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Many of the stochastic models used in inference of phylogenetic trees from biological sequence data have polynomial parameterization maps. The image of such a map-the collection of joint distributions for all parameter choices-forms the model space. Since the parameterization is polynomial, the Zariski closure of the model space is an algebraic variety which is typically much larger than the model space but amenable to study with algebraic methods. Of practical interest, however, is not thedoi:10.1137/120901568 fatcat:ly6u7fqvhzf7xdxv2boruddjpi