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

Author

Listed:
  • 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
    Australian Research Council Centre of Excellence for Plant Success)

  • Małgorzata M. O’Reilly

    (University of Tasmania)

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.

Suggested Citation

  • Albert Ch. Soewongsono & Jiahao Diao & Tristan Stark & Amanda E. Wilson & David A. Liberles & Barbara R. Holland & Małgorzata M. O’Reilly, 2025. "Matrix-analytic Methods for the Evolution of Species Trees, Gene Trees, and Their Reconciliation," Methodology and Computing in Applied Probability, Springer, vol. 27(1), pages 1-47, March.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:1:d:10.1007_s11009-025-10135-z
    DOI: 10.1007/s11009-025-10135-z
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    References listed on IDEAS

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    1. Warren B. Powell, 2016. "Perspectives of approximate dynamic programming," Annals of Operations Research, Springer, vol. 241(1), pages 319-356, June.
    2. Hautphenne, Sophie & Fackrell, Mark, 2014. "An EM algorithm for the model fitting of Markovian binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 19-34.
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