# From event labeled gene trees to species trees

## TL;DR

This paper establishes a polynomial-time method to determine if a species tree explains a gene tree with known speciation and duplication events, showing that event labels provide significant information about the species tree.

## Contribution

It proves that species trees can be characterized by rooted triples from gene trees with known event labels and introduces an efficient algorithm for finding reconciliation maps.

## Key findings

- Event-labeled gene trees contain substantial information about species trees.
- Polynomial-time algorithm for verifying species tree compatibility.
- Simulated data confirms the effectiveness of event labels in constraining solutions.

## Abstract

Background: Tree reconciliation problems have long been studied in phylogenetics. A particular variant of the reconciliation problem for a gene tree T and a species tree S assumes that for each interior vertex x of T it is known whether x represents a speciation or a duplication. This problem appears in the context of analyzing orthology data. Results: We show that S is a species tree for T if and only if S displays all rooted triples of T that have three distinct species as their leaves and are rooted in a speciation vertex. A valid reconciliation map can then be found in polynomial time. Simulated data shows that the event-labeled gene trees convey a large amount of information on underlying species trees, even for a large percentage of losses. Conclusions: The knowledge of event labels in a gene tree strongly constrains the possible species tree and, for a given species tree, also the possible reconciliation maps. Nevertheless, many degrees of freedom remain in the space of feasible solutions. In order to disambiguate the alternative solutions additional external constraints as well as optimization criteria could be employed.