Background: Since its emergence in 1968, influenza A (H3N2) has evolved extensively in genotype and antigenic phenotype. However, despite strong pressure to evolve away from human -immunity and to diversify in antigenic phenotype, H3N2 influenza shows paradoxically -limited genetic and antigenic diversity present at any one time. Here, we propose simple +immunity and to diversify in antigenic phenotype, H3N2 influenza shows paradoxically limited +genetic and antigenic diversity present at any one time. Here, we propose a simple model of antigenic evolution in the influenza virus that accounts for this apparent discrepancy.
[2]. Phylogenetic analysis of the -genetic relationships among HA sequences has revealed a distinctive genealogical tree +href="#XNelson07NatRevGenet">2
]. Phylogenetic analysis of +the relationships among HA sequences has revealed a distinctive genealogical tree showing a single predominant trunk lineage and side branches that persist for only 1–5 years before going extinct [3]. This tree shape is indicative of serial replacement of @@ -149,18 +149,19 @@The virus persists over the course of the 40-year simulation, and at the end of most simulations, there remain only a few closely related viral lineages, indicating that genealogical diversity is restricted by evolution in the two-dimensional antigenic landscape. Reduced diversity is -substantially more common in models with less mutation or models with less variable mutation -effects (Figure 1). At higher mutation rates, viruses may move apart in antigenic phenotype too -rapidly for competition to always eliminate the weaker of two diverging lineages. Similarly, with -high variance in mutational effect, there can sometimes emerge new antigenic types, too distant -from the existing population to suffer limiting competitive pressure. Both these scenarios lead to -coexistence of multiple antigenic phenotypes. We thus restrict the model to parameter regimes -with lower mutation rates and lower mutation effect variances. We primarily focus on -the model with 10Figure 1
). At higher mutation rates, viruses may move apart in +antigenic phenotype too rapidly for competition to always eliminate the weaker of two +diverging lineages. Similarly, with high variance in mutational effect, there can sometimes +emerge new antigenic types, too distant from the existing population to suffer limiting +competitive pressure. Both these scenarios lead to coexistence of multiple antigenic +phenotypes. We thus restrict the model to parameter regimes with lower mutation rates and +lower mutation effect variances. We primarily focus on the model with 10-4 mutations per infection per day and standard deviation of 4 -antigenic units. In this model, 80 out of the 100 replicate simulations show reduced -genealogical diversity (defined as less than 9 years separating contemporaneous viruses). +class="cmr-8">4 mutations +per infection per day and mutation effects with standard deviation of 0.4 antigenic +units. In this model, 80 out of the 100 replicate simulations show reduced genealogical +diversity (defined as less than 9 years of evolution separating contemporaneous viruses). We conditioned the following analysis on these 80 simulations, compiling summary statistics across this pool and presenting a detailed analysis of a single representative simulation. @@ -193,23 +194,24 @@The model exhibits annual winter epidemics in temperate regions and less periodic epidemics in the tropics (Figure 2A). Across replicate simulations, we observe average yearly attack rates of -6.8% in temperate regions and rates of 7.1% in the tropics, comparable with estimated attack -rates of influenza A (H3N2) of 3–8% per year [[10, 11]. Over the course of the simulation, the -virus population evolves in antigenic phenotype exhibiting, at any point, a handful of highly -abundant phenotypes sampled repeatedly and a large number of phenotypes appearing at low -abundance (Figure 2B). The observed antigenic map of H3N2 influenza includes substantial -experimental noise; replicate strains appear in diverse positions on the observed map. By -including measurement noise on antigenic locations (see Methods), we approximate an -experimental antigenic map of H3N2 influenza (Figure 2D). Over the 40-year simulation, -antigenic drift moves the virus population at an average rate across replicates of 1.05 antigenic -units per year, corresponding closely to the empirical rate of 1.2 units per year [9]. The -appearance of clusters in the antigenic map comes from the regular spacing of high abundance +href="#XKoelle09">11
]. Over the course of the +simulation, the virus population evolves in antigenic phenotype exhibiting, at any point, a +handful of highly abundant phenotypes sampled repeatedly and a large number of +phenotypes appearing at low abundance (Figure 2B). The observed antigenic map of +H3N2 influenza includes substantial experimental noise; replicate strains appear in +diverse positions on the observed map. By including measurement noise on antigenic +locations (see Methods), we approximate an experimental antigenic map of H3N2 +influenza (Figure 2D). Over the 40-year simulation, antigenic drift moves the virus +population at an average rate across replicate simulations of 1.05 antigenic units per year, +corresponding closely to the empirical rate of 1.2 units per year [9]. The appearance +of clusters in the antigenic map comes from the regular spacing of high abundance phenotypes combined with measurement noise. Over time, clusters of antigenically similar strains are replaced by novel clusters of more advanced strains (Figure 3A). -Across replicate simulations, clusters persist for an average of 5.0 years measured as +Across replicate simulations, clusters persist for an average of 5.0 years, measured as the time it takes for a new cluster to reach 10% frequency, peak and decline to 10% frequency. The transition between clusters occurs quickly, taking an average of 1.8 years. @@ -292,14 +294,13 @@Selective pressures can be examined by comparing which mutations fix, i.e. are incorporated into -the progenitor trunk lineage, and which mutations are lost, i.e. incorporated into side branches -bound for extinction. This approach has shown that, in influenza A (H3N2), natural selection -promotes mutations to epitope sites in the HA1 region [[13, 14]. By examining antigenic -mutations, we find a corresponding effect in simulated evolutionary trajectories (Table 1). -Trunk mutations tend to push antigenic phenotype forward along the line of primary -antigenic variation. Additionally, we find that trunk mutations occur at strikingly +href="#XWolf06">14]. By +examining antigenic mutations, we find a corresponding effect in simulated evolutionary +trajectories (Table 1). Additionally, we find that trunk mutations occur at strikingly regular intervals, with less variation of waiting times than expected under a simple random process (Figure 4). There is a relative scarcity of mutation events occurring in intervals under 1 year and a relative excess of a mutation events occurring in 2–3 year @@ -408,16 +409,16 @@
It would seem likely for one viral lineage to move in one antigenic direction, while another lineage -moves tangentially, eventually resulting in two non-interacting viral lineages. Instead, we find -that movement in a single antigenic direction is favored, resulting in most replicate simulations -showing low standing diversity (Figure 1). The origins of this pattern can be seen in the -interaction between virus evolution and host immunity (Figure 6). As the virus population +
It might seem reasonable for one viral lineage to move in one antigenic direction, while another +lineage moves tangentially, eventually resulting in two non-interacting viral lineages. Instead, we +find that movement in a single antigenic direction is favored, resulting in most replicate +simulations showing low standing diversity (Figure 1). The origins of this pattern can be seen in +the interaction between virus evolution and host immunity (Figure 6). As the virus population evolves forward it leaves a wake of immunity in the host population, and evolution away from this immunity results in the canalization of the antigenic phenotype; mutations that continue along the line of primary antigenic variation will show a transmission advantage compared to more @@ -611,9 +612,9 @@
To consider to what extent these results were contingent on the dimensionality of the underlying antigenic model, we further implemented our model in a 10-dimensional antigenic space. Here, mutations occur as 10-spheres, but the distance moved by a @@ -622,7 +623,7 @@