Mendel's Principles and Laws

Mendel's Principles/Laws

• Law of Segregation: Each gamete carries only one allele because chromosomes segregate/separate during Meiosis I and II.
• Law of Independent Assortment: Alleles of different genes assort/are distributed independently of each other during Meiosis I and II.
• Mendel's laws occur because of Meiosis I and Meiosis II.
• Mendel knew nothing of the role of Meiosis.
• Subsequent researchers correlated the movement of chromosomes with particulate inheritance using microscopy.

Review of Terms

• Gene: The fundamental physical unit of heredity, located on DNA (except in RNA viruses).
• Allele: A variant of a gene; one of a possible number of variants of a gene.
• Genotype: The genetic makeup of an organism.
• Phenotype: Observable characteristics of an organism.

Quantitative Traits

• Phenotype = Genotype + Environment + (Genotype x Environment Interaction)
• Phenotype = Genotype + Environment + G \times E
• Example: Identical twins with differences in muscular development due to different physical training (endurance running vs. weight lifting).

Mendelian Traits

• Characters not affected by the environment are considered categorical or Mendelian.
• In Mendelian traits, Phenotype = Genotype.

Why Peas?

• Grow easily.
• Produce a large number of seeds quickly (short generation time).
• Routinely self-fertilize and outcross.
• Have a number of 'categorical' traits.

How to Cross a Pea Plant

• Pea plant flowers are 'perfect' (contain both stamen and pistil).
• Steps:
  • Remove stamens from one plant before pollen production.
  • Collect pollen from mature anthers of another plant.
  • Cross-fertilize by transferring pollen from stamen to pistil.
  • Allow development of peas (seeds) in the pod.
  • Plant seeds and observe phenotypes of offspring.

Mendel's Experiments

• Looked at 7 characters of pea plants:
  • Seed coat color/flower color (grey/purple vs. white)
  • Seed color (yellow vs. green)
  • Seed shape (smooth vs. wrinkled)
  • Pod color (green vs. yellow)
  • Pod shape (inflated vs. pinched)
  • Stem height (tall vs. short)
  • Flower position (axial vs. terminal)
• Isolated true-breeding strains.
• Looked at each trait individually (initially).
• Conducted careful breeding experiments.
• Kept careful records.
• Had large sample sizes.
• Followed traits for multiple generations (3 generations).

Mendel’s 1st Law: Principle of Segregation

• The two members of a gene pair (alleles) segregate (separate) from each other during gamete formation and are randomly distributed to the offspring.
• Offspring receive one allele from each parent.
• Distinction between alleles versus genes.

Mendel’s Principle of Segregation (Terminology)

• P Generation: Parental Generation
• F1 Generation: First Filial Generation
• F2 Generation: Second Filial Generation
• F3, F4, F5, etc.: 3rd, 4th, 5th, etc. Generations
• Monohybrid Cross: True-breeding strains that differ in only ONE trait of interest.

Terminology

Reciprocal Crosses

Principle of Uniformity of F1

• F1 offspring of a monohybrid cross will exactly resemble only one parent and each other.

Traits Reappear in F2

• Mendel reasoned that information to create the trait was present in the F1 in the form of “factors” (now called genes), NOT BLENDING!
• Genes exist in alternative forms (now called alleles) that control specific traits.
• F1 has one of each allele. Since the progeny are not mixed, there is one dominant and one recessive allele.

Allele Designation

• Dominant alleles are designated with a capital letter (i.e. P).
• Recessive alleles are designated with a lowercase letter (i.e. p).

Heterozygous vs. Homozygous

• Homozygotes: Have 2 copies of the same allele.
  • PP
  • pp
• Heterozygotes: Have 1 copy of each allele.
  • Pp

Punnett Square

• Used to predict the genotypes and phenotypes of offspring.
• Example: Crossing a homozygous dominant (PP) with a homozygous recessive (pp) results in all heterozygous (Pp) F1 offspring.

Monohybrid Cross (Punnett Square)

• Crossing the F1 individuals (Pp x Pp) now.
• Gametes produced by each parent: P and p.
• Resulting progeny genotypes: PP, Pp, and pp.
• Note the 3:1 phenotypic ratio in the progeny.

Phenotypic Ratios

• If 'factors' segregate in the F1 and are then randomly distributed among offspring, then the phenotypic ratios of the F2 offspring should be 3:1.

Mendel's Determination of Ratios

• The ratios were NOT exactly 3:1.
• Example F2 ratios from Mendel’s experiments:
  • Flower color (purple : white): 3.15 : 1
  • Seeds (smooth : wrinkled): 2.96 : 1
  • Seeds (yellow : green): 3.01 : 1
  • Mean: 2.98 : 1

Statistical Analysis

• Question: If 4 offspring are produced, do we expect exactly 3:1?
• p = Probability (purple) = 3/4
• q = Probability (white) = 1/4
• Possible outcomes:
  • 4 Purple, 0 White: p^4 = (\frac{3}{4})^4 = \frac{81}{256}
  • 3 Purple, 1 White: 4p^3q = 4(\frac{3}{4})^3(\frac{1}{4}) = \frac{108}{256}
  • 2 Purple, 2 White: 6p^2q^2 = 6(\frac{3}{4})^2(\frac{1}{4})^2 = \frac{54}{256}
  • 1 Purple, 3 White: 4pq^3 = 4(\frac{3}{4})(\frac{1}{4})^3 = \frac{12}{256}
  • 0 Purple, 4 White: q^4 = (\frac{1}{4})^4 = \frac{1}{256}

Chi-Square Test

• Used to determine when a deviation from expectations is due to chance vs. a causative factor.
• Example: Mendel's Experiment: Pp x Pp resulted in 705 purple and 224 white flowers (929 total).
• Ratio: 3.15 : 1
  Are these results significantly different from the expected 3:1?

Testing Mendel’s First Law

• Law of Segregation:
  • The 2 members of a gene pair (alleles) segregate (separate) from each other during gamete formation and are randomly distributed to the offspring. (Offspring receive 1 allele from each parent.)

Chi-Square Test Details

• Formula: \chi^2 = \sum \frac{(Observed - Expected)^2}{Expected}
• If \chi^2 exceeds some critical value, reject the null hypothesis (our null hypothesis = 3:1).
• If \chi^2 < critical value, we cannot reject the hypothesis. (We conclude that the deviation of observed values from predicted is due to chance)
• Null Hypothesis (H0): There is no difference between observed and expected values.

Chi-Square Calculation Example

• Cross: Pp x Pp
• Calculate expected values based on a 3:1 ratio:
  • Purple Flowers: 0.75 \times 929 = 697
  • White Flowers: 0.25 \times 929 = 232
• Calculate the \chi^2 test statistic: \chi^2 = 0.39
• Degrees of Freedom (df) = #classes of data - 1 = 2 - 1 = 1

Chi-Square results

• P-values tell us the probability of obtaining a result equal to or "more extreme" than what was actually observed, when the null hypothesis is true.
• In our case, P = 0.54 means that 54% of the time we could expect to get results with the deviation we saw just by chance. Or, if you repeated the experiment 1000 times, 540 of those experiments would result in a deviation as great or greater than what we observed.

Mendel's Conclusions

• Mendel falsified the idea of blending inheritance.

Mendel's First Results/Conclusions

• Results of reciprocal crosses are always the same.
• The F1 resembled only one of the parents.
• The trait missing in the F1 reappeared in about 1/4 of the F2 individuals, exactly as you would predict if:
  • Alleles (factors) segregated/separated (into gametes) and reunited into offspring (randomly).
  • This is the Principle of Segregation.

Mendel’s 2nd Law: Principle of Independent Assortment

• The alleles of different genes assort independently of each other (i.e., all allele combinations are equally likely).
• Principle of segregation looked at one “gene” where alleles separated/segregated and came back together.
• Principle of independent assortment looks at 2 (or more) genes / “factors”.
• Example: Flower color and Plant Height (2 genes) - Dihybrid Cross: PpTt X PpTt

Dihybrid Cross Gametes

• PpTt x PpTt. Possible gametes: PT, Pt, pT, pt.
• Frequency of Gametes: 1/4, 1/4, 1/4, 1/4.
• 9:3:3:1 ratio.
• Note: you only see this ratio IF alleles at the 2 genes are assorting randomly with respect to each other (independent assortment).

Mendel’s Real Data from Dihybrid Cross

Implications of Mendel's Laws

• Falsified the idea of Blending Inheritance.
• Genes / "factors” controlled inheritance.