Revisiting an equivalence between maximum parsimony and maximum likelihood methods in phylogenetics

TL;DR

This paper revisits the equivalence between maximum parsimony and maximum likelihood in phylogenetics, demonstrating that slight model modifications can lead to conflicting results between the two methods.

Contribution

It shows that small changes to model assumptions break the previously established equivalence, highlighting conditions where the methods diverge.

Findings

Small model changes cause maximum parsimony and likelihood to differ.

Under bounded substitution probabilities, likelihood trees are also parsimony trees.

Equivalence holds only when substitution probabilities are sufficiently small.

Abstract

Tuffley and Steel (1997) proved that Maximum Likelihood and Maximum Parsimony methods in phylogenetics are equivalent for sequences of characters under a simple symmetric model of substitution with no common mechanism. This result has been widely cited ever since. We show that small changes to the model assumptions suffice to make the two methods inequivalent. In particular, we analyze the case of bounded substitution probabilities as well as the molecular clock assumption. We show that in these cases, even under no common mechanism, Maximum Parsimony and Maximum Likelihood might make conflicting choices. We also show that if there is an upper bound on the substitution probabilities which is `sufficiently small', every Maximum Likelihood tree is also a Maximum Parsimony tree (but not vice versa).