# Split probabilities and species tree inference under the multispecies coalescent model

## TL;DR

This paper explores how split probabilities on gene trees under the multispecies coalescent model can be used to accurately infer rooted species tree topologies, even with unrooted split data.

## Contribution

It introduces polynomial split invariants and demonstrates their effectiveness in identifying rooted species trees from split probabilities for more than five taxa.

## Key findings

- Split invariants relate split probabilities polynomially.
- Split probabilities can identify rooted species trees for >5 taxa.
- Potential exception for certain 6-taxon trees.

## Abstract

Using topological summaries of gene trees as a basis for species tree inference is a promising approach to obtain acceptable speed on genomic-scale datasets, and to avoid some undesirable modeling assumptions. Here we study the probabilities of splits on gene trees under the multispecies coalescent model, and how their features might inform species tree inference. After investigating the behavior of split consensus methods, we investigate split invariants --- that is, polynomial relationships between split probabilities. These invariants are then used to show that, even though a split is an unrooted notion, split probabilities retain enough information to identify the rooted species tree topology for trees of more than 5 taxa, with one possible 6-taxon exception.