ArticlePloS one2013
The embedding problem for markov models of nucleotide substitution.
Article in PloS one, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
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Who cites it
7 citing papers in PubMed, 26 citations in OpenAlex.
- piqtree: a python package for seamless phylogenetic inference with IQ-TREE.Molecular biology and evolution · 2026Article
- The effectiveness of selection in a species affects the direction of amino acid frequency evolution.bioRxiv : the preprint server for biology · 2025Article
- The model-specific Markov embedding problem for symmetric group-based models.Journal of mathematical biology · 2021Article
- Embeddability and rate identifiability of Kimura 2-parameter matrices.Journal of mathematical biology · 2020Article
- A New Hierarchy of Phylogenetic Models Consistent with Heterogeneous Substitution Rates.Systematic biology · 2015Article
- Genetic distance for a general non-stationary markov substitution process.Systematic biology · 2015Article
- Horizontal transfer of an adaptive chimeric photoreceptor from bryophytes to ferns.Proceedings of the National Academy of Sciences of the United States of America · 2014Article
Corrections and comments
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Authors and funding
5 authors at 3 institutions in 2 countries.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Continuous-time Markov processes are often used to model the complex natural phenomenon of sequence evolution. To make the process of sequence evolution tractable, simplifying assumptions are often made about the sequence properties and the underlying process. The validity of one such assumption, time-homogeneity, has never been explored. Violations of this assumption can be found by identifying non-embeddability. A process is non-embeddable if it can not be embedded in a continuous time-homogeneous Markov process. In this study, non-embeddability was demonstrated to exist when modelling sequence evolution with Markov models. Evidence of non-embeddability was found primarily at the third codon position, possibly resulting from changes in mutation rate over time. Outgroup edges and those with a deeper time depth were found to have an increased probability of the underlying process being non-embeddable. Overall, low levels of non-embeddability were detected when examining individual edges of triads across a diverse set of alignments. Subsequent phylogenetic reconstruction analyses demonstrated that non-embeddability could impact on the correct prediction of phylogenies, but at extremely low levels. Despite the existence of non-embeddability, there is minimal evidence of violations of the local time homogeneity assumption and consequently the impact is likely to be minor.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.