Product ratio method. The F2 data is derived from a heterozygote such as AaBb, which in its turn may be derived from parents either in coupling phase (AABB x aabb) or in repulsion phase (AAbb x aaBB). In both cases, if independent assortment holds good, then 9AB : 3Ab : 3aB : lab ratio should hold good. If chi-square test gives lack of independence between A and B, recombination frequencies can be calculated from the product ratio (z) derived as follows, where AB = a, Ab = b, aB = c and ab = d
(1) Coupling phase (AABB x aabb→AB/ab→F2) z = (b x c)/(a x d)
(2) Repulsion phase (AAbb x aaBB→Ab/aB→F2) z = (a x d)/(b x c)
The recombination frequency P (as per cent) can be obtained for calculated value of z from the Table 10.4.
Maximum likelihood method. This method is based on the principle that a recombination value (P), whose variance is minimum, will be the best estimate of recombination frequency. Therefore, P value is calculated using differential calculus, so that the probability of getting the observed results is maximum. Without giving the mathematics involved in the derivation of the formula used for such computation, we like to give here the final formula used for computation of recombination value (P).
where, S = - (a - 2b - 2c - d)
t = - 2d
n = (a + b + c + d)
As an illustration, suppose in a cross, following F2 data (n = 1415) are obtained : a = 753, b = 292, c = 351 and d = 19. The values can be substituted in the above formula as follows :
Prediction of F2 ratios for linked genes. If recombination frequency (P) is given, for linked genes one can also calculate the relative frequencies of different genotypes and phenotypes expected in F2 generation. For instance, if P = 10%, then the gametic frequencies will be : AB = .45, ab = .45, Ab = .05, aB = .05. From this information, using a checkerboard, frequencies of 16 possible combinations can be calculated, e.g. aabb = .45 x .45 = .2025 = 20.25%. In terms of recombination frequency, P, the proportion of AB/AB or ab/ab can be expressed each as ¼ (1 - P)2 in coupling phase, and as ¼P2 in repulsion phase.
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