Lectures 2: Mendelian Genetics

Mendelian Genetics

Gregor Mendel 1865

Key: Particulate Inheritance

• Discrete units of heredity (genes) that are inherited intact through the generations

Mendel's Experiments

• Used pure-breeding (genetically identical) lines of garden peas

• Examined crosses involving seven different characters

Notation for line crosses

• Parental Generations (P₁ and P₂)

• First Filial Generation F₁ = P₁ X P₂

• Second Filial Generation F₂ = F₁ X F₁

• Backcross one, B₁ = F₁ X P₁

• Backcross two, B₂ = F₁ X P₂

Monohybrid cross

• Cross between pure lines differing in a single character of interest.

• Here we consider Seed color -- Yellow versus Green
  

  What Mendel Observed

• The F₁ were all Yellow

• However, Green Segregated out in F₂
  • Strong evidence for discrete units of heredity , as "green" unit obviously present in F₁, appears in F₂

  • 3:1 ratio of Yellow : Green in F₂

Mendel also found that Parental, F₁, and F₂ Yellow peas behaved quite differently

• When examined each F₂ yellow family separately, Mendel found
  • 2/3 of the F₂ yellows give 1/2 yellow, 1/2 green

  • 1/3 of F₂ yellows gave all yellow progeny
    

  Mendel' s explanation

  
  • Genetic information exists as discrete units occurring in pairs

  • YY is the genotype of the pure Yellow line

  • yy the genotype of pure Green line
    • Y dominant to y (y is recessive to Y)

    • YY, Yy (denoted by Y-) = Yellow

    • yy = green

  • Here, the discrete units segregate out in the F₂
  

  Additional test of Mendel

  Can we account for the observed 2:1 ratio for F₂ Yellows X pure green?

  • Mendel's answer: 2/3 of F₂ Yellows are Yy, 1/3 are YY.
    • Why? Use conditional probabilities
      • Pr(Yellow F₂ is Yy) = Pr(Yy in F₂) / Pr(F₂ is Yellow) = (1/2)/(3/4) = 2/3

      • Pr(Yellow F₂ is YY) = Pr(YY in F₂) / Pr(F₂ is Yellow) = (1/4)/(3/4) = 1/3

  • Hence in the F₂ Yellow X green cross,
    • 2/3 of F₂ are Yy x yy crosses, giving 1/2 yellow, 1/2 green

    • 1/3 are YY x yy crosses, giving all yellow

    • Hence, total yellow = (1/2)(2/3) + 1/3 = 2/3, total green = (1/2)(2/3) = 1/3
  

  Genetic Notation

  • Character : Seed color
    • Yellow phenotype is dominant to green phenotype

  • Genotypes
    • YY homozygous dominant

    • Yy heterozygous

    • yy homozygous recessive

  • Alleles
    • Y is dominant

    • y is recessive
  

  Dihybrid crosses

  • Crossing pure-breeding lines differing in two characters

  • Example: for Seed shape
    • RR, Rr = round

    • rr = wrinkled

  • Cross yellow, wrinkled pure line with round green
  
  

  Mendel observed Independent Assortment

  • How are these ratios computed?
    • Pr(R-) = Pr(RR) + Pr(Rr) = 1-Pr(rr) = 3/4

    • Same for Pr(Y-) = 3/4

  • Pr(R-,Y-) = Pr(R-)*Pr(Y-)
    • = 3/4 * 3/4 = 9/16

    • Assumes R and Y are independent, i.e., Independent assortment

    • Pr(R-,yy) = 3/4 * 1/4 = 3/16

    • Pr(rr, Y-) = 1/4 * 3/4 = 3/16

    • Pr(rr, yy) = 1/4 * 1/4 = 1/16
  

  Mendel cheated (or was very lucky)

  The seven characters he used to show independent assortment were all on different chromosomes. Hence they are not linked.