Dear all
Could anyone give me the direction or hints on 'how to derive the F81
model distance formula' from its probability formula ?? The F81 distance is
given as follows :
D = -(1-([P_A]^2 + [P_C]^2 + [P_G]^2 + [P_T]^2))ln(1-(P/([P_A]^2 + [P_C]^2 +
[P_G]^2 + [P_T]^2)).
The probability formula for F81 is given as:
P(ij) = P_j + (1-P_j)*Exp[-at] for all i == j
P_j*(1-Exp[-at]) for all i != J
where P_j is the equilibrium value for the frequency of each nucleotide.
Exp is the exponential function.
at is the expected rate of change per unit time.
I use the idea given by Li's book [Molecular Evolution - The method to
derive Juke-Cantor model distance based on sequence similiarity (p.69 and
p.80] for F81 model, but it doesn't come out that what i expected.
Rgds
Rex