In rabbits, short hair is due to a dominant allele, S, and long hair to its recessive allele, s. Black hair is due to a dominant allele, B, and white hair to its recessive allele, b. When two rabbits are crossed, they produce 2518 short-haired, black offspring and 817 long-haired, black offspring. What are the possible genotypes of the parents?

According to the phenotypic percentages and ratios expressed by the offspring, we may say that one of the parents is SsBB. The other parent might be either SsBb or Ssbb.

Available data:

⇒  S is the dominant allele and codes for short hair

⇒  s is the recessive allele and codes for long hair

⇒  B is the dominant allele and codes for black hair

⇒  b is the recessive allele and codes for white hair

We need to figure out which is the genotype of the parental generation.

A way to do it is by taking the percentages and ratios of the progeny. This is,

3335 individuals 100% of the progeny

2518 black, short-haired X = 75.5%

817 black, long-haired X = 24.5%

These percentages approximate to the phenotypic ratio 3:1 from a cross between two heterozygous individuals ⇒ 75% expressing the dominant trait and 25% expressing the recessive phenotype.

The first conclusion is that, knowing that there are two genes involved, if both parents were dihybrid, the expected ratios expressed by the progeny should be 9:3:3:1. But this is not the case. So parents must express a different genotype.

Let us analyze the phenotypes of the progeny.

About the hair length

About the color

So, there are two possible options for parental genotype:

Let us perform the crosses:

Parentals) BBSs   x   BbSs

Gametes) BS, BS, Bs, Bs

                 BS, Bs, bS, bs

Punnett square)            BS        BS        Bs       Bs

                        BS      BBSS    BBSS    BBSs    BBSs

                        Bs       BBSs    BBSs    BBss     BBss

                        bS       BbSS    BbSS    BbSs    BbSs

                        bs       BbSs     BbSs     Bbss    Bbss

F1) 12/16 B-S- = 0.75 B-S- = 75% of the progeny black and short-haired

     4/16 B- ss = 0.25 B-ss = 25% of the progeny black and long-haired

Parentals) BBSs   x   bbSs

Gametes) BS, BS, Bs, Bs

                 bS, bs, bS, bs

Punnett square)            BS        BS          Bs       Bs

                        bS       BbSS    BbSS     BbSs    BbSs

                        bs        BbSs    BbSs     Bbss     Bbss

                        bS       BbSS    BbSS     BbSs    BbSs

                        bs       BbSs     BbSs     Bbss     Bbss

F1) 12/16 BbS- = 0.75 BbS- = 75% of the progeny black and short-haired

     4/16 Bbss = 0.25 Bbss = 25% of the progeny black and long-haired

Both crosses result in the same phenotypic ratios of the progeny, meaning that both options are possible.

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SsBB  and SsBB

or

SsBB and SsBb

Explanation:

To produce a ratio of offspring where the number of short haired black offspring is three times that of the long haired black offspring. Since, the long haired offspring can only be inherited in the recessive manner in two copies, thus possible genotypes of the parents could be:

SsBB  and SsBB

or

SsBB and SsBb

SsBB  and SsBB

         SB      sB

SB    SSBB   SsBB

sB     SsBB   ssBB

3/4 short haired black offspring and 1/4 long haired black offspring

SsBB and SsBb

          SB        Sb      sB       sb

SB    SSBB  SSBb  SsBB   SsBb

sB     SsBB  SsBb   ssBB    ssBb

6/8=3/4 short haired black offspring and 2/4=1/4 long haired black offspring

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