Hidden Markov Model Approaches for Biological Studies

Lou, Xiang Yang

doi:10.15406/bbij.2017.05.00139

Cited by 3 publications

(1 citation statement)

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“…Hidden Markov models (HMMs) are important centerpieces in many biological applications (Eddy, 2004; Yang Lou, 2017). They provide a natural framework for comparative biologists, particularly for relaxing assumptions about homogeneous evolution through time and across taxa without vastly increasing the number of parameters (e.g., Felsenstein & Churchill, 1996; Galtier, 2001; Penny, McComish, Charleston, & Hendy, 2001; Beaulieu, O’Meara, & Donoghue, 2013; Beaulieu & O’Meara, 2016).…”

Section: Introductionmentioning

confidence: 99%

Generalized Hidden Markov Models for Phylogenetic Comparative Datasets

Boyko

Beaulieu

2020

Preprint

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1. Hidden Markov models (HMM) have emerged as an important tool for understanding the evolution of characters that take on discrete states. Their flexibility and biological sensibility make them appealing for many phylogenetic comparative applications. 2. Previously available packages placed unnecessary limits on the number of observed and hidden states that can be considered when estimating transition rates and inferring ancestral states on a phylogeny. 3. To address these issues, we expanded the capabilities of the R package corHMM to handle n-state and n-character problems and provide users with a streamlined set of functions to create custom HMMs for any biological question of arbitrary complexity. 4. We show that increasing the number of observed states increases the accuracy of ancestral state reconstruction. We also explore the conditions for when an HMM is most effective, finding that an HMM outperforms a Markov model when the degree of rate heterogeneity is moderate to high. 5. Finally, we demonstrate the importance of these generalizations by reconstructing the morphology of the ancestral angiosperm flower. Exactly opposite to previous results, we find the most likely state to be a spiral perianth, spiral androecium, whorled gynoecium. The difference between our analysis and previous studies was that our modeling allowed for the correlated evolution of several flower characters.

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Section: Introductionmentioning

confidence: 99%

Generalized Hidden Markov Models for Phylogenetic Comparative Datasets

Boyko

Beaulieu

2020

Preprint

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Generalized hidden Markov models for phylogenetic comparative datasets

Boyko

Beaulieu

2020

Methods Ecol Evol

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Hidden Markov models (HMMs) have emerged as an important tool for understanding the evolution of characters that take on discrete states. Their flexibility and biological sensibility make them appealing for many phylogenetic comparative applications. Previously available packages placed unnecessary limits on the number of observed and hidden states that can be considered when estimating transition rates and inferring ancestral states on a phylogeny. To address these issues, we expanded the capabilities of the R package corHMM to handle n‐state and n‐character problems and provide users with a streamlined set of functions to create custom HMMs for any biological question of arbitrary complexity. We show that increasing the number of observed states increases the accuracy of ancestral state reconstruction. We also explore the conditions for when an HMM is most effective, finding that an HMM is an appropriate model when the degree of rate heterogeneity is moderate to high. Finally, we demonstrate the importance of these generalizations by reconstructing the phyllotaxy of the ancestral angiosperm flower. Partially contradicting previous results, we find the most likely state to be a whorled perianth, whorled androecium, whorled gynoecium. The difference between our analysis and previous studies was that our modelling explicitly allowed for the correlated evolution of several flower characters.

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Markov Chains of Molecular Processes of Biochemical Materials

Orchidea Maria

2024

Int J Phys Res Appl

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Biochemical systems are analytically investigated after encoding the properties of the dynamics, which rule the time evolution of the transition properties, using some Markov models, such as the Hierarchical Markov-State Models. The present paper is aimed at analytically writing the (finite) Markov chain originating from the considered Markov models. Within this framework, the interaction with the environment is considered, and the ergodicity of the systems obtained from numerical simulation is controlled and compared with the qualities of the Markov chain. The (von Neumann) conditions to be imposed on the Bloch equations for the biomaterial structures to be described analytically in a consistent way are governed. The formalisms of the ’heat bath’ and that of the control of the numerical errors ensure the good measure-theoretical framework and the ergodicity of the finite chain, respectively. The finite Markov chains are investigated and the analytical expressions are presented, after which the Hierarchical Markov-State-Model provides the time evolution of the transition probabilities in biochemical systems. The notion of heat bath is used to describe the interactions of the biomaterial with the environment and thus to control the uses of the projection operators in the Markovian processes where the appropriate measure is defined; the stochastic equations allow one to obtain the wanted measure from the probability spaces. The cases in which a violation of the Markov property of the process occurs, i.e. in open systems, or dissipative processes are also considered. Furthermore, in complex molecules in biological systems, these features are investigated to be possibly even more dramatic. As far as molecular processes are concerned, this occurrence is associated with the appearance of chaotic effects with certain characteristics of potential surfaces: rather than the technique of isocommittors, the method of projectors in measure spaces is used for the Nakajima-Zwanzig paradigm for the density operator; this latter method complementary compares the time-convolution-less technique. The finite Markov chains are finally proven to be ergodic after the control of the numerical errors which provide the Sinai-Markov partitions to be applied for the analysis of the measure space of the Markov chain, that is, one endowed with a Hilbert measure. The von Neumann conditions are therefore newly demonstrated to be apt to be applied to the Bloch equations for biomaterial structures after the use of the notion of heat bath, from which the measure space arises. The qualities of the Hierarchical Markov-Sate Models which bring the analytical expression of the time evolution of probabilities of biomaterials are therefore newly analytically studied.

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Hidden Markov Model Approaches for Biological Studies

Cited by 3 publications

References 117 publications

Generalized Hidden Markov Models for Phylogenetic Comparative Datasets

Generalized Hidden Markov Models for Phylogenetic Comparative Datasets

Generalized hidden Markov models for phylogenetic comparative datasets

Markov Chains of Molecular Processes of Biochemical Materials

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