Distance between DNA Sequences - Jukes-Cantor Model

According to the model of Jukes and Cantor [9] each base in the DNA sequence has an equal chance of mutating, and when it does, it is replaced by some other nucleotide uniformly. For a mutation probability of $3 \alpha \Delta t$ during each infinitesimally small period of time $\Delta t$ (frequency), the chance of a nucleotide x remaining unchanged over a period of T time units is (recall exercise #2):

$$P_{x \rightarrow x} = \frac{1}{4} (1 + 3 e^{-4 \alpha T})$$

Given a branch in the tree, the probability that the site is different at the two endpoints is therefore:

$$P_{u \neq v} = 1 - P_{x \rightarrow x} = \frac{3}{4} (1 - e^{-4 \alpha T})$$

Other Related Models

• Kimura's 2-parameters model [10]
  Very similar to Jukes-Cantor model only there are two different rates
  • purine-purine(A,G) or pyrmidine-pyrmidine(C,T)
  • purine-pyrmidine or pyrmidine-purine
• Extensions of the Kimura's model to asymmetric base frequencies [4,12].