Can we avoid 'SIN' in the house of 'No Common Mechanism'?

TL;DR

This paper investigates whether statistical inconsistency (SIN) can be avoided in phylogenetic tree reconstruction under 'no common mechanism' models, revealing that it depends on the model and method used.

Contribution

It provides a framework to analyze the conditions under which SIN can be avoided in NCM models, highlighting the dependence on specific models and reconstruction methods.

Findings

SIN can be avoided in certain NCM models

The possibility of avoiding SIN depends on the reconstruction method

Results connect mathematical theory with biological relevance

Abstract

In 'no common mechanism' (NCM) models of character evolution, each character can evolve on a phylogenetic tree under a partially or totally separate process (e.g. with its own branch lengths). In such cases, the usual conditions that suffice to establish the statistical consistency of tree reconstruction by methods such as maximum likelihood (ML) break down, suggesting that such methods may be prone to statistical inconsistency (SIN). In this paper we ask whether we can avoid SIN for tree topology reconstruction when adopting such models, either by using ML or any other method that could be devised. We prove that it is possible to avoid SIN for certain NCM models, but not for others, and the results depend delicately on the tree reconstruction method employed. We also describe the biological relevance of some recent mathematical results for the more usual 'common mechanism' setting. Our results are not intended to justify NCM, rather to set in place a framework within which such questions can be formally addressed.