Topology of viral evolution

Abstract

The tree structure is currently the accepted paradigm to represent evolutionary relationships between organisms, species or other taxa. However, horizontal, or reticulate, genomic exchanges are pervasive in nature and confound characterization of phylogenetic trees. Drawing from algebraic topology, we present a unique evolutionary framework that comprehensively captures both clonal and reticulate evolution. We show that whereas clonal evolution can be summarized as a tree, reticulate evolution exhibits nontrivial topology of dimension greater than zero. Our method effectively characterizes clonal evolution, reassortment, and recombination in RNA viruses. Beyond detecting reticulate evolution, we succinctly recapitulate the history of complex genetic exchanges involving more than two parental strains, such as the triple reassortment of H7N9 avian influenza and the formation of circulating HIV-1 recombinants. In addition, we identify recurrent, large-scale patterns of reticulate evolution, including frequent PB2-PB1-PA-NP cosegregation during avian influenza reassortment. Finally, we bound the rate of reticulate events (i.e., 20 reassortments per year in avian influenza). Our method provides an evolutionary perspective that not only captures reticulate events precluding phylogeny, but also indicates the evolutionary scales where phylogenetic inference could be accurate. n On the Origin of the Species in 1859, Darwin first proposed the phylogenetic tree as a structure to describe the evolution of phenotypic attributes. Since then, the advancement of modern sequencing has spurred development of a number of phylogenetic inference methods (1, 2). The tree structure effectively models vertical or clonal evolution, mediated by random mutations over multiple generations (Fig. 1A). Phylogenetic trees, however, cannot capture horizontal, or reticulate, events, which occur when distinct clades merge together to form a new hybrid lineage ( Fig. 1B and SI Appendix, Fig. S1). In nature, horizontal evolution can occur through species hybridization in eukaryotes, lateral gene transfer in bacteria, recombination and reassortment in viruses, viral integration in eukaryotes, and fusion of genomes of symbiotic species (e.g., mitochondria). These horizontal genetic exchanges create incompatibilities that mischaracterize the species tree (3). Doolittle (4) argued that molecular phylogeneticists have failed to identify the "true tree of life" because the history of living organisms cannot be understood as a tree. One may wonder what other mathematical structures beyond phylogeny can capture the richness of evolutionary processes.Current techniques that detect reticulate events can be divided into phylogenetic and nonphylogenetic methodologies. Phylogenetic methods detect incongruence in the tree structure of different segments (5-8). Nonphylogenetic methods probe for homoplasies (shared character traits independently arising in different lineages by convergent or parallel evolution) or similar inconsistencies in sequence alignment (9-...

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“…Since v is a reticulation in P 1 , it is stable only on ℓ 1 is a subdivision of T in N ′′ . Therefore T is displayed in N ′′ .…”

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“…The later study was consistent with patterns found in laboratory-based approaches and employed a combination of phylogeny and population genetics techniques to quantify segment linkage. A novel approach, which examined the underlying topology of phylogenetic trees to infer reassortment events, found frequent linkage between genes of the polymerase complex in avian strains [33 ].…”

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