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A phylogenetic variety is an algebraic variety parameterized by a statisticalmodel of the evolution of biological sequences along a tree. Understanding thisvariety is an important problem in the area of algebraic statistics withapplications in phylogeny reconstruction. In the broader area of algebrastatistics, there have been important theoretical advances in computing certaininvariants associated to algebraic varieties arising in applications. Beyondthe dimension and degree of a variety, one is interested in computing otheralgebraic degrees, such as the maximum likelihood degree and the Euclideandistance degree. Despite these efforts, the current literature lacks explicitcomputations of these invariants for the particular case of phylogeneticvarieties. In our work, we fill this gap by computing these invariants forphylogenetic varieties arising from the simplest group-based models ofnucleotide substitution Cavender-Farris-Neyman model, Jukes-Cantor model,Kimura 2-parameter model, and the Kimura 3-parameter model on smallphylogenetic trees with at most 5 leaves.

Computing algebraic degrees of phylogenetic varieties