Figure 1.
Global migration patterns of influenza A (H3N2) estimated from sequence data between 2002–2008.
Arrows represent movement of influenza from one region to another, with arrow width proportional to the rate of migration of a single lineage of influenza. Arrows representing migration rates of less than 0.1 migration events per lineage per year were removed from the figure for clarity. Circle areas are proportional to a region's eigenvector centrality, a measure of the importance of a node in the migration network. The eigenvector centrality is equal to the expected stationary distribution when tracing the history of a lineage backwards in time [30].
Table 1.
Means and 95% confidence intervals across resampled replicates for the total rates of immigration from all other regions and emigration to all other regions for each region measured in terms of migration events per lineage per year.
Figure 2.
Genealogy of 2165 influenza A (H3N2) viruses sampled from 1998 to 2009.
Each point represents a sampled virus sequence, and the color of the point shows the location where it was sampled. Samples are explicitly dated on the -axis. Tracing a vertical line gives a contemporaneous cross-section of virus isolates. The genealogy is sorted so that lineages that leave more descendants are placed higher on the
-axis than other, less successful lineages. This sorting places the trunk along a rough diagonal, and it places lineages that are more genetically similar to the trunk higher on the
-axis than lineages that are farther away from the trunk. The tree shown is the highest posterior tree generated by the Markov chain Monte Carlo (MCMC) procedure implemented in the software program Migrate v3.0.8 [14], [20].
Figure 3.
Estimation of the geographic location of the trunk of the influenza tree over time.
(A) Probability that the trunk of the influenza tree exists in a particular region at a particular point in time. Trunks were obtained from sampled genealogies generated from the spatially and temporally tagged sequences. At each point in time, some sampled genealogies will have one region as the trunk, while other sampled genealogies will have a different region as the trunk. This plot encapsulates this uncertainty. At each point in time, the width of region represents the mean proportion from 0 to 100% of sampled genealogies bearing this region as trunk. At times when one color dominates the -axis, we can be fairly certain that the trunk of the genealogy is in this location. Other times, when there is a mix of colors, we are not so certain. (B) Distance to the trunk, measured in terms of years, for each sampled influenza sequence. Here, points represent individual tips of the influenza tree colored as in Figure 2. The height of each point on the
-axis shows the mean distance to the trunk across the full range of estimated genealogies. Bars identify the closest sample to the trunk within a 4 month window of time. Bars are colored according to regions of these samples.
Table 2.
Means and 95% credible intervals over sampled genealogies for the location of the genealogy trunk between the years of 1998 and 2007.
Figure 4.
Analysis of epidemiological simulations for a source-sink model (i) and an equal contacts model (ii) of spatial structure.
(A) Histogram of sampled sequence dates. Five hundred sequences were sampled randomly from each deme of the simulated virus population over a 10 year time period in proportion to abundance. The seasonality of the North and the South are reflected in the temporal sampling patterns. (B) Inferred genealogy from sampled sequences. Each point represents a sampled virus sequence, and the color of the point shows the location where it was sampled. The genealogy shown represents the highest posterior tree. (C) Inferred location of the trunk of the genealogy over time. Trunks were obtained from a posterior sample of genealogies by taking a random lineage present between years 9 and 10 and tracing its ancestry backward in time. Uncertainty of the trunk location is captured by this methodology. In times when one color dominates the -axis, we can be fairly certain that the trunk of the genealogy is in this location. Other times, when there is a mix of colors, we are not so certain.
Table 3.
Mean estimates and 95% credible intervals for effective population size , rate of migration
and trunk proportion for each region in simulated data sets based on 500 samples from each deme over a 10 year period.