Phylogenetic tree models: An algebraic view
Elizabeth Allman (August 30, 2011)
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Phylogenetics is the branch of biology concerned with inferring evolutionary relationships between currently extant species. For instance, are humans more closely related to chimpanzees or to gorillas on an evolutionary tree? A typical phylogenetic analysis from molecular data might consist of sampling gene sequences from a number of species, aligning them, and performing a statistical analysis to choose a tree that best displays the evolutionary relationships of taxa.
While phylogenetic analyses are usually undertaken with standard statistical approaches such as Maximum Likelihood or MCMC in a Bayesian framework, these require formulating a probabilistic model of the DNA substitution process on a tree. Because many of these models are naturally given by polynomial parameterizations, by considering the algebraic varieties these maps define, the viewpoint of algebraic geometry can be used to gain theoretical understanding of the limits and advantages of such models.
The talk begins with an introduction to phylogenetics, and then addresses how algebraic techniques are being used to advance the theoretical end of this field. Surprising connections will be made between seemingly disparate areas of mathematics.