Maximum Likelihood: Testcross Data

Z = Log₁₀[]

We found the best estimate of Q by plotting the Z value. We determined where Z peaked as the best estimate of Q.

To find the maximum likelihood of Q we take the Log(L) and then take the first derivative of Log(L) and set this equal to zero. For test cross data we have four classes. We can reduce these four classes to two classes, recombinant and parental.

L = Q^x(1-Q)^n-x

Where Q is the probability of crossover and x is the observed number of recombinant progeny in the testcross.

Log(L) = Log{Q^x(1-Q)^n-x}

= Log + xLog(Q) + (n-x)Log(1-Q)

dLog(L) = 0 +  x  + -(n-x) = 0
  dQ                   Q       1-Q

 x  =  n-x  =  x  =
 Q      1-Q == (O) ==  n

= x/n = number of recombinants/total observed

Example:

=  x  =  287 + 288  =  575 
           n           1200           1200

      = 0.479

This is the same answer we got by plotting the Lod score.