In cattle, coats may be solid white, solid black, or black-andwhite spotted. When true-breeding solid whites are mated with true-breeding solid blacks, the \(\mathrm{F}_{1}\), generation consists of all solid white individuals. After many \(\mathrm{F}_{1} \times \mathrm{F}_{1}\) matings, the following ratio was observed in the \(\mathrm{F}_{2}\) generation: \(12 / 16\) solid white \(3 / 16\) black-and-white spotted \(1 / 16\) solid black Rxplain the mode of inheritance governing coat color by determining how many gene pairs are involved and which genotypes yield which phenotypes. Is it possible to isolate a true-breeding strain of black-and-white spotted cattle? If so, what genotype would they have? If not, explain why not.

Step by step solution

01

Identify the ratio of phenotypes

The given ratio in the F2 generation is \(12/16\) solid white, \(3/16\) black-and-white spotted, and \(1/16\) solid black. We can simplify this ratio by dividing each number by the greatest common divisor, which is 1 in this case. Thus, the simplified ratio is 12:3:1.

02

Determine the number of gene pairs involved

The observed ratio in the F2 generation (12:3:1) is very close to the classic dihybrid ratio of 9:3:3:1, which means that two gene pairs are likely involved in determining the coat color. To fit our given ratio into the classic dihybrid pattern, we need to combine some of the categories. Combining the 9:3 and 3:1 ratios, we get the 12:3:1 ratio observed in this problem.

03

Assign genotypes to each phenotype

Let the two gene pairs for coat color be A and B. We know that the F1 generation consists of all solid white individuals which were a result of mating between true-breeding solid white and solid black cattle. Since solid white is dominant, we can assign AABB to solid white individuals, aabb to solid black individuals, and AAbb, AaBB, or AaBb to the spotted phenotype.

04

Determine if you can isolate a true-breeding strain of black-and-white spotted cattle

A true-breeding strain would require homozygous genotypes, meaning that all alleles in the genotype are the same. However, as previously determined, black-and-white spotted cattle have heterozygous genotypes (AAbb, AaBB, or AaBb). Therefore, it is not possible to isolate a true-breeding strain of black-and-white spotted cattle due to the presence of heterozygous genotypes for the coat color gene pairs. In conclusion, the inheritance of coat color in cattle involves two gene pairs, with AABB being solid white, aabb being solid black, and AAbb, AaBB, or AaBb representing black-and-white spotted individuals. It is not possible to isolate a true-breeding strain of black-and-white spotted cattle due to these heterozygous genotypes.

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