Algebraic Geometry of Phylogenetic Models
Phylogenetic statistical models can be used to determine evolutionary relationships between species. These models have the structure of algebraic varieties and understanding their geometry is important for proving many of their properties. For various biological reasons, phylogenetic mixture models are often a better model for species evolution. The variety of probability distributions associated to an r-tree mixture model is in general a join variety. In this talk, we examine some of the algebraic geometry underlying phylogenetic mixture models. In particular, we will show some computational tools for determining their generating sets.