Dihybrid Crosses and Independent Assortment

The dot point instructs you to conduct practical investigations predicting variations in offspring genotype. A practical instruction cannot carry a written response, so it is examined with Predict — conduct → predict.

Plan: state the cross, predict the ratio, justify it from the mechanism, convert to numbers, then state the condition it depends on.

Both parents are heterozygous at both loci, so each is AaBb, where A gives yellow seed and a gives green, and B gives round seed and b gives wrinkled. Each parent produces four gamete types — AB, Ab, aB and ab — in equal proportions, so the cross is set out as a four-by-four Punnett square of sixteen equally likely boxes.

The prediction is a nine to three to three to one phenotypic ratio: nine yellow round, three yellow wrinkled, three green round and one green wrinkled. Only the double recessive genotype aabb gives green wrinkled, which is why that class is a single box out of sixteen.

The ratio follows from independent assortment. Each bivalent orients randomly at the metaphase I plate, so which allele of the seed-colour gene enters a gamete is independent of which allele of the seed-shape gene does. The two traits therefore behave as two separate three to one crosses running at once, and multiplying three-quarters yellow by three-quarters round gives nine-sixteenths, which is where the nine comes from.

With 320 offspring each sixteenth is twenty plants. The prediction is therefore 180 yellow round, 60 yellow wrinkled, 60 green round and 20 green wrinkled — figures which sum to 320, and that check is worth making before writing them down.

The prediction holds only if the two genes lie on different chromosomes. If they were linked, the parental combinations would be over-represented and the recombinant classes correspondingly rare, so the observed counts would depart from nine to three to three to one in a direction that reveals the linkage. The numbers are also expected values, so a real sample of 320 would deviate somewhat by chance.

The dot point's words are constructing and interpreting information from Punnett squares, and construct is not in the accepted verb set, so this content is examined with Explain — construct → explain.

Plan: name the principle, take each consequence as a linked pair, then answer the question directly.

The nine to three to three to one ratio depends entirely on independent assortment, which requires the two genes to lie on different chromosomes. Genes on the same chromosome travel into a gamete together unless a crossover separates them, so the assumption the ratio rests on is not met.

In an unlinked cross the four gamete types are equally frequent at one quarter each. With linkage the two parental combinations — the pairs the parent itself inherited together — are produced far more often, and the two recombinant combinations only when a crossover occurs between the loci. The four gamete types are therefore no longer equally likely, and every box in the Punnett square inherits that inequality.

How far the ratio departs depends on how close the loci are. A crossover is more likely to fall between two distant loci than two adjacent ones, so tightly linked genes give very few recombinants and a severely distorted ratio, while loosely linked genes give a ratio approaching nine to three to three to one. This is why linkage is a matter of degree rather than a yes or no property.

Because the recombinant frequency reflects the distance between the loci, the departure from the expected ratio can be measured rather than merely noted. The proportion of recombinant offspring estimates how far apart the genes lie, which is the basis of genetic mapping — so the failed prediction yields information the successful one could not.