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Summary: THE IDENTIFIABILITY OF TREE TOPOLOGY FOR
PHYLOGENETIC MODELS, INCLUDING COVARION
AND MIXTURE MODELS
ELIZABETH S. ALLMAN AND JOHN A. RHODES
Abstract. For a model of molecular evolution to be useful for
phylogenetic inference, the topology of evolutionary trees must be
identifiable. That is, from a joint distribution the model predicts,
it must be possible to recover the tree parameter.
We establish tree identifiability for a number of phylogenetic
models, including a covarion model and a variety of mixture models
with a limited number of classes.
The proof is based on the introduction of a more general model,
allowing more states at internal nodes of the tree than at leaves,
and the study of the algebraic variety formed by the joint distribu-
tions to which it gives rise. Tree identifiability is first established
for this general model through the use of certain phylogenetic in-
variants.
1. Introduction
In phylogenetics, probabilistic models of the evolution of biological
sequences (DNA or proteins, for example) are used to infer evolutionary
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