Matrix-analytic Methods for the Evolution of Species Trees, Gene Trees, and Their Reconciliation

Albert Ch. Soewongsono (), Jiahao Diao (), Tristan Stark (), Amanda E. Wilson (), David A. Liberles (), Barbara R. Holland () and Małgorzata M. O’Reilly ()
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Albert Ch. Soewongsono: University of Tasmania
Jiahao Diao: University of Tasmania
Tristan Stark: University of Tasmania
Amanda E. Wilson: Temple University
David A. Liberles: Temple University
Barbara R. Holland: University of Tasmania
Małgorzata M. O’Reilly: University of Tasmania

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 1, 1-47

Abstract: Abstract We consider the reconciliation problem, in which the task is to find a mapping of a gene tree into a species tree. In this paper we present a method, where for a given choice of parameters, we are able to compute the likelihood for alternative reconciliations. We describe a Markovian binary tree (MBT) model for the evolution of species trees, a quasi-birth-and-death (QBD) model for the evolution of gene trees, and provide a recursive algorithm to compute the likelihood of a given reconciliation between a species tree and a gene tree. We derive our results using the theory of matrix-analytic methods, prove them using rigorous mathematics together with decomposition of sample path arguments, and describe 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.

Keywords: Matrix-analytic methods; Markovian binary tree; Quasi-birth-and-death process; Species tree; Gene tree; Reconciliation; Likelihood; 60J80; 60J22; 92D25; 65H10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10135-z

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