# Topological metrizations of trees, and new quartet methods of tree inference

## TL;DR

This paper introduces new topological metrizations of trees and develops fast, statistically consistent methods for inferring large phylogenetic trees from rooted triples and quartets, applicable under the multispecies coalescent model.

## Contribution

It presents novel topological metrizations and quartet-based inference methods that improve the speed and statistical consistency of phylogenetic tree reconstruction.

## Key findings

- New rooted triple and quartet metrizations introduced
- Fast methods for large tree inference developed
- Applicable to species tree inference under multispecies coalescent

## Abstract

Topological phylogenetic trees can be assigned edge weights in several natural ways, highlighting different aspects of the tree. Here the rooted triple and quartet metrizations are introduced, and applied to formulate novel fast methods of inferring large trees from rooted triple and quartet data. These methods can be applied in new statistically consistent procedures for inference of a species tree from gene trees under the multispecies coalescent model.