibodies in the mucus can be influenza-specific (as opposed to being specific to another virus) it did not seem so clear that these antibodies are strain-specific in the sense of identifying viruses that differed by a single mutation.
Antigenic selection at the point of transmission is difficult to observe directly and difficult to distinguish from antigenic replication selection in the donor host, as Lumby et al., 2018 point out. We believe that much of the value in a theoretical study like this one lies in identifying potentially fruitful avenues for experiment that would not otherwise be obvious.
We have added the following text to the Discussion section:
“A key proposal of our study is that population-level antigenic selection and homotypic protection are mediated by antibody neutralization (most likely sIgA) at the point of transmission. […] While we cannot rule out a powerful immediate cellular response that was differentially evaded in the various subjects, we believe that our model, coupled with existing understanding of the timing of cellular responses and the speed of influenza replication, provides a more parsimonious explanation.”
- With this in the background I was not clear about the first of the claimed key results, that 'sIgA antibody neutralisation protects experienced hosts against reinfection'. It is certainly true is that a model incorporating selection during the transmission process (plus delayed within-host selection) is consistent with a range of observed data describing influenza infection and evolution. However, this is not the same as what is claimed. The hypothesis of the importance of sIgA antibody neutralisation is shown to be more consistent with the data than other models, but that does not imply that the hypothesis is true.
We agree with the reviewer’s comment. Our central claim is that one needs neutralization prior to virus exponential growth in order to simultaneously explain (a) homotypic reinfection, (b) the absence of observable antigenic mutants in reinfected hosts, and yet also (c) strong population level selection for antigenic novelty and apparent individual protection against reinfection.
We have revised the text to emphasize that mucosal sIgA neutralization is a biologically plausible mechanism that could produce neutralization prior to growth, but that our work is could be consistent with other mechanistic accounts (yet to be described) that produce a “strong-weak-(strong)” pattern of antigenic selection. That is, strong selection at the point of transmission, weak selection during virus exponential growth, and (potentially) strong selection again only late in infection.
We have modified the text in multiple places, including those noted in above, to make these points clear.
- Given the modelling that has been done, it would seem straightforward to evaluate this claim further. Within-host selection is delayed, but not entirely absent. As such, the expected frequency of a novel antigenic variant at the time of transmission to a new host will in the mean be higher than it would otherwise be under pure neutrality. It should be possible compare this change in the expected variant frequency to that produced by the transmission process (illustrated in Figure 4E). Averaging over stochastic effects, what proportion of the selection is due to within-host processes and what is due to selection during transmission? In the manuscript, it is claimed without further details that within-host evolution is 'dominated' by inoculation selection. What does this really mean?
We thank the reviewer for this excellent suggestion, which we have implemented using our analytical model. It forms the basis of a new figure, Figure 4.
We have revised the text to avoid the language of one form of selection “dominating” and now discuss the relative contributions of drift, replication selective effects, and inoculation selective effects to the survival of new variants at the point of transmission. In addition to adding Figure 4, we have added the following two passages to the Results section and Discussion section, respectively, in the main text:
“Onward transmission of new variants can be facilitated by natural selection—replication selection, inoculation selection or both. […] But again, it is difficult to estimate how much this synergy matters in practice without knowing more about that factors that govern homotypic reinfection and heterotypic reinfection.”
3) On the model of within-host viral load, this paper follows a commonly applied model of (roughly speaking) exponential growth followed by exponential decline. However, Pawelek et al. (2012) argue that a more bimodal pattern of behaviour is more realistic, a second peak arising from the re-emergence of susceptible cells that have been made refractory to infection by interferon. Would this increase the effect of within-host selection?
The double peak discussed in Pawelek et al., 2012 was observed in experimental infections of naive horses, and the observed second peak is much lower than the first. In human kinetics data (Hadjichrysanthou et al., 2016) and animal transmission experiments (Canini et al., 2020; Le Sage et al., 2020) it is common to see clearly single-peaked infections.
Furthermore, for realistic (incomplete) degrees of antibody binding escape, we expect both old and new antigenic variant population sizes to decline even due to antigenic limiting factors, though we naturally expect the new variant to decline more slowly.
The upshot is that clearance should be rapid following the mounting of the adaptive response in the experienced hosts where we expect selection to take place.
We have added an Appendix section (5.4) that discusses these points to our overview of parameter and model uncertainty (5).
Further, the work of Tsang et al. (2015) notes a proportion of transmission events occurring four or more days post the onset of symptoms; if within-host selection kicks in two days after infection it seems likely that within-host selection has a non-negligible effect even if events at transmission are the primary driver of selection.
It is first important to clarify that we chose to model an antibody response that is fully “on” at 48 hours. The aim was to be as harsh as possible to our hypothesis that asynchrony between diversity and selection could limit adaptation. The true timing and the rate of ramp-up is not well understood, but is likely to be slower, as we discuss in Appendix section 2.
Variation in observed transmission times might also reflect the timing of viral and resultant immune kinetics in those individuals. Empirical data suggests that inter-individual variation in such quantities is possible, and if individuals have slower initial growth and a later immune response, they may transmit later without having a longer period of antibody-mediated selection
That is, Tsang et al., 2015 show that transmission might sometimes occur relatively late in infection but this is unlikely to be the case in an individual with an immune response that is capable of exerting efficient selection pressure.
In addition, the added discussion of synergy between replication and inoculation selection referenced in 1.5 provides a clearer quantification of this effect (see Figure 4): later transmissions will aid new variant survival roughly proportional to
4) I don't believe that the model presented is a good one for infection in immunocompromised individuals. To the best of my knowledge the oscillations shown in Figure 3B and C have not been observed in clinical cases. My suspicion is that the model ignores some of the complexities of within-host infection in a way that gives a reasonable picture of a typical infection, but that falls short when it comes to longer-term infections. The point being made here is that selection for antigenic variants can be effective during longer infections; I would accept this point fairly readily, but the data of Figure 3 did not make me particularly more convinced.
We agree with the reviewer that the oscillations in the numbers of target cells and virions could be un-biological. The target cell replenishment was intended as a means of prolonging infection and modeling compromised innate immunity within our minimal model, since the minimal model treats the innate response implicitly, rolling it into target cell depletion.
In the revised manuscript, we have removed the original Figure 3 and replaced it with a verbal argument that references Figure 1G and our new general replicator equation figure (Figure 7). These make the conceptual/modeling point without the need for additional assumptions, and without potentially distracting and un-biological model output.
5) It is claimed that Figure 5 shows that proposed model of global influenza evolution better mimics empirical observations of the global population with regard to changes in the antigenic type of the virus. However, while it is clear from the figure that different models give different results, no indication of the observed behaviour of the global population is given in the Figure. The claim may be true. However, what is the observed distribution of changes in the global population to which Figure 5D provides a better match?
The key behavior we are attempting to explain with Figure 5 is that observed in Figure 1 and Figure 2 of Smith et al., 2004. We of course cannot reproduce these images in our main text, but we now explicitly reference those figures by number both in the caption to Figure 5 and in subsection “Inoculation selection produces realistically noisy between-host evolution” and subsection “Small-population-like evolution”.
While antigenic cluster transitions over time generally move directionally away from the root, within a cluster a more neutral pattern is observed, where substitutions can move in any direction in antigenic space. Bedford et al., 2012 attributed this pattern of seeming within-cluster neutrality to titration and estimation noise, but this is unlikely to be true for the Smith et al. map as each virus was assayed in duplicate or triplicate with high repeatability.
6) I was confused by Figure 7. Based on the methods I think that the term emergence describes the appearance of a variant in the population in such a way that it will not subsequently die out through genetic drift.
We see that this was a terminological issue, and precision is important when describing a cross-scale evolutionary process. We have edited the text to be clearer about mutation, observability, and stochastic extinction, both within-host and at the population level. We have substituted other phrases such as “first successful mutation” and “antigenic diversification”, where most appropriate.
Figure 7 then shows the distribution of emergence times under the case of an immediate recall response and a delayed recall response. My expectation would be that under an immediate recall response, positive selection would begin to apply to the variant earlier, making its emergence more likely to happen sooner, but the figure shows the opposite effect. I may have missed something in the explanation.
We have added a note to the figure caption to clarify this:
“Note that time of first successful mutation tends to be later with an immediate recall response than with a delayed recall response. This occurs because the cumulative number of viral replication events grows more slowly in time at the start of the infection because of the strong, immediate recall response.”
For our parameters, this total event effect swamps the stochastic extinction effect noted by the reviewer. But even the stochastic extinction effect may not necessarily favor new variant emergence in the presence of an early (versus delayed) antibody response. If the new variant achieves only partial immune escape escape, its stochastic extinction probability may be higher in the presence of antibodies than in their absence.
Antibodies controlling the old variant population may also keep the target cell population from being depleted, but this effect is marginal for our parameters, as new variants that survive stochastic extinction tend to be produced well before substantial target cell depletion occurs.
Interestingly, as we note in Appendix section 5.1.1, this means that the antibodies that maximally promote replication selection are the ones that begin when
7) Appendix 6: To the best of my understanding, the idea that large effect antigenic changes can occur in multiple backgrounds is not contradicted by the work of Koelle and Rasmussen. In that work a distinction is made between 'good' and 'bad' genetic backgrounds, characterised by the extent of mutational load in a sequence, however, there can be multiple 'good' backgrounds or at least, multiple backgrounds good enough for a variant to appear multiple times in the global population before fixation.
Koelle and Rasmussen do not argue that cluster transitions are only viable in a single genetic background. But they do argue that the rarity of good backgrounds is limiting for the virus, and is crucial to setting the pace of antigenic evolution and producing a spindly phylogeny with punctuated cluster transitions of intermediate size:
“Successful establishment can only occur when a large antigenic mutation arises in a good genetic background (Figure 2C), a jackpot combination”; “These analyses indicate that deleterious mutation loads should lower the rate of antigenic evolution (Figure 1E).”; “ Our analyses also indicate that deleterious mutation loads increase the average size of antigenic variants that establish in the long run (Figure 1D); observed patterns of punctuated antigenic evolution (Smith et al., 2004) may thus be better reproduced with a model that integrates sublethal deleterious mutations than one that ignores these mutation.”
That there are multiple cases of synchronous, polyphyletic antigenic cluster transitions casts doubt on these claims. If major antigenic changes appeared infrequently due to the rarity of jackpot cases of a good mutant in a good background, it would be very surprising to see two or three distinct and synchronous jackpots after years of none. So, while mutational load may play an important role in determining which lineages are fittest, synchronous polyphyly suggests that it is unlikely to set the clock of antigenic evolution. Rather, it suggests that accumulating population immunity may be crucial in setting the clock. Selection at the point of transmission begins to provide an explanation for how this could be the case.
We have now added similar text to the above to our discussion of deleterious load and other non-antigenic fitness to clarify that our point is about what limits the rate at which observable changes arise in the global population.
As another thought here, is the work of Strelkowa and Lassig, (2011) relevant as a proposed explanation for the pattern of global viral evolution, competition?
We thank the reviewer for pointing this out. Our work is consistent with the possibility of population-level clonal interference. As we note, neutralization of within-host adaptation is most likely necessary, but perhaps not sufficient, to explain why global scale influenza antigenic adaptation is not faster.
In particular, the polyphyletic emergence of antigenicity-altering substitutions suggests that when the time is right for an antigenic change, multiple lineages may compete to supply that change. Conversely, when population immunity has not risen to sufficiently high levels, the mutants may arise but lose in competition with adaptive non-antigenic mutants. That said, it is striking that typically when these polyphyletic emergences occur, they involve the same antigenicity altering substitutions across lineages.
We have added text to this effect to relevant parts of the Discussion section and Appendices, in particular subsection “Population immunity sets the clock of antigenic evolution” and Appendix section 7.3.
8) Appendix 7: The concept of selection acting both in the transmission process and during within-host replication is not entirely novel; Lumby et al. (2018) make this distinction in the context of influenza transmission and within-host growth (and further discuss the idea of a selective bottleneck). The idea that selection during the transmission process could play a role in the adaptation of global influenza populations has been raised very recently (Lumby et al., 2020) if not beforehand. This work therefore builds upon thinking about selection during viral transmission in the published literature.
We thank the reviewer for the Lumby et al., 2018 reference, which we have added in several places, most notably to help discuss the question of why it is so difficult to document antigenic selection at the point of transmission (see 1.3).
We have also added subsection “Relationship to influenza virus transmission prior bottleneck literature”, where we discuss prior literature on influenza bottlenecks, including whether selection might act there and if so how. In this section, we cite key prior work that hypothesized such effects, including Han et al., 2019; Lumby et al., 2018; Petrova and Russell, 2018.
Reviewer #2:
Essential revisions:
The paper is virtually all modeling except for a bit of deep sequencing data in Figure 1. Yet the authors strongly posit specific molecular mechanisms (such as secretory IgA) as driving the selection. While these mechanisms certainly seem plausible, the model is really just distinguishing between selection at transmission versus selection within-host after transmission. It would therefore be better to phrase more of the paper in those terms, and then perhaps in Introduction and Discussion section speculate about specific mechanisms that would drive different forms of selection.
We agree with the reviewer that it is not possible to establish conclusively the mechanism of selection at the point of transmission from our modeling work.
“We focus on sIgA neutralization at the point of transmission because it is a biologically plausible mechanism by which the temporal pattern of antigenic selection during infection could be strong (at the point of transmission), subsequently weak (during exponential growth), and then possibly strong (toward the end of infection). Other biological mechanisms that produce such a pattern would be consistent with our results. We have weakened the mechanistic language in the Abstract and Introduction (see quoted example below) and added more text of mechanisms to the Discussion to address this, and to clarify how this relates to existing literature on “selective bottlenecks” Antibody immunity at the point of transmission in previously infected or vaccinated individuals should reduce the initial probability of reinfection (Le Sage et al., 2020); secretory IgA antibodies on mucosal surfaces (sIgA) are likely to play a large role (Wang et al., 2017, see Appendix 2).”
Overall, I find these models informative and plausible. However, the comparison of the model predictions to real data is fairly limited and mostly qualitative.
This is true, but unfortunately unavoidable. As we now say in the Discussion section:
“This is a modeling study, and a mainly theoretical one. This is out of necessity. Quality experiments of the kind that are necessary to observe selection at the point of transmission directly and measure its strength have not been published, and we were unable to find any experimental measurements of within-host competition between known antigenic variants.”
Can the authors comment on the dynamics of infection in children? There is some evidence that infection times are longer in children than adults (Ng et al., 2016). Does this suggest that 'replication selection' could occur in children? If so, children make up a substantial proportion of the world population and would likely have a large impact on global transmission dynamics.
The reviewer raises an interesting point. Longer durations of replication in children could be a function of a weak specific antibody response. This would make it unlikely for them to exert selection pressure.
Indeed, there is some evidence that children require multiple infections before they begin to develop specific antibody immunity to influenza, which may make them less efficient inoculation selectors up to that point. We discuss this in detail in Appendix section 2, and have added a brief point to subsection “Importance of host heterogeneity”:
“Hosts with more focused immune responses—highly specific antibodies that neutralize old antigenic variant virions well and new antigenic variant virions poorly—could be especially good inoculation selectors and important sources of population-level antigenic diversity. Hosts who develop less specific memory responses, such as very young children (Neuzil et al., 2006), could be less important.”
How would the model change in cases where influenza infects the lower respiratory tract? This would change the size of the target cell population substantially.
While this does change the target cell population, it should still produce a period of exponential growth in the absence of antibody selection, followed by the imposition of non-antigenic limiting factors. As we state in in the main text, target cell depletion should most properly be considered as a proxy for a range of non-antigenic limiting factors, particularly the action of the innate immune system – many of which do indeed act by decreasing the virus’s cellular resources (e.g. through inflammation).
That said, truly chronic, prolonged influenza infections are excellent opportunities for antigenic diversification Xue et al., 2017, and we discuss this in light of our model.
We have added the following to subsection “Limitations and remaining uncertainties”:
“These factors limit the virus regardless of whether the infection remains confined to the upper respiratory tract or also invades the lower respiratory tract, thereby gaining access to additional target cells Koel et al., 2019. The key is that non-antigenic factors prevent persistent large virus populations.”
The authors should be clearer that when speaking about 'wild-type' and 'mutant' viruses, they refer to antigenicity and not the genotype. For example, in subsection “Model overview”, when the authors talk about 'within-host virus diversity' are they talking about the random accumulation of mutations or the random accumulation of antigenic variants? Also in the Results section, there would be a difference in the probability of a new variant infection and a new antigenic variant infection, so they should be clear about which they are referring to.
We thank the reviewer for this suggestion, which will substantially clarify the manuscript. We have revised language throughout the paper to refer to “old antigenic variants” and “new antigenic variants” and been explicit throughout that we are discussing antigenic phenotypes, particularly in HA.
How does a cellular immune response affect viral titer? Do T-Cells help to mount an immune response? I think the authors are using adaptive immunity and antibody-mediated immunity interchangeably when they aren't fully interchangeable. In particular, vaccination and infection might elicit different levels of T-cell immunity.
We agree with the reviewer that our manuscript most directly addresses antibody immunity and memory B-cell responses, as we are interested in the escape from antibody-binding observed at the population level in influenza virus HA proteins. We have reworded the text throughout to refer specifically to the antibody response rather than the adaptive response in general.
In the interest of tractability and encoding the mechanistic hypothesis, we made our model as simple as possible. But we agree that there are interesting implications for other forms of adaptive immunity. For instance, many forms of adaptive immunity may reduce severity without necessarily promoting antigenic evolution. As we say in the main text:
“The antibody response we introduce at 48 hours is qualitative—it is modeled simply as an increase in the virion decay rate for matching virions. This response could represent IgA, but other antigenicity-specific mode of virus control could also be subsumed under the increased virion decay rate, for instance IgG antibodies, or antibody dependent cellular cytotoxicity (ADCC). The key point we establish is that none of these mechanisms efficiently replication select because they all emerge once non-antigenic limiting factors have come into play. They speed clearance but should not substantially alter viral evolution. A corollary to this point is that there are many mechanisms—and interventions—that could reduce the severity of influenza infections without substantially speeding up antigenic evolution, including universal vaccines.”
How 'target-cell' limited is influenza really in practice? If it is, how would infections in immunocompromised individuals occur? I assume the rate of cellular replenishment is the
same, and that rate of target cell depletion would also be the same.
Following existing within-host influenza kinetics models (e.g. Baccam et al., 2006, Pawelek et al., 2012, Luo et al., 2012, Hadjichrysanthou et al., 2016), we interpret target cell depletion as a combination of virus-mediated cell death and innate immune responses that act to limit cell availability through inflammation, cell death, and so on. We describe this explicitly in subsection “Limitations and remaining uncertainties”. In immune-compromised individuals the waning of these effects (which tend to be short-lived) allows for a consistent supply of infectible cells. That said, we do not believe the cycling behavior of replenishment and depletion showed in the example immune-compromised kinetics from Figure 3 is biological; we have modified the figure to avoid giving the impression that it is (see response to reviewer 1).
Reviewer #3:
This is an interesting manuscript that uses mathematical modeling to argue that the timing of within-host selection is crucial to understanding antigenic evolution in influenza. In particular, it argues that selection by antibodies on mucosal surfaces during initial infection is the key driver of adaptation. This seems important, although I had a hard time following the argument in places.
We are pleased that the reviewer finds the work novel and important. We have worked to clarify the structure of the argument throughout, most notably by:
1) Expanding the initial model description, so that the reader is equipped with terminology and notation prior to encountering model results.
2) Adding subsection headings to the Results, with the aim of clarifying the structure of the argument.
Essential revisions:
1) I would appreciate a clear, concise statement of which aspects of observed flu dynamics (e.g., reinfected hosts without escape mutants, global patterns of evolution, etc.) the model hits and which it doesn't, and which really distinguish it from what I understand to be the alternative model, that adaptation is driven by selection in partially immune hosts.
We have addressed this by moving some of the Appendix text out of the Appendix and making them the beginning of the main text Discussion section:
“Any explanation of influenza virus antigenic evolution—and why it is not even faster—must explain why population level antigenic selection is strong but within-host antigenic evolution is difficult to observe.”
“We hypothesized that antibodies present in the mucosa at the time of virus exposure can effectively block transmission, but have only a small effect on viral replication once cells become productively infected. Antigenic selection after successful infection therefore begins with the mounting of a recall response 48–72 hours post infection. In this case, selection pressure can be strong at the point of transmission, but subsequently weak until after 48 hours. This mechanistic paradigm reconciles strong but not perfect sterilizing homotypic immunity with rare observations of mutants in successfully reinfected experienced hosts.”
2) Related: I'm not sure I've understood what the point of the paper is. I thought from the Abstract that it was going to show that using a more realistic model of within-host evolution lets you get the right rate of global antigenic evolution, but after reading the paper I think that maybe that's not the case, and the authors are saying that there are also some interesting complications at the population level that would need to be taken into account. Putting it another way: I couldn't tell at times whether the point was that this was the first model of within-host evolution that included the known facts about immune dynamics, allowing it to say X about flu, or whether it was showing using influenza dynamics that a particular model of the immune system is correct.
We agree with the reviewer that the previous version of the manuscript failed to make our central point clear.
The point of our paper, first and foremost, is that influenza viruses possess both of the fundamental materials of adaptation within a single reinfected host: diversity and selection pressure. We propose that antigenic adaptation nonetheless fails to occur because of the temporal asynchrony between diversity and selection pressure.
This central finding then has implications for population level adaptation. Notably, existing models of influenza within-host evolution and the ready availability of large-effect antigenic substitutions would seem to imply that influenza adaptation should be rapid within reinfected experienced hosts, and that this could lead to rapid antigenic diversification at the population level. We are then able to explain why population-level diversification may be a slower process, with new variants only seen after a new antigenic variant has circulated long enough to generate substantial population immunity.
We have changed wording throughout the text to highlight that the central findings concern why within host adaptation is not more rapid, and that the implications for population level patterns, though of substantial interest, are just that – implications.
3) As can be seen from Table 1, there is a lot going on in the model. The authors spend a lot of time giving intuition about the role of key features, but it would be nice if they could do even more, or even present a more stripped-down version of the model in the main text and save more details for the Appendix.
The other two reviewers shared this concern, and we agree that it was an issue. As we explain in our response to reviewer 1, we have now added a more detailed model description, with examples, prior to the Results section.
[Editors’ note: what follows is the authors’ response to the second round of review.]
Essential revisions:
1) The manuscript is presenting a thorough analysis of a model with qualitative comparison to data that establishes the plausibility of the model, rather than a quantitative comparison with alternative models by fitting data. The authors should frame the Abstract, Introduction and Discussion section to make this point more clear.
We have now revised the Abstract and Introduction to make it clear that our study is theoretical, and aimed at establishing the plausibility of a mechanism that could then be investigated empirically. In particular:
We have changed a key sentence in the Abstract to use more conditional language and emphasize that this is a modeling exercise: “Using a mathematical model, we show that the temporal asynchrony between within-host virus exponential growth and antibody-mediated selection could limit within-host antigenic evolution”.
Similarly, we have changed the summary of our results in the Abstract to: “Our results provide a theoretical explanation for how virus antigenic evolution can be highly selective at the global level but nearly neutral within host”.
We have also added the following final paragraph to the end of the Introduction:
“Our modeling results suggest a plausible mechanism that can explain otherwise poorly reconciled empirical patterns, and should motivate further experimental investigation of the mechanisms of immune protection and natural selection on influenza virus antigenic phenotypes at the point of transmission.”
2) The reviewers agreed that the comparison to data is limited, and they have a suggestion that could strengthen the paper. However, the authors could chose to ignore this suggestion and only discuss it as a potential test of the model:
Figure 5 shows that there is a clear and large difference between the outcomes of the models involving or not involving an immediate recall response, which would seem to give scope for a quantitative comparison of antigenic evolution rates. As you know, the maps of antigenic change, first shown in Smith et al., 2004, are displayed within a quantitative metric space, where one square on the map corresponds to a specific change in titre. Is it possible to convert the antigenic change of Figure 5 to an approximate change in HI titre (e.g. per year) that might be compared with the antigenic maps of Smith et al. or an alternative measurement of the rate of antigenic change?
We agree with the reviewers that this would be an interesting comparison. We feel, however, that the single-chain to first-fixation model presented in Figure 5 is more appropriate for predicting the distribution of observed antigenic fixations rather than the yearly rate of antigenic change in the dominant variant, since the latter depends upon numbers of simultaneous chains, accumulating population immunity, and clonal interference amongst emerged types. In our opinion, this would require a principled population-level model.
Instead, we have attempted to highlight more clearly where the model does speak to Smith et al. style data: in predicting within-cluster backward fixations and drift alongside rarer forward jumps. We have added the following paragraph to the discussion of Figure 5:
“In particular, we note that whereas an immediate recall response would predict strong near-constant directed evolution of virus antigenic phenotypes away from existing immunity (Figure 5B,C), a realistically-timed recall response predicts that small-effect, drift-like, antigenic substitutions will be observed. […] Exact rates of antigenic evolution will depend upon how these emergence processes intersect with population-level epidemic dynamics and competition among variants.”
3) Your original submission made a distinction between two paths:
i)"Transmission selection": This just means that a host with a variant-dominated infection will tend to transmit more, because they can transmit to hosts who are immune to an old variant.
ii) "Inoculation selection": This is when there is competition within a diverse inoculum and immunity favors the new variant by clearing out the old type.
One can expects that under inoculation selection, the absolute rate at which new antigenic-mutant infections arise increases as immunity to the old type increases, whereas under transmission selection they arise at a constant absolute rate. It would be good if the authors could add a discussion about the consequences of these selection paths to the manuscript and also discuss whether global patterns are consistent with one or the other.
We now call “transmission selection” simply “population-level selection”, as we think this increases clarity and avoids adding unnecessary new terminology. We retain the discussion of it in subsection “Tight bottlenecks lead to loss of generated diversity and mean new variants reach consensus through founder effects”: “Neutralization at the point of transmission thus not only gives new antigenic variant infections their transmission advantage (population-level selection) but may also increase the rate at which these new antigenic variant infections arise (inoculation selection).”
We agree with the reviewer about this empirical prediction, which we discussed in subsection “Population immunity sets the clock of antigenic evolution”. We have revised that section to highlight this point more clearly, including adding a reference to polyphyletic emergence events of new antigenic variants:
“If immunity to the old variant only gives new variants a population-level transmission advantage (population-level selection), we anticipate a constant rate of population-level antigenic diversification, with selective sweeps once a new variant has a sufficient population-level advantage over the old variant. […] That said, alternative explanations are possible, such as reduced rates of stochastic loss of new variants at higher scales (e.g. the epidemic scale) with increased population immunity.”