On the dispersion index of a Markovian molecular clock
Abstract
The number of nucleotide substitutions accumulated in a gene or in a lineage is an important random variable in the study of molecular evolution. Of particular interest is the ratio of the variance to the mean of that random variable, often known as the dispersion index. Because nucleotide substitution is most commonly modeled by a continuous-time four-state Markov chain, this paper provides a systematic method of computing the dispersion indices exhibited by a continuous-time four-state Markov chain. Using this method along with computer algebra and Monte Carlo simulation, this paper offers partially proven conjectures that were supported by thorough computer experiments. It is believed that the Tamura model, the equal-input model and the Takahata-Kimura model always exhibit dispersion indices less than 2. It is also believed that a general four-state model can be chosen to exhibit a dispersion index of any desired magnitude, although the chance of a randomly chosen such model exhibiting a dispersion index greater than 2 is as small as about 2%. Relevance of these findings to the neutral theory is discussed.
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The distribution of intervals between substitution events, commonly described by a Poisson distribution, adds large confidence intervals to date estimates.
“This distribution of intervals between substitution events ('ticks') - commonly described by a POISSON DISTRIBUTION 12 - adds large confidence intervals to date estimates because the time taken to produce the observed substitutions cannot be known precisely.”
From The modern molecular clock (2003) · cites this paper as [12]
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- Authors
- Zheng, Q.
- Affiliations
- National Center for Toxicological Research (US)
- Corresponding author
- Zheng, Qi
- Venue
- Mathematical Biosciences
- Publisher
- Elsevier BV
- Published
- 2001-08
- Volume
- 172
- Issue
- 2
- Pages
- 115-128
- ISSN
- 0025-5564 (ISSN-L)
- OpenAlex
- W2017522674
- Cited by
- 17
- References
- 43
- Citations by year
- 2024: 1 · 2018: 1 · 2017: 1 · 2016: 1 · 2015: 1 · 2012: 1
- FWCI
- 0.73
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Mathematical Biosciences (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Genomics and Phylogenetic Studies
- Keywords
- dispersion index, molecular clock, nucleotide substitution, continuous-time Markov chains, variance-to-mean ratio, neutral theory, molecular evolution
- MeSH terms
- Computer Simulation, Markov Chains, Models, Genetic, Monte Carlo Method, Evolution, Molecular
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