Figure 1.
HIV Inter-Host and Human Flu H3N2 Phylogeny Trees.
Inferred phylogeny of the HIV-1, subtype B virus at a geographical global scale (Env gene, region C2V5) (Left), and the Human Influenza A Virus (haemagglutinin gene HA), subtype H3N2, at the same scale (Right). Details on the inference method used are reported in the main text. In each phylogenetic tree, we use a color code to visually identify viruses isolated in the same temporal interval. For example, we colored in red all the branches of leaves isolated between 2000 and 2005 for the HIV-1 virus (left), while, for instance, blue is used in the phylogenetic tree of Human Flu (right) to mark all the leaves isolated in the year 2001. In the phylogenetic tree of the Human Flu, leaves isolated in the same temporal interval cluster in the same clade and there is just one evolutionary lineage, the so called “Trunk” (marked in grey), connecting all of them. These patterns are not observed in the phylogenetic tree of the HIV-1 virus. The tree of the Human-Flu H3N2, moreover, is visibly much more imbalanced with the respect to the HIV-1 one. Details on the definition of the imbalance level and its quantification are in the main text.
Table 1.
Properties of the data-set used for the inference of the phylogenetic trees.
Figure 2.
Quantification of tree shape imbalance with the metrics of Table 2.
In this graph we show the values of the imbalance metrics defined in Table 2 for all the six inferred trees of RNA viruses: HIV Inter-Host, Measles Virus, Swine Flu H1N1, Avian Flu H5N1, HIV Intra-Host and Human Flu H3N2. Phylogenies in the x-axis have been ordered according to increasing values of the expected degree of imbalance (see main text for details).
Table 2.
Imbalance Metrics.
Figure 3.
New comparison strategy results.
Top line: Mean topological distance from root to leaves (), mean depth (
) and asymmetry metric
for all the inferred phylogenetic trees we considered, computed with the methodology discussed in the main text. Vertical dashed lines mark sizes
. In the bottom lines we report the rescaled values for all the curves, where we compare the asymptotic imbalance level of the phylogenies isolating the linear trend of the curves for
and
, revealing in this way the asymptotic behavior with the functional form
. Solid lines are rescaled values of
,
and
while dashed lines are for the relative extrapolations. In the inset we report the numerical values of
for each phylogeny.
Figure 4.
Relative behavior of ,
and
for subtrees of different time intervals.
We focus here on the phylogenies of three RNA virus phylogenetic trees (Human-Flu H3N2 (top), HIV Inter-Host (middle), Measles virus (bottom),) considering the imbalance properties of their sub-trees, extracted with a temporal criterion. Each sub-tree is associated to a temporal interval (reported in the legend of the pictures), reflecting the years of isolation of its leaves. For example, in the case of Human Flu H3N2, the curve refers to the sub-tree enclosing all the strains, in our data-set, isolated between 1973 and 2001. For each sub-tree in this set we show the mean topological distance (
), the mean depth (
) and the asymmetry
computed with the methodology presented in the main text. Asymptotic extrapolations of these curves are reported in the File S1.