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.