In rabbits, black hair depends on a dominant allele, B, and brown hair on a recessive allele, b. Short hair is due to a dominant allele, S, and long hair to a recessive allele, s. If a true-breeding black short-haired male is mated with a brown long-haired female, describe their offspring. What will be the genotypes of the offspring? If two of these F1 rabbits are mated, what phenotypes would you expect among their offspring? In what proportions?

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1. Identify the genotypes of the parent rabbits. A true-breeding black short-haired male would have the genotype BBSS, as black hair (B) and short hair (S) are dominant traits. A brown long-haired female would have the genotype bbss, as brown hair (b) and long hair (s) are recessive traits.
2. Determine the gametes produced by each parent. The male can only produce B S gametes due to his homozygous dominant genotype. The female can only produce b s gametes due to her homozygous recessive genotype.
3. Perform a Punnett square using the gametes from each parent to find the genotypes of the F1 generation. Since the male produces only B S gametes and the female produces only b s gametes, all F1 offspring will have the genotype BbSs.
4. Analyze the F1 generation's genotype (BbSs) to determine their phenotype. Bb results in black hair since B is dominant over b, and Ss results in short hair since S is dominant over s. Thus, all F1 offspring will be black and short-haired.
5. Predict the phenotypes of the F2 generation by mating two F1 rabbits (BbSs x BbSs). Use a Punnett square to determine the possible genotypes and corresponding phenotypes, considering both traits (hair color and hair length). Calculate the phenotypic ratios to determine the proportions of each phenotype among the F2 offspring.