  We present a method of dimensional reduction for the general Markov model of
sequence evolution on a phylogenetic tree. We show that taking certain linear
combinations of the associated random variables (site pattern counts) reduces
the dimensionality of the model from exponential in the number of extant taxa,
to quadratic in the number of taxa, while retaining the ability to
statistically identify phylogenetic divergence events. A key feature is the
identification of an invariant subspace which depends only bilinearly on the
model parameters, in contrast to the usual multi-linear dependence in the full
space. We discuss potential applications including the computation of split
(edge) weights on phylogenetic trees from observed sequence data.
