Maximum likelihood estimation and natural pairwise estimating equations are identical for three sequences and a symmetric 2-state substitution model

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Consider the problem of estimating the branch lengths in a symmetric 2-state substitution model with a known topology and a general, clock-like or star-shaped tree with three leaves. We show that the maximum likelihood estimates are analytically tractable and can be obtained from pairwise sequence comparisons. Furthermore, we demonstrate that this property does not generalize to larger state spaces, more complex models or larger trees. Our arguments are based on an enumeration of the free parameters of the model and the dimension of the minimal sufficient data vector. Our interest in this problem arose from discussions with our former colleague Freddy Bugge Christiansen.

TidsskriftTheoretical Population Biology
Sider (fra-til)1-4
StatusUdgivet - 2024

Bibliografisk note

Funding Information:
We are grateful to the editor Marcy Uyenoyama and the reviewer for comments and suggestions that substantially improved the presentation.

Publisher Copyright:
© 2024 The Authors

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