Genetics – Dihybrid Crosses, Linked Genes & X-Linked Inheritance

Review of Mendelian Dihybrid Crosses

• Dihybrid = tracking two traits simultaneously instead of one.
• Each parent contributes 4 alleles total (2 per gene).
• Punnett‐square setup identical to single‐gene crosses, just doubled in dimensions (4×4 grid).
• Strategy for solving complex problems (e.g. Labrador coat‐colour):
  • Start with most recessive phenotype among the offspring.
  • Because recessive = aa (homozygous), one recessive allele must have come from each parent.
  • This instantly reveals half of each parent’s genotype.
  • Build upwards: determine all possible parental genotypes that can generate every required puppy colour.
  • After hypothesising parental genotypes, prove by a full dihybrid Punnett square and circle the genotypes that yield the demanded phenotypes.
  • If three colours are required, ensure all three appear in predicted ratios.

Troubleshooting the Labrador‐Puppy Assignment

• Students report difficulty → instructor suggestion:
  1) Start with recessive puppy, 2) remember offspring = half mom + half dad.
• Quick tutorial offered; typical resolution time ≈ 2 minutes once approach understood.

Unexpected Post-Mendel Results & Introduction of Morgan Genetics

• Real organisms often deviated from Mendel’s law of independent assortment when genes sat on the same chromosome.
• Thomas Hunt Morgan (1910) used Drosophila melanogaster (fruit fly).
  • Advantages:
  • >100 eggs per mating.
  • Life-cycle 10-15 days; \approx \frac{365}{15} \approx 24 generations / year.
  • Cheap, tiny, minimal space/food.
  • Clear sexual dimorphism → easy male/female separation.
• If genes truly assorted independently, a dihybrid test-cross would yield 1 : 1 : 1 : 1 phenotypic ratio (25 % each).
• Morgan’s actual ratios ~45 % : 45 % : 5 % : 5 % ⇒ evidence of linked genes.

Concept of Linked Genes & Crossing Over

• Genes close together on the same chromosome tend to be inherited together.
• Crossing‐over in prophase I of meiosis can separate linked genes.
• Probability of separation ∝ physical distance between loci.
• Analogy: magnets — closer magnets hold hands when strands cross; farther ones separate.

Chromosome Mapping

• Goal: create a linear map showing gene order & relative distances.
• Unit = centimorgan (cM) a.k.a. mapping unit (MU).
  • 1\,\text{cM} = 1\% recombination frequency.
• Recombination frequency (RF) =
  \text{RF} = \frac{\text{recombinant offspring}}{\text{total offspring}} \times 100\%
• Steps to map (3+ genes):
  1. Convert each given % RF directly to MU.
  2. Locate the two genes with the largest separation → place at opposite ends.
  3. Position remaining genes between them using the remaining distances.
  4. Use subtraction to deduce missing intervals.
• Interpretation:
  • Smaller distance ⇒ stronger linkage, lower recombinant %, higher chance of co-inheritance.
  • Larger distance ⇒ weaker linkage, more recombination.

Simple Example (A, B, C)

• Data: A\leftrightarrow B = 22\%, A\leftrightarrow C = 10\%.
• Largest = 22 → draw A …..22 MU….. B.
• C is 10 MU from A → place C 10 MU to the right of A (12 MU left of B).
• Derived interval: C\leftrightarrow B = 22-10 = 12\,\text{MU}.
• Linkage hierarchy: A–C (10 MU) more tightly linked than C–B (12 MU).

Classroom Table Example (B, L, N, W)

• Table supplies pairwise MUs; sometimes one distance is missing & solved by subtraction.
• After mapping, typical exam questions:
  1. Draw the map (horizontal or vertical accepted).
  2. Indicate pair most likely & least likely to undergo recombination.

Non-numeric “eyeball” version

• Diagrams may show gene ticks without numbers; students infer closeness visually.

Sex-Linked (X-Linked) Inheritance — Core Rules

• Course simplification: all sex-linked traits are X-linked, none Y-linked.
• Male genotype: X^{?}Y → hemizygous (only one allele for X genes).
  • Males can never be carriers; they either express or lack the trait.
• Female genotype: X^{?}X^{?} → may be homozygous or heterozygous (carrier).
• Transmission logic:
  1. Fathers pass their X only to daughters (sons get the Y).
  2. Mothers pass an X to both sons & daughters.
• Consequences:
  • Affected father + unaffected mother ⇒
  • All sons unaffected (received father’s Y).
  • All daughters at least carriers (receive the single affected X).
  • Recessive X-linked diseases appear predominantly in males; females require two mutant alleles.

Worked Problem: Duchenne (Pseudo-Hypertrophic) Muscular Dystrophy (MD)

• Statement: “seen only in boys born to apparently normal parents.”
• Diagnosis:
  • Must be recessive (parents phenotype normal).
  • Trait is X-linked.
• Legend: X^{D} = normal, X^{d} = MD.
• Parental genotypes producing an affected son:
  • Father: X^{D}Y (normal).
  • Mother: X^{D}X^{d} (carrier).
• Punnett check (simplified row/column):
  • Sons: X^{D}Y (normal), X^{d}Y (affected).
  • Daughters: X^{D}X^{D} (normal), X^{D}X^{d} (carrier).
• Why boys only?
  • Boys express disease with one mutant allele.
  • Girls need two, which requires affected father and carrier/affected mother — improbable here because affected males die young and seldom reproduce.

Practical Tips & Ethical Notes

• Chromosomal mapping = relative, not absolute: think “Edmonton–Red Deer–Calgary” distances, not coordinate grid.
• Fruit-fly labs: ethical to minimise suffering; CO₂ used for sedation, not killing.
• Real-world relevance: linkage studies underpin modern genetic counseling & locate disease genes.
• Parents may feel guilt in X-linked disorders; important to communicate the involuntary nature of allele transmission.

Quick Reference Equations & Numbers

• Generations per year (fruit fly): 24\;\text{gen} = \frac{365\,\text{days}}{15\,\text{days · gen}^{-1}}.
• Recombination ↔ map units: 1\,\text{cM} = 1\% RF.
• Missing interval: d{AC} = d{AB} - d_{BC} (when A–B largest).

With these structured notes you can:
• Set-up and justify any dihybrid cross.
• Construct & interpret linkage maps.
• Solve recessive & dominant X-linked pedigree problems.
• Explain experimental choices (why fruit flies, why rapid cycles) and ethical considerations.