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Difficulty: MediumMendel's Second Law and Dihybrid Inheritance

In rabbits (*Oryctolagus cuniculus*), black fur color (BB) is dominant over brown fur color (bb), and short hair (SS) is dominant over long hair (ss). If a heterozygous black, short-haired rabbit (BbSsBbSs) is crossed with a homozygous recessive brown, long-haired rabbit (bbssbbss), what proportion of the offspring is expected to possess brown fur and short hair?

  1. A
    116\frac{1}{16}
  2. 14\frac{1}{4}Answer
  3. C
    316\frac{3}{16}
  4. D
    916\frac{9}{16}

Answer

The expected proportion of offspring with brown fur and short hair is 14\frac{1}{4} (or 25%25\%).
A dihybrid test cross involves crossing a doubly heterozygous individual (BbSsBbSs) with a doubly homozygous recessive individual (bbssbbss). The heterozygous parent produces four distinct gamete combinations (BSBS, BsBs, bSbS, and bsbs) with equal probability (14\frac{1}{4} each). Combining these with the single gamete type (bsbs) from the recessive parent yields four phenotypic classes in a 1:1:1:11:1:1:1 ratio: Black/Short (BbSsBbSs), Black/Long (BbssBbss), Brown/Short (bbSsbbSs), and Brown/Long (bbssbbss). Therefore, the proportion of offspring exhibiting brown fur and short hair (bbSsbbSs) is 14\frac{1}{4} (or 25%25\%).

Step-by-Step Solution

1
Determine gamete genotypes produced by each parent
The heterozygous parent (BbSsBbSs) produces four types of gametes (BSBS, BsBs, bSbS, bsbs) in equal proportions (14\frac{1}{4} each). The homozygous recessive parent (bbssbbss) produces only one type of gamete (bsbs).
According to Mendel's Law of Independent Assortment, alleles for different traits segregate independently into gametes.
2
Perform the dihybrid test cross (BbSs×bbssBbSs \times bbss)
Offspring genotypes formed are: 14 BbSs\frac{1}{4}\ BbSs, 14 Bbss\frac{1}{4}\ Bbss, 14 bbSs\frac{1}{4}\ bbSs, and 14 bbss\frac{1}{4}\ bbss.
Combine each gamete from the heterozygous parent with the single gamete type (bsbs) from the recessive parent.
3
Identify the target phenotype and calculate its proportion
Brown fur and short hair corresponds to the bbSsbbSs genotype, which has a frequency of 14\frac{1}{4}.
Brown fur requires homozygous recessive alleles (bbbb), and short hair requires at least one dominant allele (SS).

Key Concept

Dihybrid Test Cross Ratio
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Topics

Mendel's Second Law and Dihybrid Inheritance

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