Matrix-analytic methods for the evolution of species trees, gene trees, and their reconciliation

TL;DR

This paper introduces matrix-analytic methods to model and compute the likelihood of gene trees within species trees, aiding reconciliation analysis with incomplete data.

Contribution

It develops a novel matrix-analytic framework for modeling species and gene tree evolution and provides efficient algorithms for likelihood computation in reconciliation problems.

Findings

Efficient algorithms for likelihood computation

Application to incomplete data scenarios

Physical interpretation of metrics

Abstract

We consider the reconciliation problem, in which the task is to find a mapping of a gene tree into a species tree, so as to maximize the likelihood of such fitting, given the available data. We describe a model for the evolution of the species tree, a subfunctionalisation model for the evolution of the gene tree, and provide an algorithm to compute the likelihood of the reconciliation. We derive our results using the theory of matrix-analytic methods and describe efficient algorithms for the computation of a range of useful metrics. We illustrate the theory with examples and provide the physical interpretations of the discussed quantities, with a focus on the practical applications of the theory to incomplete data.