Genetics Cross in Summer Squash

This question describes a genetics cross experiment involving two traits in summer squash: fruit colour and fruit shape. We are given information about the dominance of alleles for each trait:

• White colour (W) is dominant over yellow colour (w).
• Disc shape (D) is dominant over sphere shape (d).

The cross is between two plants, both of which have white fruit and sphere shape. The offspring produced from this cross show a specific ratio of phenotypes: 3/4 white, sphere and 1/4 yellow, sphere. We need to determine the genotype of the parents involved in this cross based on the offspring ratio.

Analyzing Offspring Ratios for Summer Squash Traits

Let's analyze the offspring ratio for each trait separately.

Fruit Colour Analysis

The offspring show 3/4 white and 1/4 yellow fruit. This is a classic 3:1 phenotypic ratio, which indicates a monohybrid cross between two heterozygous parents for the colour gene.

• Phenotypes: White (dominant) and Yellow (recessive)
• Ratio: 3 White : 1 Yellow
• Deduction: This ratio is obtained when the parents are both heterozygous (Ww) for the colour gene.

So, for the fruit colour, both parents must have the genotype Ww. The cross for colour is $Ww \times Ww$.

Let's verify this:

The genotypes are 1 WW : 2 Ww : 1 ww. The phenotypes are 3 White : 1 Yellow (since WW and Ww are white). This matches the 3/4 white and 1/4 yellow ratio observed in the offspring.

Fruit Shape Analysis

The offspring show 4/4 (or 100%) sphere shape. All offspring have the recessive shape phenotype.

• Phenotypes: Sphere (recessive) and Disc (dominant)
• Ratio: All Sphere
• Deduction: Since the sphere shape (d) is recessive, the phenotype sphere corresponds to the genotype dd. If all offspring are dd, and each parent contributes one allele for shape, then both parents must contribute a 'd' allele. This means both parents must be homozygous recessive (dd) for the shape gene.

So, for the fruit shape, both parents must have the genotype dd. The cross for shape is $dd \times dd$.

Let's verify this:

The genotype is 1 dd, and the phenotype is 1 Sphere. This matches the observation that all offspring are sphere.

Determining Parental Genotype

We determined the parental genotype for each trait separately:

• For colour: Ww × Ww
• For shape: dd × dd

Since the parents are stated to be a cross between a white, sphere plant and a white, sphere plant, both parents must have the same combined genotype.

Combining the genotypes for both traits, the genotype of each parent must be Wwdd.

Therefore, the cross is $Wwdd \times Wwdd$.

Verification of the Cross Wwdd × Wwdd

Let's predict the offspring phenotypes from the cross $Wwdd \times Wwdd$:

• Colour segregation: Ww × Ww gives 3/4 White and 1/4 Yellow.
• Shape segregation: dd × dd gives 1 Sphere.

Assuming independent assortment of the genes, the phenotypic ratio of the offspring will be the product of the individual trait ratios:

Ratio = (Colour Ratio) × (Shape Ratio)

Ratio = $(3/4 \text{ White} : 1/4 \text{ Yellow}) \times (1 \text{ Sphere})$

Ratio = $3/4 \text{ White, Sphere} : 1/4 \text{ Yellow, Sphere}$

This predicted ratio exactly matches the offspring ratio given in the question (3/4 white, sphere and 1/4 yellow, sphere).

Thus, the genotype of the parents is Wwdd × Wwdd.