Simulation data and code

Please see README.txt for full description of files

Simulation code and data

Please see README file for full description

MOESM1 of Sickle haemoglobin, haemoglobin C and malaria mortality feedbacks

Additional file 1. Supplementary Methods and Supplementary Tables

Methods.

<p>(<b>A</b>) Virus genealogy is tracked at the inter-host level. The genealogy is periodically sampled and the resulting tree is used for analysis. <b>(B)</b> Hosts acquire immunity to viral epitopes following infection. Fully naïve hosts are always infected following contact at rate β. The risk of reinfection is based on the similarity to previously encountered strains, as measured through the number of previously encountered epitopes: and is at most 100%. Where <i>f</i> is the fraction of previously encountered epitopes and σ is the strength of crossimmunity. Lower <i>σ</i> values correspond to weaker competition between strains. A form of generalized immunity is attained for σ>0.8 in the five epitope case, relating to a reduced risk of reinfection following previous exposure to any strain. <b>(C)</b> Mean pairwise genealogical diversity π is measured by averaging the pairwise distance in years between random contemporaneous samples on the genealogical tree. <b>(D)</b> The MK related index is calculated as the ratio of the antigenic mutation rate on the trunk of the genealogy (red) versus the antigenic mutation rate on the sidebranches (black). The trunk of the genealogy was determined by tracing back viral lineages that survived until the end of the simulation and excluding the last 5 years. Antigenic changes are represented by color changes on tree branches (top-tree). The rate of antigenic change on the sidebranches is calculated as the number of antigenic changes on the sidebranches divided by the total length of the side branches in years. The rate of antigenic change on the trunk is calculated as the number of antigenic changes on the trunk divided by the total length of the trunk in years.</p

Changes in the proportions of hosts that are infectious with different strains and the related phylogenetic behavior with increasing mutation rate.

<p>Phylogenetic trees are based on samples of directly measured virus genealogy in the simulation, and only the last 40 years are visualized in the figure (for the complete genealogy over the whole time period see ). Diversity π is calculated as the mean distance, measured in years, for the coalescence of random pairs of contemporaneous samples in a tree. The MK related index (MKR) is calculated as the ratio of the antigenic mutation rate on the trunk (fixed) versus the antigenic mutation rate on the sidebranches. <b>(A)</b> Model with no mutation, a single antigenic type persists under neutral evolution. When there are no antigenic mutations a genealogical tree which follows neutral viral evolution exists. Genetic diversity for this tree relates to population dynamics only – to incidence and the prevalence. <b>(B)</b> Model with low mutation rate of ξ = 7.5×10⁻⁶ antigenic-mutations per day. Successive strain replacement with higher epidemic peaks is observed. Rare antigenic mutations are advantageous and are more likely to fix and have viable offsprings, consequently lowering genetic diversity. <b>(C)</b> The introduction of a higher mutation rate ξ = 7.5×10⁻⁵ leads to antigenic and genetic divergence. Dynamics are ruled by endemic or cyclic behavior of discordant antigenic strains. Mutations are more likely to be deleterious, facing competition from the two prevalent strains. Phylogenetic patterns include two deep branches representing each strain and a low rate of coalescence between strains. <b>(D)</b> For a mutation rate ξ = 7.5×10⁻⁴ epidemiological behavior resembles the evolution free framework (<a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003104#ppat-1003104-g003" target="_blank">Figure 3</a>). Phylogenetic patterns exhibit high genetic diversity and weak negative selection pressure. <b>(E)</b> Loss of strain structure due to high mutation rate ξ = 7.5×10⁻³. At this high mutation rate the antigenic traits are no longer heritable and each linage displays a constantly varying antigenic phenotype. No selection forces are measured and genetic diversity is expected to be determined by random coalescence. <b>(F)</b> Summary statistics and typical trees for varying mutation rates and fixed crossimmunity (filled area within rectangles indicates 1σ confidence interval for 5 repeated runs). Simulation parameters are the same as those described in <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003104#ppat-1003104-g003" target="_blank">Figure 3</a>, but include the possible extinction of strains, and mutations to individual epitopes at a specified rate ξ (see <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003104#s4" target="_blank">methods</a> for full description of epidemiological parameters).</p

Mutation-competition simulation parameters.

<p>Mutation-competition simulation parameters.</p

H3N2 simulation parameters.

<p>H3N2 simulation parameters.</p

Changes in the proportions of hosts that are infectious with different strains within a 2 variants per epitope, 5 epitope system in an “evolutionary free” framework: for all of the possible 32 strains the existence of at least one carrier was assured and no antigenic mutations were introduced.

<p>The superimposed time series were smoothed and ordered back to front by peak prevalence, maintaining the least prevalent strain in the front. The 3th highest peaking strain was outlined as an example. Single strain dominance was calculated based on the quantity ε from <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003104#ppat.1003104-Recker1" target="_blank">[22]</a>. Major peaks of incidence are generally associated with one or two dominant antigenic-phenotypes with ε = 0.36±0.07 (mean ± standard-deviation across 5 simulations) and a myriad of lower prevalence ones. Antigenic-phenotypes reemerge with alternating frequency. This simulation includes a single homogeneously mixed host population of 40M hosts, contact rate β = 0.6 and a 4 day recovery rate. Each epitope unencountered by the host contributes to a 17.5% increase in the risk of infection with a different strain (see <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003104#s4" target="_blank">methods</a> for full description of epidemiological parameters).</p

Changes in genetic diversity and the McDonald-Kreitman related index (MKR) for varying strengths of strain competition and antigenic mutation rates.

<p><b>(A)</b> Mean pairwise genetic diversity π is measured as the mean distance, measured in years, for the coalescence of random pairs of contemporaneous samples in a tree. Diversity measurement is capped by twice the simulation run length which amounts to 240 years. <b>(B)</b> The MKR is measured as the ratio between the trunk antigenic mutation rate (fixed) and the sidebranches antigenic mutation rate. Evidence of positive selection is observed when the MKR index is significantly above one, and negative selection when it is significantly below one. Areas of strong positive selection are associated with lower genetic diversity as a small subset of the population contributes to long term viral evolution. Strong negative selection is associated with disruptive selection maintained by existing strains. <b>(C)</b> Diversity for varying strengths and directions of selection as measured by the MKR index. Diversity decreases with stronger positive selection <i>ρ</i> = −0.85 (Pearson's correlation right of dotted line), and increases for stronger negative selection <i>ρ</i> = −0.28. The harmonic mean of the prevalence is also strongly correlated with genetic diversity <i>ρ</i> = 0.76 (heat map). <b>(D)</b> Typical trees for varying strengths of strain competition and antigenic mutation rate. Effective competition combined with a limited availability of antigenic mutations results in narrower trees with lower pairwise diversity. This figure was parameterized to use R0 = 3 and a population size of 50M to limit stochastic extinctions for a large parameter range (see <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003104#s4" target="_blank">methods</a> for full description of epidemiological parameters).</p

Phylogenetic tree reconstruction of H3 depicting major antigenic clusters and including the associated pairwise diversity.

<p>Phylogenetic tree with highest posterior likelihood was reconstructed using 377 representative sequences sampled between 1968–2009. Colors represent estimated antigenic clusters (Hong-Kong 1968 – Perth 2009). Approximately half of the samples include an established cluster annotation <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003104#ppat.1003104-Smith1" target="_blank">[18]</a> and three additional clusters relating to: California 2004, Brisbane 2007, and Perth 2009. Additional sequences were sampled uniformly overtime on a bi-annual scale. Phylogenetic tree was reconstructed using Bayesian MCMC analysis <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003104#ppat.1003104-Drummond1" target="_blank">[58]</a>, <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003104#ppat.1003104-Lemey1" target="_blank">[59]</a> and includes state reconstruction for unannotated sequences and ancestral sequences. Diversity skyline was calculated for the same representative tree. Branches with colors differing from their main neighboring cluster represent uncertainty in the reconstruction, rather than actual cluster changes.</p