Manon, Christopher AllenWe study presentations for subalgebras of invariants of the coordinate algebras of binary symmetric models of phylogenetic trees studied by Buczynska and Wisniewski. These algebras arise as toric degenerations of projective coordinate rings of weight varieties of the Grassmannian of two planes associated to the Pl\"ucker embedding, and as toric degenerations of rings of invariants of Cox-Nagata rings.en-USDissertationMathematicsModuliPhylogeneticsPolytopeToric Variety