  Recently there have been several attempts to provide a whole set of
generators of the ideal of the algebraic variety associated to a phylogenetic
tree evolving under an algebraic model. These algebraic varieties have been
proven to be useful in phylogenetics. In this paper we prove that, for
phylogenetic reconstruction purposes, it is enough to consider generators
coming from the edges of the tree, the so-called edge invariants. This is the
algebraic analogous to Buneman's Splits Equivalence Theorem. The interest of
this result relies on its potential applications in phylogenetics for the
widely used evolutionary models such as Jukes-Cantor, Kimura 2 and 3
parameters, and General Markov models.
