An Approximation Algorithm for Ancestral Maximum-Likelihood and Phylogeography Inference Problems under Time Reversible Markov Evolutionary Models

Mohammad-Hadi Foroughmand-Araabi; Sama Goliaei; Kasra Alishahi

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arXiv · 2308.06561

An Approximation Algorithm for Ancestral Maximum-Likelihood and Phylogeography Inference Problems under Time Reversible Markov Evolutionary Models

Mohammad-Hadi Foroughmand-Araabi·Sama Goliaei·Kasra Alishahi

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Abstract

The ancestral maximum-likelihood and phylogeography problems are two fundamental problems involving evolutionary studies. The ancestral maximum-likelihood problem involves identifying a rooted tree alongside internal node sequences that maximizes the probability of observing a given set of sequences as leaves. The phylogeography problem extends the ancestral maximum-likelihood problem to incorporate geolocation of leaf and internal nodes. While a constant factor approximation algorithm has been established for the ancestral maximum-likelihood problem concerning two-state sequences, no such algorithm has been devised for any generalized instances of the problem. In this paper, we focus on a generalization of the two-state model, the time reversible Markov evolutionary models for sequences and geolocations. Under this evolutionary model, we present a $2\log_2 k $-approximation algorithm, where $k$ is the number of input samples, addressing both the ancestral maximum-likelihood and phylogeography problems. This is the first approximation algorithm for the phylogeography problem. Furthermore, we show how to apply the algorithm on popular evolutionary models like generalized time-reversible (GTR) model and its specialization Jukes and Cantor 69 (JC69).

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Mohammad-Hadi Foroughmand-Araabi, Sama Goliaei, Kasra Alishahi. 2023-08-12. An Approximation Algorithm for Ancestral Maximum-Likelihood and Phylogeography Inference Problems under Time Reversible Markov Evolutionary Models. https://arxiv.org/abs/2308.06561

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