About this Research Topic
The field of phylogenetics has been undergoing a gradual paradigm shift away from the notion of the strictly bifurcating, completely resolved species trees to a recognition that species are containers of allelic variation for each gene. It is very well established that differences in lineage sorting due to genetic drift lead to differences in phylogenetic tree topologies. Gene flow in ancestral populations and independent lineage sorting of polymorphisms is fully expected to generate topological conflicts between gene trees in reticulating (e.g., sexually recombining) species. Both extant and ancestral species could exhibit this phenomenon, so ancestral species should not be regarded as node points in a fully resolved bifurcating tree, but instead can be thought of as spatiotemporal clouds of individual genotypes with all their inherent allelism. Thus, a central issue in systematic biology is the reconstruction of populations and species from numerous gene trees with varying levels of discordance. However, the increasing complexity of research in phylogenetics requires new concepts and computational tools from the mathematical and statistical sciences. Several mathematical fields not classically considered part of applied mathematics have contributed in recent years to the study of a variety of biological problems. One such field is algebraic geometry, in particular its computational aspects relying on tools from symbolic computation.
In this Research Topic, we focus on applications of algebra and geometry to phylogenetics and phylogenomics to explore new approaches for undertaking comparative genomic and phylogenomic studies much more rapidly and robustly than existing tools allow. This Research Topic includes:
1. polyhedral geometry of a distance-based method for phylogenetic tree reconstruction,
2. study statistics, such as Fréchet means and Fermat Weber points, on a space of phylogenetic trees,
3. developing supervised/unsupervised learning methods on a space of phylogenetic trees,
4. investigating algebraic properties of the parametric space of an evolutionary model for a phylogenetic tree.
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