# Models of nucleotide substitution

**Models of nucleotide substitution** are mathematical equations built to predict the probability (or proportion) of nucleotide change expected in a sequence.

## Jukes and Cantor's one-parameter model

**JC69** is the simplest of the models of nucleotide substitution.^{[1]} The model assumes that all nucleotides has the same rate () of change to any other nucleotides. The probability that any nucleotide remains the same from time 0 to time 1 is;

must be read; probability (or proportion, in this case it is equivalent) that becomes at time . For the probability that any nucleotide changes to any other nucleotide we write . The probability for time is;

The second part of the equation denotes the probability that the nucleotide was changed from time 0 and 1, but then got back to its initial states on time 2. The model can be rewritten in a differential equation with the solution;

Or if we want to know the probability of nuleotide to change to nucleotide ;

With time, the probability will approach 0.25 (25%).

## Kimura's two-parameters model

Mostly known under the name **K80**, this model was developed by Kimura in 1980 as it became clear that all nucleotides substitutions weren't occurring at an equal rate. Most often, transitions (changes between A and G or C and T) are more common than transversions.^{[2]}

## Further Reading

- Yang, Z. (2006).
*Computational Molecular Evolution*. Oxford University Press.

## References

- ↑ Jukes, T.H. and Cantor, C.R. (1969). "Evolution of protein molecules". In Munro, H.N. (editor).
*Mammalian protein metabolism*. Academic Press, New York. pp. 21–123. - ↑ Kimura, M. (1980). "A simple method for estimating evolutionary rate of base substitution through comparative studies of nucleotide sequences".
*Journal of Molecular Evolution*.**16**: 111–120.