Estimating Trees from Filtered Data: Identifiability of Models for Morphological Phylogenetics

TL;DR

This paper proves that parameters of certain morphological phylogenetic models are identifiable with at least 8 leaves, ensuring statistical consistency of model-based inference methods like maximum likelihood and Bayesian analysis.

Contribution

It establishes the identifiability of model parameters in morphological phylogenetics models with finite state spaces, addressing a key gap for statistical consistency.

Findings

Parameters are identifiable for trees with ≥8 leaves.

7 leaves suffice if the tree topology is known.

Identifiability fails for 4-taxon trees.

Abstract

As an alternative to parsimony analyses, stochastic models have been proposed (Lewis, 2001), (Nylander, et al., 2004) for morphological characters, so that maximum likelihood or Bayesian analyses may be used for phylogenetic inference. A key feature of these models is that they account for ascertainment bias, in that only varying, or parsimony-informative characters are observed. However, statistical consistency of such model-based inference requires that the model parameters be identifiable from the joint distribution they entail, and this issue has not been addressed. Here we prove that parameters for several such models, with finite state spaces of arbitrary size, are identifiable, provided the tree has at least 8 leaves. If the tree topology is already known, then 7 leaves suffice for identifiability of the numerical parameters. The method of proof involves first inferring a full distribution of both parsimony-informative and non-informative pattern joint probabilities from the parsimony-informative ones, using phylogenetic invariants. The failure of identifiability of the tree parameter for 4-taxon trees is also investigated.