Robust, Universal Tree Balance Indices

Balance indices that quantify the symmetry of branching events and the compactness of trees are widely used to compare evolutionary processes or tree-generating algorithms. Yet existing indices have important shortcomings, including that they are unsuited to the tree types commonly used to describe the evolution of tumours, microbial populations, and cell lines. The contributions of this article are twofold. First, we define a new class of robust, universal tree balance indices. These indices take a form similar to Colless’ index but account for node sizes, are defined for trees with any degree distribution, and enable more meaningful comparison of trees with different numbers of leaves. Second, we show that for bifurcating and all other full m-ary cladograms (in which every internal node has the same out-degree), one such Colless-like index is equivalent to the normalised reciprocal of Sackin’s index. Hence we both unify and generalise the two most popular existing tree balance indices. Our indices are intrinsically normalised and can be computed in linear time. We conclude that these more widely applicable indices have potential to supersede those in current use.

TREE IMAGE OF SIBERIA: LARCH

The dendroimage image of Siberia is considered in the context of geopoetics and ethnodendrology. For the first time the proposed analysis systematizes the motives associated with the image of larch, one of the main trees in the region. The research materials are scientific works on ethnography and folklore studies, Russian and Russian-language fiction about Siberia written in the XIX-XX centuries. The name of the tree reflects its dual status: coniferous and deciduous simultaneously. The “gender” of the larch is also indeterminate: male / female. The larch has an «intermediate» position in the system of the most important dendroimages of the Siberian text: between cedar and birch. It can be associated with universal tree mythologemes (World Tree, Tree of Life and Death, family tree, etc.), but it most clearly embodies the basic concept of Siberia as a space of violence, hard labor, exile, concentration camps.

Evolution of the PRD1-adenovirus lineage: a viral tree of life incongruent with the cellular universal tree of life

Double-stranded DNA viruses of the PRD1-adenovirus lineage are characterized by homologous major capsid proteins containing one or two β-barrel domains known as the jelly roll folds. Most of them also share homologous packaging ATPases of the FtsK/HerA superfamily P-loop ATPases. Remarkably, members of this lineage infect hosts from the three domains of life, suggesting that viruses from this lineage could be very ancient and share a common ancestor. Here we analyzed the evolutionary history of these cosmopolitan viruses by inferring phylogenies based on single or concatenated genes. These viruses can be divided into two supergroups infecting either eukaryotes or prokaryotes. The latter can be further divided into two groups of bacterioviruses and one group of archaeoviruses. This viral tree is thus incongruent with the cellular tree of life in which Archaea are closer to Eukarya and more divergent from Bacteria. We discuss various evolutionary scenarios that could explain this paradox.