Question

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.

Short answer

Answer: The mode of inheritance governing 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.

Step-by-step solution

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.

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.

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.

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.

Key concepts

Mendelian Inheritance

Mendelian inheritance is a set of principles related to the transmission of genetic characteristics from parents to offspring, discovered by Gregor Mendel in the 19th century. It is based on the idea that inheritance is controlled by discrete units called genes, which occur in pairs known as alleles.
In Mendelian genetics, individuals inherit one allele from each parent, making up their genotype. These alleles can be either dominant or recessive.

• Dominant alleles are expressed when present, overriding the recessive allele.
• Recessive alleles are masked when paired with a dominant allele and only show their effect when paired together.

Understanding the Mendelian principles helps explain the patterns we see in genetic inheritance, such as those involving coat colors in cattle, modeled in the exercise. By using true-breeding individuals, one can study how phenotypic traits are passed on over generations.

Phenotypic Ratios

Phenotypic ratios describe the proportion of different observable traits or characteristics—phenotypes—in a population. These ratios are determined by the underlying genotypes and the interactions between their alleles.
For example, in the exercise involving cattle coat color, the phenotypic ratio observed in the F2 generation was 12 solid white: 3 black-and-white spotted: 1 solid black.

• We simplify this into a 12:3:1 ratio or compare it to traditional Mendelian ratios, observing how it aligns with a dihybrid cross, indicating the involvement of two gene pairs.
• The appearance of these ratios helps in deducing which combinations of alleles are present in the population and which traits are dominant or recessive.

By studying phenotypic ratios, students gain insights into inheritance patterns and can predict the possible outcomes of genetic crosses.

Dihybrid Cross

A dihybrid cross involves the crossing of two organisms that are heterozygous for two specific traits. This type of genetic cross highlights how alleles of two different genes assort independently during gamete formation, a principle explained by Mendel's law of independent assortment.
In our cattle coat color exercise, the 12:3:1 ratio suggests a modification of the classical 9:3:3:1 dihybrid ratio, indicating two gene pairs influence coat color.

• By assigning genotypes like AABB for solid white, aabb for solid black, and various heterozygous combinations (e.g., AAbb, AaBB, AaBb) for black-and-white spotted, we reflect the dihybrid combinations.
• The complexity of the phenotypic expressions in dihybrid crosses can be daunting, but by focusing on predicted ratios and considering how genes interact, such exercises offer valuable genetic insights.

This exercise illustrates how dihybrid crosses can be adapted to explain variance in more nuanced traits, such as cattle coats, where simple Mendelian ratios don't seem to fit at first glance.