We 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.