Circumstances in which parsimony but not compatibility will be provably misleading

TL;DR

This paper analyzes the limitations of the maximum compatibility method in phylogenetics, demonstrating that it can reliably identify true splits in data with many taxa despite high homoplasy, whereas maximum parsimony may fail under similar conditions.

Contribution

It provides explicit formulas for the performance of maximum compatibility and compares its effectiveness to maximum parsimony in challenging data scenarios.

Findings

Maximum compatibility can detect true splits with many taxa despite many random characters.

Maximum parsimony may fail to identify original homoplasy-free characters in certain models.

The study offers theoretical insights into the reliability of phylogenetic inference methods.

Abstract

Phylogenetic methods typically rely on an appropriate model of how data evolved in order to infer an accurate phylogenetic tree. For molecular data, standard statistical methods have provided an effective strategy for extracting phylogenetic information from aligned sequence data when each site (character) is subject to a common process. However, for other types of data (e.g. morphological data), characters can be too ambiguous, homoplastic or saturated to develop models that are effective at capturing the underlying process of change. To address this, we examine the properties of a classic but neglected method for inferring splits in an underlying tree, namely, maximum compatibility. By adopting a simple and extreme model in which each character either fits perfectly on some tree, or is entirely random (but it is not known which class any character belongs to) we are able to derive exact and explicit formulae regarding the performance of maximum compatibility. We show that this method is able to identify a set of non-trivial homoplasy-free characters, when the number $n$ of taxa is large, even when the number of random characters is large. By contrast, we show that a method that makes more uniform use of all the data --- maximum parsimony --- can provably estimate trees in which {\em none} of the original homoplasy-free characters support splits.