On matrix-analytic Markov modulated models for evolution: application potential and future directions required to advance the field.
- 1School of Natural Sciences (Mathematics), University of Tasmania, Hobart, TAS, Australia.
- 2Australian Research Council Centre of Excellence for Plant Success, University of Tasmania, Hobart, TAS, Australia.
Abstract
Markov modulated (MM) models in the theory of matrix-analytic methods (MAMs) are a class of probabilistic models whose key feature is an underlying Markov environment that drives the evolution of some complex and unpredictable system. Our goal in this paper is to emphasise their great potential for understanding evolution and the need for close multidisciplinary collaborations between probabilists and evolutionary biologists to advance the field. We give an overview of the fundamental MM models in MAMs, namely quasi-birth-and-death processes (QBDs) and stochastic fluid models (SFMs), in which the fluctuations in the level variable are modulated by fluctuations in the phase variable. We illustrate their application potential in evolution through an example of phylogenetic inference, state a general tree likelihood formula applicable to a wide range of MM models, and discuss future directions required to advance the theory of MM models as well as in the applications of the existing theory to evolutionary contexts.
Related
- Exact barycentric rational interpolation of analytic functions with an application to the Bessel functions
- Bayesian Implementation of the Factor‐Analytic Mixed Model and Application to Embeddings
- On the Invertibility of the Potential-Density Mapping for the Vlasov-Poisson System in Analytic Spaces
- Jet rigidity of Mather's β-function and complexified KAM curves holomorphic in potential for analytic standard maps
- Operator splitting methods for non-autonomous evolution equations comprising three parts, with application to the Bloch-Torrey equation of MRI
BibTeX
@article{oreilly2026matrixanalytic,
title = {{On matrix-analytic Markov modulated models for evolution: application potential and future directions required to advance the field.}},
author = {Małgorzata M O'Reilly and Barbara R Holland},
journal = {Frontiers in systems biology},
year = {2026},
month = oct,
doi = {10.3389/fsysb.2026.1906462},
url = {https://europepmc.org/article/MED/42908515},
note = {CC BY},
}
RIS
TY - JOUR
TI - On matrix-analytic Markov modulated models for evolution: application potential and future directions required to advance the field.
AU - Małgorzata M O'Reilly
AU - Barbara R Holland
PY - 2026
DA - 2026/10/07
JO - Frontiers in systems biology
DO - 10.3389/fsysb.2026.1906462
UR - https://europepmc.org/article/MED/42908515
AB - Markov modulated (MM) models in the theory of matrix-analytic methods (MAMs) are a class of probabilistic models whose key feature is an underlying Markov environment that drives the evolution of some complex and unpredictable system. Our goal in this paper is to emphasise their great potential for understanding evolution and the need for close multidisciplinary collaborations between probabilists and evolutionary biologists to advance the field. We give an overview of the fundamental MM models in MAMs, namely quasi-birth-and-death processes (QBDs) and stochastic fluid models (SFMs), in which the fluctuations in the level variable are modulated by fluctuations in the phase variable. We illustrate their application potential in evolution through an example of phylogenetic inference, state a general tree likelihood formula applicable to a wide range of MM models, and discuss future directions required to advance the theory of MM models as well as in the applications of the existing theory to evolutionary contexts.
SN - 2674-0702
ER -