Write a code in computer (using R programing language) to estimate the stationary distributions. In each of the above models choose a value of each parameter and hence estimate the stationary distribution. Illustrate both short and long-term behavior of the transition functions. You may choose several parameters and graphically illustrate the convergence of the probabilities to the stationary distribution. Interpret the probabilities calculated while analyzing both short-term and long-term behavior.

i. Jukes-Cantor model (1969): 3r 3r c r r 3r 3r. In the above matrix the parameter, r 0, denotes the rate (transition rate) at which one type of nucleotide changes to another. ii. Kimura model (1980) a /-(r 2s) r -(r 2s iii. Felsenstein model (1981) a /-a(1 -pa) apa apt ape g apa -a (1 -pa) apc apg -a (1 -pe) apt apa t apa. ape -a(1 -pe) apg i. Jukes-Cantor model (1969): 3r 3r c r r 3r 3r. In the above matrix the parameter, r 0, denotes the rate (transition rate) at which one type of nucleotide changes to another. ii. Kimura model (1980) a /-(r 2s) r -(r 2s iii. Felsenstein model (1981) a /-a(1 -pa) apa apt ape g apa -a (1 -pa) apc apg -a (1 -pe) apt apa t apa. ape -a(1 -pe) apg