Jukes Cantor
Expand: Needs more about the math and a chart graphic of the amino acid substitutions.
Jukes Cantor has one parameter, α, which is the probability of any one nucleotide changing to another. Thus, the probability of a site remaining constant at time t is:
pii(t) = 1 / 4 + 3 / 4e − 4αt
And the probability of a site changing is:
pij(t) = 1 / 4 − 1 / 4e − 4αt
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[edit] 1 Substitution Matrix
The instantaneous rates for substitutions can be expressed in a substitution matrix:
![Q = \left[ \begin{array}{cccc}
-3 \alpha & \alpha & \alpha & \alpha \\
\alpha & -3 \alpha & \alpha & \alpha \\
\alpha & \alpha & -3 \alpha & \alpha \\
\alpha & \alpha & \alpha & -3 \alpha \end{array} \right]](/wiki/files/math/7/1/d/71d49e3da4ac138a2e53fe400b3aa544.png)
The diagonal makes each row sum to 0.
[edit] 2 Assumptions
Jukes Cantor makes some very unrealistic assumptions:
- All substitutions equally likely, treated the same, and there's only a single substitution type.
- The frequencies of the nucleotides are assumed to be equal--sites are composed of 25% of each nucleotide.
- All sites have the same probability of substitution and evolve at the same rate.
- The rate of substitution is constant through time.
- Sites are independent.
- The probability of a site changing is not dependent on its history (a Markov process).
[edit] 3 Links
[edit] 4 References
- Jukes, T. H. and C. R. Cantor. 1969. Evolution of protein molecules. Pp. 21-123 in H. N. Munro, ed. Mammalian protein metabolism. Academic Press, New York.