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## Models of DNA evolutionA number of different Markov ## Additional recommended knowledge
## DNA Evolution as a Continuous Time Markov Chain## Continuous Time Markov Chains
- where each individual entry, refers to the probability that state will change to state in time .
where the top-left and bottom-right blocks correspond to
## Deriving the Dynamics of SubstitutionConsider a DNA sequence of fixed length be the column vector of probabilities of states and at time . Let be the state-space. For two distinct - , let
be the transition rate from state to state . Similarly, for any , let: The changes in the probability distribution for small increments of time are given by: In other words (in frequentist language), the frequency of 's at time is equal to the frequency at time minus the frequency of the Similarly for the probabilities . We can write these compactly as: where, or, alternately: where, is the ## ErgodicityIf all the transition probabilities, are positive,
## Time Reversibility
Not all stationary processes are reversible, however, almost all DNA evolution models assume time reversibility, which is considered to be a reasonable assumption. Under the time reversibility assumption, let , then it is easy to see that:
## Most Common Models of DNA Evolution## JC69 model (Jukes and Cantor, 1969)JC69 is the simplest substitution model. There are several assumptions. It assumes equal base frequencies () and equal mutation rates. The only parameter of this model is therefore μ, the overall substitution rate. Distance between two sequences is given by where
## K80 model (Kimura, 1980)Distinguish between Transition(A <-> G within purines or T <-> C within pyrimidines) and Transversion(between purines and pyrimidines) (α/β) Equal base frequencies () Rate matrix The Kimura two-parameter distance is given by: where
## F81 model (Felsenstein 1981)Unequal base frequencies () Rate matrix
## HKY85 model (Hasegawa, Kishino and Yano 1985)Distinguish between Transition and Transversion (α/β) Unequal base frequencies () Rate matrix
## T92 model (Tamura 1992)One frequency only π
The evolutionary distance between two noncoding sequences according to this model is given by where
## TN93 model (Tamura and Nei 1993)Distinguish between two different types of Transition (A <-> G) is different to (C<->T) Unequal base frequencies () Rate matrix
## GTR: Generalised time reversibleGTR is the most general neutral, independent, finite-sites, time-reversible model possible. It was first described in a general form by Simon Tavaré in 1986. The GTR parameters consist of an equilibrium base frequency vector, Π = (π Therefore, GTR (for four characters, as is often the case in phylogenetics) requires 6 substitution rate parameters, as well as 4 equilibrium base frequency parameters. However, this is usually eliminated down to 9 parameters plus μ, the overall number of substitutions per unit time. When measuring time in substitutions (μ=1) only 9 free parameters remain. In general, to compute the number of parameters, you count the number of entries above the diagonal in the matrix, i.e. for n trait values per site , and then add For example, for an amino acid sequence (there are 20 "standard" amino acids that make up proteins), you would find there are 209 parameters. However, when studying coding regions of the genome, it is more common to work with a codon substitution model (a codon is three bases and codes for one amino acid in a protein). There are 4
## References- Jukes, T.H. and C.R. Cantor. (1969)
*Evolution of Protein Molecules*, pp. 21-132. Academic Press, New York. - Kimura, M. (1980) A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences.
*Journal of Molecular Evolution*,**16**, 111-120. - Hasegawa, M., H. Kishino, and T. Yano. (1985) Dating of human-ape splitting by a molecular clock of mitochondrial DNA.
*Journal of Molecular Evolution*,**22**, 160-174. - Felsenstein, J. (1981) Evolutionary trees from DNA sequences: a maximum likelihood approach.
*Journal of Molecular Evolution*,**17**, 368-376. - Gu, X. and W. Li. 1992. Higher rates of amino acid substitution in rodents than in man.
*Molecular Phylogenetics and Evolution*,**1**:211-214. [1] - Li, W.-H. D.L. Ellsworth, J. Krushkal, B.H.-J. Chang, and D. Hewett-Emmett. 1996. Rates of nucleotide substitution in primates and rodents and the generation-time effect hypothesis.
*Molecular Phylogenetics and Evolution*,**5**:182-187. [2] - Tamura, K. 1992. Estimation of the number of nucleotide substitutions when there are strong transition-transversion and G+C content biases.
*Molecular Biology and Evolution***9**:678-687. [3] - Tamura, K., and M. Nei. 1993. Estimation of the number of nucleotide substitutions in the control region of mitochondrial DNA in humans and chimpanzees.
*Molecular Biology and Evolution***10**:512-526. [4]
Categories: Bioinformatics | Phylogenetics | Computational phylogenetics |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Models_of_DNA_evolution". A list of authors is available in Wikipedia. |