Network science inspires novel tree shape statistics

Abstract

The shape of phylogenetic trees can be used to gain evolutionary insights. A tree’s shape specifies the connectivity of a tree, while its branch lengths reflect either the time or genetic distance between branching events; well-known measures of tree shape include the Colless and Sackin imbalance, which describe the asymmetry of a tree. In other contexts, network science has become an important paradigm for describing structural features of networks and using them to understand complex systems, ranging from protein interactions to social systems. Network science is thus a potential source of many novel ways to characterize tree shape, as trees are also networks. Here, we tailor tools from network science, including diameter, average path length, and betweenness, closeness, and eigenvector centrality, to summarize phylogenetic tree shapes. We thereby propose tree shape summaries that are complementary to both asymmetry and the frequencies of small configurations. These new statistics can be computed in linear time and scale well to describe the shapes of large trees. We apply these statistics, alongside some conventional tree statistics, to phylogenetic trees from three very different viruses (HIV, dengue fever and measles), from the same virus in different epidemiological scenarios (influenza A and HIV) and from simulation models known to produce trees with different shapes. Using mutual information and supervised learning algorithms, we find that the statistics adapted from network science perform as well as or better than conventional statistics. We describe their distributions and prove some basic results about their extreme values in a tree. We conclude that network science-based tree shape summaries are a promising addition to the toolkit of tree shape features. All our shape summaries, as well as functions to select the most discriminating ones for two sets of trees, are freely available as an R package at http://github.com/Leonardini/treeCentrality.

Deep clustering of bacterial tree images

“…The most challenging clusters to differentiate using shape statistics alone are clusters 6, 7 and 9, which happen to be the three smallest clusters, with shape statistics being able to differentiate each of them from only 3 of the other clusters. This result is in general agreement with the findings in [ 39 , 40 ] which evaluate the power of tree shape statistics in distinguishing between different tree shapes.…”

“…We also compared tree shape statistics and our clustering patterns. For this purpose, we computed a set of tree shape statistics [ 37 , 38 ] for the trees on each cluster. We computed both unnormalized (electronic supplementary material, figure S2) as well as normalized versions ( figure 9 ) of each statistic, with the exception of those that are intrinsically normalized.…”

Phylogenetic identification of influenza virus candidates for seasonal vaccines

“…Phylogenetic trees capture patterns of descent among groups of organisms and should, in principle, capture information about fitness (18,19). The tree's branch lengths reflect either the time or the genetic distance between branching events, while its shape specifies the patterns of relatedness, ancestry, and descent among the organisms (18,20,21). Phylogenetic trees have become essential tools in phylodynamics and infectious disease: They are used to estimate the basic reproduction number (22), parameters of transmission models (23), and aspects of underlying contact networks (24)(25)(26)(27) to predict the short-term growth and fitness of influenza virus trees (18,19,21) and, in densely sampled datasets, even to infer person-to-person transmission events and timing (28)(29)(30)(31).…”

A new universal system of tree shape indices

“…Conservation biologists use phylogenetic diversity values to determine which actions will preserve the most biodiversity (Tucker et al, 2017; Veron et al, 2019). Tree balance indices are used to compare models and to infer parameter values in systematic biology (Mooers and Heard, 1997; Purvis and Agapow, 2002), virology (Chindelevitch et al, 2021; Barzilai and Schrago, 2023), epdiemiology (Leventhal et al, 2012; Colijn and Gardy, 2014), and oncology (Scott et al, 2020; Noble et al, 2022). Computer scientists seek to balance binary trees to make them more efficient as data structures (Albers and Westbrook, 2005).…”