# Species Trees Forcing Parsimony to Fail

## TL;DR

This paper demonstrates that the parsimony method for inferring species trees can fail under specific conditions involving three consecutive inner edges with certain lengths, especially as species trees grow larger.

## Contribution

It proves that no matter the true 9-taxon or larger species tree topology, parsimony fails if it contains three specific consecutive inner edges with particular length proportions.

## Key findings

- Parsimony fails with certain edge length configurations.
- Failure probability increases with species tree size.
- Applicable only when such edge length conditions are not met.

## Abstract

To the known fact that Parsimony method sometimes fails on the problem of inferring species trees from gene trees, here we proved that no mater of what topology the true 9-taxon and greater species tree is the only thing one needs to break down Parsimony is to have in this species tree three consecutive inner edges not going through the root but perhaps ending on it with lengths T1, T2, T3 of some proportions. Obviously, the probability to meet these lengths is growing in general with the size of species tree. Therefore, Parsimony may be applied only when the described lengths of edges cannot be met in the tree.