  We find presentations for subalgebras of invariants of the coordinate
algebras of binary symmetric models of phylogenetic trees studied by Buczynska
and Wisniewski in \cite{BW}. These algebras arise as toric degenerations of
rings of global sections of weight varieties of the Grassmanian of two planes
associated to the Pl\"ucker embedding, and as toric degenerations of rings of
invariants of Cox-Nagata rings.
