  A phylogenetic variety is an algebraic variety parameterized by a statistical
model of the evolution of biological sequences along a tree. Understanding this
variety is an important problem in the area of algebraic statistics with
applications in phylogeny reconstruction. In the broader area of algebra
statistics, there have been important theoretical advances in computing certain
invariants associated to algebraic varieties arising in applications. Beyond
the dimension and degree of a variety, one is interested in computing other
algebraic degrees, such as the maximum likelihood degree and the Euclidean
distance degree. Despite these efforts, the current literature lacks explicit
computations of these invariants for the particular case of phylogenetic
varieties. In our work, we fill this gap by computing these invariants for
phylogenetic varieties arising from the simplest group-based models of
nucleotide substitution Cavender-Farris-Neyman model, Jukes-Cantor model,
Kimura 2-parameter model, and the Kimura 3-parameter model on small
phylogenetic trees with at most 5 leaves.
