In cattle, coats may be solid white, solid black, or black-and-white spotted. When true-breeding solid whites are mated with true-breeding solid blacks, the generation consists of all solid white individuals. After many matings, the following ratio was observed in the generation:
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Explain 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.

Verified step by step guidance

1. Step 1: Identify the phenotypes and initial cross results. True-breeding solid white cattle crossed with true-breeding solid black cattle produce an F1 generation of all solid white individuals. This suggests that the white coat color is dominant over black, or that the white phenotype masks the black in the heterozygous state.
2. Step 2: Analyze the F2 generation ratio. The problem states that after many F1 matings, the F2 generation shows a ratio of solid white, solid black, and black-and-white spotted individuals. This indicates that more than one gene pair is involved, and that the spotted phenotype arises from a specific combination of alleles.
3. Step 3: Propose the number of gene pairs and their roles. Since three phenotypes appear, consider two gene pairs: one controlling pigment color (e.g., white vs. black) and another controlling spotting pattern (e.g., presence or absence of spots). Assign genotypes such as WW or Ww for white, ww for black, and a second gene with SS or Ss for spotting, ss for no spots.
4. Step 4: Determine genotype-phenotype relationships. Solid white individuals likely have at least one dominant white allele (W_), solid black individuals are homozygous recessive for white (ww) and homozygous recessive for spotting (ss), while black-and-white spotted individuals have the black genotype (ww) combined with at least one dominant spotting allele (S_).
5. Step 5: Assess the possibility of isolating a true-breeding spotted strain. True-breeding spotted cattle would need to be homozygous for both the black color gene (ww) and the spotting gene (SS). If the spotted phenotype requires heterozygosity or interaction between alleles, true-breeding may not be possible. Otherwise, if spotted cattle with genotype wwSS exist, they can be bred true-breeding for the spotted phenotype.

Key Concepts

Incomplete Dominance and Epistasis

This concept explains how different alleles interact to produce intermediate or novel phenotypes rather than simple dominant-recessive patterns. In cattle coat color, the presence of solid white, solid black, and spotted patterns suggests interactions like incomplete dominance or epistasis, where one gene's expression can mask or modify another's effect.

Dihybrid Crosses and Mendelian Ratios

Understanding how two gene pairs segregate and assort independently is essential to interpret the observed phenotypic ratios in offspring. Dihybrid crosses produce characteristic ratios (e.g., 9:3:3:1), which help determine the number of genes involved and their interaction patterns in producing coat color phenotypes.

True-Breeding Strains and Genotype-Phenotype Relationships

True-breeding strains are homozygous for the genes controlling a trait, consistently producing the same phenotype. Identifying whether spotted cattle can be true-breeding requires understanding which genotypes correspond to each phenotype and if the spotted pattern results from heterozygosity or a specific homozygous genotype.