Dihybrid cross

Mendel's explanation of the results of a dihybrid cross

    Given the principles revealed in a monohybrid cross, Mendel hypothesized that the result of two characters segregating simultaneously (a dihybrid cross) would be the statistical product of their independent occurrence. Consider two characters, seed color and seed shape. As previously shown, Y dominates y to determine seed color. Mendel also showed that the "round" R factor dominates the "wrinkled" r factor to determine seed shape. He then proceeded to test his hypothesis experimentally.

    The P cross is between true-breeding lines of wrinkled yellow peas (rrYY) and round green peas (RRyy). The F1 offspring are therefore all RrYy, and are all round and yellow. In forming the F2 plants, the alleles at the two loci segregate independently. That is, the chance of getting an R allele and a Y allele is 1/2 x 1/2, of getting an R and a y 1/2 x 1/2, and so on. Thus, all four possible diallelic combinations occur in equal proportions, and each has a probability of 1/4. The same is true for both parents. Given four possible gamete types in each parent, there are 
4 x 4 = 16 possible F2 combinations, and the probability of any particular dihybrid type is 1/4 x 1/4 = 1/16. The phenotypes and phenotypic ratios of these 16 genotype can be determined by inspection of the diagram above, called a Punnet Square after the geneticist who first used it.

    Alternatively, recall that the phenotypic ratio expected for either character is 3:1, either 3 "Y" : 1 "y", or 3 "R" : 1 "R". Then, algebra tells us that

(3Y + 1y) x (3R + 1r) = 9YR + 3Yr + 3Ry + 1 ry

    That is, we expect a characteristic 9:3:3:1 phenotypic ratio of round-yellow : wrinkled-yellow : round-green : wrinkled-green pea seeds.

    To predict the genotypic ratios, recall that for each gene the ratio is 1:2:1 :: AA:Aa:aa . Then, algebraically

(1YY + 2Yy + 1yy) x (1RR + 2Rr + 1rr) = 1 YYRR + 2 YYRr + 1 YYrr + 2YyRR + 4YyRr + 2 yyRR + 1yyRR + 2yyRr + 1yyrr

    That is, we expect a characteristic 1:2:1:2:4:2:1:2:1 ratio of the nine possible genotypes. These nine genotypes can be grouped into four phenotypes, for example 1 YYRR + 2 YYRr + 2 YyRR + 4 YyRr = 9Y-R- round, yellow peas. The ratio of these phenotypes is of course 9:3:3:1.

    Mendel reported the results of several dihybrid crosses
, of which (7)(7-1)/2 = 21 are possible with seven characters. He performed several trihybrid crosses as well.


Homework:

(1) Repeat the analysis above for a cross of RRYY x rryy.

(2) Predict the phenotypic and genotypic ratios of a
trihybrid cross. Pea plants may be tall or short: use T for the tall allele, which is dominant to the t allele for short plants. How would you diagram such a cross?


Figure 2002 by Griffiths et al.; all text material 2013 by Steven M. Carr