An Arrow-type result for inferring a species tree from gene trees

TL;DR

This paper investigates the theoretical limits of inferring a species tree from multiple gene trees, especially under conditions of incomplete taxon coverage, and demonstrates that certain desirable properties cannot all be achieved in such cases.

Contribution

It establishes an arrow-type impossibility result showing that no method can satisfy all four desirable properties with partial taxon coverage.

Findings

Complete taxon coverage allows for all properties to be satisfied

Partial coverage makes it impossible to satisfy all four properties simultaneously

The Adams consensus method works under complete coverage

Abstract

The reconstruction of a central tendency `species tree' from a large number of conflicting gene trees is a central problem in systematic biology. Moreover, it becomes particularly problematic when taxon coverage is patchy, so that not all taxa are present in every gene tree. Here, we list four desirable properties that a method for estimating a species tree from gene trees should have. We show that while these can be achieved when taxon coverage is complete (by the Adams consensus method), they cannot all be satisfied in the more general setting of partial taxon coverage.