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New figure: sensitivity of viral diversity to mutation parameters.

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1 parent 91136b3 commit cd4dd125ca1e4f95cc3db033c969abdeac6c0ff6 @trvrb committed Mar 4, 2012
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  1. +7 −7 canal.bbl
  2. +1 −1 canal.css
  3. BIN canal.pdf
  4. +16 −5 canal.tex
  5. BIN figures/param.png
  6. +223 −188 index.html
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@@ -66,13 +66,6 @@ Smith DJ, Lapedes AS, de~Jong JC, Bestebroer TM, Rimmelzwaan GF, et~al. (2004)
\newblock Science 305: 371--376.
\bibAnnoteFile{Smith04}
-\bibitem{Koelle11}
-Koelle K, Ratmann O, Rasmussen D, Pasour V, Mattingly J (2011) A dimensionless
- number for understanding the evolutionary dynamics of antigenically variable
- rna viruses.
-\newblock Proc R Soc Lond B Biol Sci Advance access.
-\bibAnnoteFile{Koelle11}
-
\bibitem{Monto93}
Monto A, Sullivan K (1993) {Acute respiratory illness in the community.
Frequency of illness and the agents involved.}
@@ -128,6 +121,13 @@ Adams B, McHardy A (2011) The impact of seasonal and year-round transmission
\newblock Proc R Soc B 278: 2249--2256.
\bibAnnoteFile{Adams11}
+\bibitem{Koelle11}
+Koelle K, Ratmann O, Rasmussen D, Pasour V, Mattingly J (2011) A dimensionless
+ number for understanding the evolutionary dynamics of antigenically variable
+ rna viruses.
+\newblock Proc R Soc Lond B Biol Sci Advance access.
+\bibAnnoteFile{Koelle11}
+
\bibitem{Finkelman07}
Finkelman B, Viboud C, Koelle K, Ferrari M, Bharti N, et~al. (2007) {Global
patterns in seasonal activity of influenza A/H3N2, A/H1N1, and B from 1997 to
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@@ -1,4 +1,4 @@
-/* canal.css from canal.tex (TeX4ht, 2012-02-28 16:37:00) */
+/* canal.css from canal.tex (TeX4ht, 2012-03-04 21:24:00) */
body {
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@@ -111,9 +111,19 @@ \section*{Results and Discussion}
\subsection*{Antigenic evolution and genealogical patterns}
-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. However, in 20 out of the 100 replicate simulations, we observed a major bifurcation of antigenic phenotype and a consequent increase in incidence and genealogical diversity. These simulations were removed from the analysis. Similar to Koelle et al. \cite{Koelle11}, we assume that although the historical evolution of H3N2 influenza followed the path of a single lineage, it could have included a major bifurcation. Here, we focus on one representative simulation out of the 80 low-diversity outcomes.
+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~\ref{param}). 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). We conditioned the following analysis on these 80 simulations, compiling summary statistics across this pool and presenting a detailed analysis of a single representive simulation.
-The virus persists over the course of the 40-year simulation, infecting a significant fraction of the host population through annual winter epidemics in temperate regions and through less periodic epidemics in the tropics (Figure~\ref{evol}A). 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 \cite{Monto93,Koelle09}. 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~\ref{evol}B). 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~\ref{evol}D). 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 \cite{Smith04}. 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~\ref{phenotypes}A). 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.
+%%% Figure 1: param %%%
+\begin{figure}[tb]
+ \centering
+ \makebox[\textwidth]{
+ \includegraphics{figures/param}
+ }
+ \caption{\textbf{Genealogical diversity at the end of 40-years across 100 simulations for varying mutational parameters.} Genealogical diversity varies with (A) mutation rate and with (B) standard deviation of mutation effect. Points represent individual simulation outcomes and gray bars represent medians and interquartile ranges across replicate simulations. Outcomes with diversity greater than 9 years are shown in blue and outcomes with diversity less than 9 years are shown in black. Counts of these two classes are shown in blue and black, respectively. Genealogical diversity is measured in years, mutation rate is measured in mutations per infection per day and standard deviation of mutation effect is measured in antigenic units.}
+ \label{param}
+\end{figure}
+
+The model exhibits annual winter epidemics in temperate regions and less periodic epidemics in the tropics (Figure~\ref{evol}A). 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 \cite{Monto93,Koelle09}. 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~\ref{evol}B). 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~\ref{evol}D). 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 \cite{Smith04}. 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~\ref{phenotypes}A). 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.
%%% Figure 1: evol %%%
\begin{figure}[tb]
@@ -182,9 +192,10 @@ \subsection*{Correspondence between model and data}
Although multiple epidemiological/evolutionary mechanisms have been proposed to explain the restricted genetic diversity and rapid population turnover of influenza A (H3N2) \cite{Ferguson03,Tria05,Koelle06,Recker07}, our results show that a simple model coupling antigenic and genealogical evolution exhibits broad explanatory power. We find a strong correspondence between the antigenic and genealogical patterns generated by our model (Figure~\ref{evol}) and patterns of genetic and antigenic evolution exhibited by influenza A (H3N2) \cite{Fitch97,Smith04}. Our model simultaneously captures seasonal attack rates, the rate and pattern of antigenic drift, genealogical diversity and geographic migration patterns.
-Our model suggests that punctuated antigenic evolution need only be explained by a lack of mutational opportunity and predicts that more detailed classification of influenza strains will support a relatively small number of predominant phenotypes. Rather than each influenza strain possessing a unique antigenic location, many strains group together as shared antigenic phenotypes (Figure~\ref{evol}B). We suggest that a large proportion of intra-cluster variation in the observed antigenic map is due to experimental noise, rather than each strain possessing a unique antigenic location. The relationship between Figure \ref{evol}B and Figure \ref{evol}D illustrates this effect, where a large number of antigenic locations emerge from a comparatively small number of unique antigenic phenotypes. Additionally, our model accurately predicts the contrasting dynamics of other types/subtypes of influenza. We find that lowering mutation size/effect or lowering intrinsic $R_0$ results in decreased incidence, slower antigenic movement and greater genealogical diversity, all distinguishing characteristics of H1N1 influenza and influenza B (Figure~\ref{h1n1}).
+Our model suggests that punctuated antigenic evolution need only be explained by a lack of mutational opportunity and predicts that more detailed classification of influenza strains will support a relatively small number of predominant phenotypes. Rather than each influenza strain possessing a unique antigenic location, many strains group together with shared antigenic phenotypes (Figure~\ref{evol}B). We suggest that a large proportion of intra-cluster variation in the observed antigenic map is due to experimental noise, rather than each strain possessing a unique antigenic location. The relationship between Figure \ref{evol}B and Figure \ref{evol}D illustrates this effect, where a large number of antigenic locations emerge from a comparatively small number of unique antigenic phenotypes. Additionally, our model accurately predicts the contrasting dynamics of other types/subtypes of influenza. We find that lowering mutation size/effect or lowering intrinsic $R_0$ results in decreased incidence, slower antigenic movement and greater genealogical diversity, all distinguishing characteristics of H1N1 influenza and influenza B (Figure~\ref{h1n1}).
+
+The historical record of influenza evolution suggests that bifurcation of viral lineages is rare, but possible. We have observed no bifurcations in H1N1 influenza from 1918 to 1957 and again from 1977 to 2010, no bifurcations in H2N2 influenza from 1957 to 1968 and no bifurcations of H3N2 influenza from 1968 to 2010. We have observed one bifurcation in influenza B from 1980 to 2010. Thus, ignoring differences between influenza types and subtypes, we have very roughly observed a rate of one major bifurcation in 155 years of evolution. In our model, in 20 out of 100 replicate simulations, we observe a deep bifurcation in the viral genealogy, which translates to observing one deep bifurcation in 200 years of evolution. Thus, we suggest that the 20 of 100 simulations where deep branching occurs are not necessarily evidence of poor model fit. Similar to Koelle et al. \cite{Koelle11}, we assume that although the historical evolution of H3N2 influenza followed the path of a single lineage, it could have included a major bifurcation.
-The historical record of influenza evolution suggests that bifurcation of viral lineages is rare, but possible. We have observed no bifurcations in H1N1 influenza from 1918 to 1957 and again from 1977 to 2010, no bifurcations in H2N2 influenza from 1957 to 1968 and no bifurcations of H3N2 influenza from 1968 to 2010. We have observed one bifurcation in influenza B from 1980 to 2010. Thus, ignoring differences between influenza types and subtypes, we have very roughly observed a rate of one major bifurcation in 155 years of evolution. In our model, in 20 out of 100 replicate simulations, we observe a deep bifurcation in the viral genealogy, which translates to observing one deep bifurcation in 200 years of evolution. Thus, we suggest that the 20 of 100 simulations where deep branching occurs are not necessarily evidence of poor model fit.
In our model, when antigenic phenotype remains static, there may be multiple consecutive seasons without appreciable incidence (Figure~\ref{evol}A), a pattern apparently absent from H3N2 influenza \cite{Finkelman07}. Additionally, we observe antigenic trajectories that are more linear and deterministic than the highly clustered trajectory observed by Smith et al.\ \cite{Smith04}. We suggest that any model exhibiting punctuated evolution broadly consistent with the punctuated change seen in the experimental antigenic map will show similar patterns of incidence. We can `fix' the incidence patterns, but at the cost of too smooth an antigenic map (Figure~\ref{mutationcomp}). Evolutionary patterns of the neuraminidase (NA) protein may provide an explanation. Epitopes in the HA and NA proteins are jointly responsible for determining antigenicity \cite{Nelson07NatRevGenet}, and it is now clear that levels of adaptive evolution are similar between HA and NA \cite{Bhatt11}. Thus, changes in NA may be driving incidence patterns as well, resulting in an observed timeseries of incidence partially divorced from the antigenic map of HA. Incorporating antigenic evolution of NA could thus yield a rougher antigenic map for HA, more closely matching experimental results, while simultaneously yielding smoother year-to-year incidence patterns.
@@ -208,7 +219,7 @@ \subsection*{Linear antigenic movement}
\subsection*{Winding back the tape}
-The 40-year simulation of influenza dynamics shows broad correspondence with observed patterns. However, year-to-year details are not captured, e.g.\ years that undergo antigenic transitions in the 40-year simulation do not match up with observed years of antigenic transitions. Over long time spans, this level of detailed correspondence seems impossible to achieve in this sort of stochastic system, where evolution is often driven by chance mutations of large antigenic effect. However, correspondence in the shorter term may be possible. To test this, we examined repeatability in replicate simulations, showing what happens when we ``wind back the tape'' \cite{GouldWonderfulLife} on the evolution of the virus. We ran 100 replicate simulations, each starting from the endpoint of the representative 40-year simulation shown in Figure \ref{evol}. The starting point for these replicate simulations was the exact end state of the 40-year simulation, including the frequencies of every virus strain and the entire host immune profile. These replicate simulations were run for an additional 6 years, and all evolutionary and epidemiological parameters were identical to the initial 40-year simulation.
+The 40-year simulation of influenza dynamics shows broad correspondence with observed patterns. However, year-to-year details are not captured, e.g.\ years that undergo antigenic transitions in the 40-year simulation do not match up with observed years of antigenic transitions. Over long time spans, year-to-year correspondence seems impossible to achieve in this sort of stochastic system, where evolution is often driven by chance mutations of large antigenic effect. However, correspondence in the shorter term may be possible. To test this, we examined repeatability in replicate simulations, showing what happens when we ``wind back the tape'' \cite{GouldWonderfulLife} on the evolution of the virus. We ran 100 replicate simulations, each starting from the endpoint of the representative 40-year simulation shown in Figure \ref{evol}. The starting point for these replicate simulations was the exact end state of the 40-year simulation, including the frequencies of every virus strain and the entire host immune profile. These replicate simulations were run for an additional 6 years, and all evolutionary and epidemiological parameters were identical to the initial 40-year simulation.
Initially, we find a great detail of repeatability; during the first year of evolution, every replicate virus population undergoes a similar antigenic transition (Figure~\ref{replicateevol}), resulting in a repeatable peak in northern hemisphere incidence (Figure~\ref{replicateinc}). After three years, repeatability has mostly disappeared, with antigenic phenotype and incidence appearing highly variable across replicates (Figure~\ref{replicateevol}, Figure~\ref{replicateinc}). The 1--2 year timescale of repeatability can be explained by the presence of standing antigenic variation. In the initial virus population, there are several novel antigenic variants present at low frequency (Figure~\ref{immunity}), one of which, without fail, comes to predominate the virus population.
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