Simulation of nucleotide substitution rates in a DNA using JC69 model

Abstract

Exploring the exponential of a matrix, we derived the rate matrix by extending the Poisson distribution to Differential equation. The solution of which gave rise to the continuous time Markov transition probability matrix  From who estimated the MLE of JC69 substitution model as approximately equal to 0.2 we generated the probability transition matrix  with the four states as Adenine (  Guanine , Cytosine ) and Thymine  Using   and Excel with varying values for rate with a constant time of 1, the simulation showed that at the point when rate tends to infinity, over which a nucleotide sequence had been allowed to evolve, the proportion of nucleotides of each type  and  will reach   for each. And this limiting distribution is called the stationary distribution and is maintained.