Question

Total number of progeny of a dihybrid cross is 1280 in the F2 generation. How many are recombinants?
(a) 240
(b) 360
(c) 480
(d) 720

Answer 1

Hint: The crosses in which the parents differ from each other with respect to two pairs of alleles or contrasting characters are called dihybrid crosses. For example, Mendel crossed a double dominant pea plant having round and yellow seeds with a double successive plant having wrinkled and green seeds. Similarly, he crossed a tall, red-flowered pea plant with a dwarf, white- flowered plant. Mendel considered the 9:3:3:1 dihybrid phenotypic ratio as the result of the combined operations of two monohybrid crosses each of which would result in a 3:1 ratio.

Complete answer:
At first, true- breeding pure line varieties, which differed in two pairs of contrasting characters were produced by repeated self-fertilization. Then, two such varieties were crossed to raise the F1 hybrid generation. The F1 hybrids were then interbred to raise the F2 generation. The selfing of F1 hybrids produced a mixed F2 progeny with four phenotypic combinations in the ratio 9:3:3:1. In addition to parental combinations, two new phenotypic combinations appeared in F2 generations, namely round- green and wrinkled-yellow. They can be called recombinants.
In dihybrid cross total number of progeny = 16
In dihybrid cross number of recombinant progeny = 6
Therefore, Number of recombinant = $\cfrac { \left( 1280\times 6 \right) }{ 16 } =480$
So, the correct answer is (c) 480

Additional information:
- The 9:3:3:1 dihybrid phenotypic ratio can be further expanded as the dihybrid genotypic ratio 1:2:2:4:1:2:1:2:1
- The product of the two monohybrid ratios ${ \left( 3+1 \right) }^{ 2 }$ is equal to the dihybrid ratio i.e. ${ \left( 3+1 \right) }^{ 2 }=\left( 9+3+3+1 \right) $
- This is in conformity to the law of probability, called product law which holds the chance of two or more independent events occurring together is the product of the chances of their separate occurrence.

Note: On the basis of his findings from a dihybrid cross, Mendel formulated the Principle of Independent Assortment. Later on, Correns developed this as the law of independent Assortment, which is now regarded as the second Mendelian law of heredity. It holds that the factors for different pairs of contrasting characters behave as independent units so that their distribution in the gametes and also in succeeding generations is independent of each other. So according to this law, the alleles assort independently in random combinations.