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Dimensional reduction for phylogenetic tree models

We present a general method of dimensional reduction for phylogenetic tree models. The method reduces the dimension of the model space from exponential in the number of extant taxa, to quadratic in the number of taxa. 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 model space. We discuss potential applications including the computation of split (edge) weights on phylogenetic trees from observed sequence data.