Dihybrid Inheritance

Dihybrid inheritance involves the simultaneous inheritance of two genes, each with two alleles, located on different chromosomes. This builds on monohybrid genetics and introduces Mendel's second law — the law of independent assortment.

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Mendel's Second Law — The Law of Independent Assortment

Mendel's second law states that alleles of different genes assort independently of one another during gamete formation, provided the genes are located on different chromosomes (i.e., they are unlinked).

• During meiosis I, homologous chromosomes line up randomly at the metaphase plate.
• The orientation of one pair of homologous chromosomes is independent of the orientation of another pair.
• This means that the allele inherited for one gene does not influence which allele is inherited for another gene (when the genes are on different chromosomes).

Key Point: Independent assortment only applies to genes on different chromosomes. Genes on the same chromosome are linked and tend to be inherited together (covered in a later lesson).

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The Dihybrid Cross

Worked Example 1 — Pea Plant Seed Characteristics

In pea plants:

• Seed shape: Round (R) is dominant over wrinkled (r)
• Seed colour: Yellow (Y) is dominant over green (y)

These two genes are on different chromosomes, so they assort independently.

Cross: RrYy × RrYy (both parents are heterozygous for both genes)

Gametes from each parent: RY, Ry, rY, ry (four types of gamete, produced in equal proportions)

	RY	Ry	rY	ry
RY	RRYY	RRYy	RrYY	RrYy
Ry	RRYy	RRyy	RrYy	Rryy
rY	RrYY	RrYy	rrYY	rrYy
ry	RrYy	Rryy	rrYy	rryy

Counting the Phenotypes

From the 16 possible offspring:

Phenotype	Genotypes	Count
Round, yellow	R_Y_	9
Round, green	R_yy	3
Wrinkled, yellow	rrY_	3
Wrinkled, green	rryy	1

Expected phenotypic ratio: 9:3:3:1

This 9:3:3:1 ratio is the signature of a dihybrid cross with complete dominance at both loci and independent assortment.

Key Definition: The underscore notation (e.g., R_) means "either homozygous dominant or heterozygous" — the second allele can be either R or r without affecting the phenotype when the dominant allele is present.

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Predicting Offspring Ratios

Shortcut Method — The Branch Diagram

Rather than drawing a full 4×4 Punnett square, you can use the branch (forked-line) method:

1. Consider each gene separately as a monohybrid cross.
2. Multiply the probabilities from each gene to find the combined probability.

For Rr × Rr: 3/4 round, 1/4 wrinkled For Yy × Yy: 3/4 yellow, 1/4 green

Combined probabilities:

• Round and yellow: 3/4 × 3/4 = 9/16
• Round and green: 3/4 × 1/4 = 3/16
• Wrinkled and yellow: 1/4 × 3/4 = 3/16
• Wrinkled and green: 1/4 × 1/4 = 1/16

This confirms the 9:3:3:1 ratio and is much quicker than a full Punnett square.

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Worked Example 2 — Guinea Pig Coat

In guinea pigs:

• Black coat (B) is dominant over brown (b)
• Short hair (S) is dominant over long hair (s)

Cross: BbSs × BbSs

Using the branch method:

• Bb × Bb → 3/4 black : 1/4 brown
• Ss × Ss → 3/4 short : 1/4 long

Phenotype	Probability	Ratio out of 16
Black, short	3/4 × 3/4 = 9/16	9
Black, long	3/4 × 1/4 = 3/16	3
Brown, short	1/4 × 3/4 = 3/16	3
Brown, long	1/4 × 1/4 = 1/16	1

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