Phlyogenetic Algebraic Geometry Overview:
Algorithms for phylogenetic reconstruction are a fundamental tool of biomedical research. Accurate and easily computable phylogenies allow researchers to make informed decisions based on the genetic relationships among taxa. This allows for the classification of long understood organisms, and for improved understanding of recently discovered or rapidly evolving organisms. All phylogenetic reconstructions rely on the choice of an evolutionary model and an algorithm for converting observable data to a phylogenetic tree.
Invariants are relationships which frequencies of observed data should satisfy if they evolved under a given tree and model of evolution. Invariant based reconstruction was originally found to be less effective at reconstruction than more traditional methods. These shortcomings were to be expected given that initial efforts in this area did not use all possible phylogenetic invariants. Recent work by algebraic geometers has led to the construction of complete lists of phylogenetic invariants for certain models of evolution. On four taxa data reconstruction using a complete list of invariants outperformed many traditional methods.
Development of Invariant Based Reconstruction Algorithms:
The goal is to develop accurate phylogenetic reconstruction algorithms based on invariants which can be directly applied to phylogenetic reconstructions involving a large number of taxa. These algorithms should compete with and improve upon the traditional reconstruction algorithms such as neighbor-joining or maximum likelihood analysis.
Invariant Based Cophylogeny:
Phylogenetic invariants offer flexibility in that they may be trained to handle complex situations with which traditional algorithms have difficulty. This flexibility allows the development of invariant based phylogenetic reconstruction algorithms in the setting of cophylogeny where the evolutionary trees for both a host and a parasite are constructed simultaneously.