According to the Jukes-Cantor model, given a proportion p of sites with different nucleotide sequences, the expected number of evolutionary changes between the two sequences is

Question

According to the Jukes-Cantor model, given a proportion p of sites with different nucleotide sequences, the expected number of evolutionary changes between the two sequences is

d = -3/4ln(1-(4/3p))

(a) What is the practical domain of d = f(p)?

(b) How many evolutionary changes are predicted by the model if half of the sites contain different nucleotide sequences? d =

(c) What's the solution to d=4? p=

Answer 1

A) 1-(4/3)p > 0

1 > (4/3)p

3/4 > p

Since p ≥ 0,

0 ≤ p < 3/4 = 0.75

B)

d = -3/4ln(1-(4/3)(1/2))

d = (-3/4) ln (1-(2/3)) = (-3/4) ln (1/3)

d ≈ 0.823959

C)

4 = -3/4ln(1-(4/3)p)

-16/3 = ln(1-(4/3)p)

e^(-16/3) = 1 - (4/3)p

(4/3)p = 1 - e^(-16/3)

p = (3/4)*(1-e^(-16/3))

p ≈ 0.746379

Answer 2

(a) 1 - (4/3)p > 0

(b) d = -3/4ln(1-(4/3)(1/2)))

(c) 4 = -3/4ln(1-(4/3p))