Dihybrid Crosses & Linked Genes

Dihybrid Crosses

• Examine inheritance of two traits simultaneously (e.g.
  EeVv \times EeVv)
• F1 gametes (if genes assort independently): EV,\ Ev,\ eV,\ ev
• Punnett square (4×4) → phenotypic ratio 9:3:3:1 for
  dominant–dominant : dominant–recessive : recessive–dominant : recessive–recessive

Independent Assortment (Unlinked Genes)

• Genes on different chromosomes (or far apart on same chromosome) segregate
  independently during meiosis
• Dihybrid test cross with unlinked genes (heterozygote BbLl × double‐recessive
  bbll) yields 1:1:1:1 phenotypic ratio

Linked Genes

• Located close together on the same chromosome → tend to be inherited together
• Parental gametes far more frequent than recombinant gametes
• Example (rabbit): B = black fur, L = long hair
  • Parental chromosomes in heterozygote: \text{BL/bl}
  • Test cross BL/bl \times bl/bl gave offspring counts \approx 47\% BL (black-long), \approx 47\% bl (non-black-short), \approx 3\% B l, \approx 3\% b L → linkage confirmed

Dihybrid Test Cross

• Definition: cross of double-heterozygote with double-recessive
• Uses:
  • Detect linkage (deviation from 1:1:1:1)
  • Calculate map distance (see below)

Gene Mapping (Map Units / cM)

• Recombination frequency = \dfrac{#\,\text{recombinants}}{\text{total offspring}} \times 100
• 1\,\text{map unit (centiMorgan)} = 1\% recombination
• Previous rabbit data: (2+3)/100 \approx 5\% → genes \approx 5\, map units apart

Key Ratios & Probabilities

• Independent assortment F2 phenotype: 9:3:3:1 (self-cross of dihybrid)
• Probability for one specified combo (e.g. black solid dog from BbSs \times BbSs):
  P(black) = 3/4;\ P(solid) = 3/4;\ P(black \cap solid) = 3/4 \times 3/4 = 9/16
• Test cross with unlinked genes: 1:1:1:1

Problem-Solving Steps

1. Identify dominance relationships for each gene.
2. Determine whether genes are linked (use test-cross data).
3. List possible gametes (consider linkage and crossing-over).
4. Construct Punnett square or use probability rules.
5. Derive genotype & phenotype ratios; calculate recombination % if needed.

Terminology

• F_1: first filial generation (offspring of parental cross)
• Parental vs recombinant types: phenotypes matching vs differing from parents
• CentiMorgan (cM): unit of genetic distance equal to 1\% recombination
• Wild type: most common phenotype/allele in natural populations