Chapter 3 Notes: Basic Principles of Heredity

Mendel and Foundations

• Mendel's background and goals

  • Gregor Mendel (1822–1884) trained as a monk and teacher; studied mathematics, physics, and biology.
  • Conducted careful, quantitative breeding experiments with garden peas to discover basic principles of heredity.
  • Was unaware of chromosomes, genes, or Darwin's natural selection; his work laid the groundwork for genetics before those concepts were understood.

• Garden peas: why they were advantageous for genetic study

  • Short generation time
  • Easy to control breeding and prevent self-fertilization
  • Many purebred varieties available
  • Traits exist in two easily-differentiated forms
  • Used careful statistical analysis and hypothesis-driven breeding experiments

Genetic Terminology (Table 3.1)

• Gene: An inherited factor (region of DNA) that helps determine a characteristic.
• Allele: One of two or more alternative forms of a gene.
• Locus: Specific place on a chromosome where an allele occupies.
• Genotype: Set of alleles possessed by an individual organism.
• Heterozygote: An individual with two different alleles at a locus.
• Homozygote: An individual with two identical alleles at a locus.
• Phenotype or trait: The appearance or manifestation of a characteristic.
• Character or trait: An attribute or feature possessed by an organism.

Genotype vs. Phenotype

• Genotype = the alleles at a particular locus (the nucleotide sequence).
• Phenotype = the expression of the genotype, influenced by other genes and the environment.
• Note: An organism does not inherit its phenotype directly; it inherits the genotype, which interacts with the environment to produce the phenotype.

Monohybrid Crosses and Principles

• Monohybrid cross = follows 1 character; the character is typically an "either/or" trait with 2 forms.
• True-breeding (true breeders) = homozygous for one trait.
• F1 generation phenotypes reflect only one of the parental phenotypes.
• F2 generation shows both parental phenotypes in a 3:1 phenotypic ratio.
• Reciprocal crosses (switching which trait is carried by the male gamete) yield the same results for Mendelian traits.
• Mendel tested 7 different characters and observed the same 3:1 F2 phenotypic ratio for all.

Mendel’s Four Major Conclusions

1) Alleles account for variation in inherited characters

• Organisms possess 2 alleles for each character.

• Convention: the allele seen in the F1 phenotype is written with an uppercase letter (e.g., $R$); the other allele is lowercase (e.g., $r$).
  2) The two alleles separate during gamete formation (Law of Segregation)

• Example: for a heterozygote $Rr$, the gametes contain 50% $R$ and 50% $r$.

• Fertilization restores a zygote with two alleles (e.g., $Rr$).
  3) If two alleles differ, the dominant allele determines the organism’s appearance; the recessive allele’s effect is masked

• Example: Round seed allele $R$ is dominant to wrinkled allele $r$; RR and Rr yield round seeds; rr yields wrinkled seeds.
  4) Alleles separate with equal probability to gametes (another statement of the Law of Segregation)

• In a true-breeding cross or a heterozygote, each gamete has an equal chance of carrying either allele.

  • Enzyme example illustrating dominance
  • Round allele (R) codes for an enzyme that converts starch from a linear to a branched form.
  • Wrinkled allele (r) is mutated and codes for a nonfunctional enzyme; starch accumulates as sucrose, causing water uptake and swelling in developing seeds.
  • Genotypes: $RR$ or $Rr$ yield rounded seeds (functional enzyme); $rr$ yields wrinkled seeds (no functional enzyme).
  • A single $R$ allele is sufficient to produce enough functional enzyme to prevent water swelling.
  • This demonstrates dominance: the presence of one functional allele masks the recessive phenotype.

Law of Segregation in Practice

• For true breeders:
  • AA × AA yields all AA offspring (all dominant phenotype).
  • aa × aa yields all aa offspring (all recessive phenotype).
• For a heterozygote Aa cross:
  • Gametes: 50% A, 50% a
  • Offspring genotypes: 1/4 AA, 1/2 Aa, 1/4 aa
  • Phenotypes: 3/1 dominant to recessive (3 Round : 1 Wrinkled in the pea example)

Punnett Squares and Cross Types

• Punnett square: a visual tool to predict offspring genotypes and phenotypes from parental genotypes.
• Test cross: cross an individual with an unknown genotype but a dominant phenotype (AA or Aa) with a homozygous recessive (aa) to determine the unknown genotype.
  • If the unknown is Aa, offspring phenotypes will be 1:1 (dominant:recessive).
  • If the unknown is AA, all offspring will show the dominant phenotype.
• Backcross: crossing an F1 (e.g., Aa) with one of the parental genotypes (e.g., aa) yields a 1:1 genotype and phenotype ratio (Aa:aa or 1:1).
• How to tell genotype from phenotype: perform a testcross if the dominant phenotype could be AA or Aa.

Probability in Mendelian Inheritance

• Rules of Probability are used to predict genetic cross outcomes.
• Law of Segregation ensures 2 alleles separate with equal probability to each gamete.
• Rule of Multiplication (AND): The probability that two independent events both occur is the product of their probabilities.
  • $P(A ext{ and } B) = P(A) imes P(B)$
• Rule of Addition (OR): The probability that either of two mutually exclusive events occurs is the sum of their probabilities.
  • P(A ext{ or } B) = P(A) + P(B)
    ext{(for mutually exclusive events)}

Applying Probability to Genetics

• Offspring genotypes from Aa × Aa: $frac{1}{4} ext{AA}, frac{1}{2} ext{Aa}, frac{1}{4} ext{aa}$
• Offspring phenotypes: $3:1$ for dominant to recessive.
• An example with two independent monohybrid traits uses both Rule of Multiplication and Rule of Addition to compute dihybrid outcomes.

Dihybrid Cross and Independent Assortment

• Mendel tested peas with two traits (e.g., round vs wrinkled and yellow vs green seeds).
• Principle of Independent Assortment: alleles at different loci separate independently of one another.
• Classic dihybrid cross: RRYY × rryy yields F1 genotype RrYy; self-fertilization yields F2 with a phenotypic ratio of $9:3:3:1$ (round yellow : round green : wrinkled yellow : wrinkled green).
• Mechanism: Alleles at different loci separate independently due to independent assortment during meiosis.

Dihybrid Cross: Practical Setup

• Example cross: RRYY × rryy
  • All F1 gametes: RY
  • F1 genotype: RrYy
  • Self-fertilization of F1 yields F2 with four phenotype classes in a 9:3:3:1 ratio.
• For dihybrid problems, you can break the problem into two monohybrid crosses (one for each trait) and then combine results using multiplication and addition rules.
• The 9:3:3:1 ratio emerges when two dihybrid heterozygotes (RrYy × RrYy) are crossed or when two independently assorting loci each have 2 alleles with complete dominance.

Gamete Formation and Genotype Combinations

• For two genes, each parent is diploid, producing haploid gametes with one allele from each gene.
• Example: Genotypes and possible gametes from AA BB, Aa Bb, etc.: AA, AB, Aa, aB, etc. (illustrative general principle: each gene contributes one allele per gamete).

Applying Probability to Dihybrid Crosses

• Consider cross Rr Yy × Rr Yy.
• Seed shape (R): cross Rr × Rr gives probabilities for R allele in gametes: 1/2 R, 1/2 r.
• Seed color (Y): cross Yy × Yy gives probabilities for Y allele in gametes: 1/2 Y, 1/2 y.
• To obtain a genotype such as RR yy, multiply probabilities: $frac{1}{4} imes frac{1}{4} = frac{1}{16}$
• For overall dihybrid results, combine the independent probabilities for each trait to get the 9:3:3:1 expectation.

Two Monohybrid Crosses: Break Di-hybrid into Two Steps

• Cross 1 (shape): Round (R) vs Wrinkled (r) gives 3/4 Round (R_) and 1/4 Wrinkled (rr).
• Cross 2 (color): Yellow (Y) vs Green (y) gives 3/4 Yellow (Y_) and 1/4 Green (yy).
• Combine results: 3/4 × 3/4 = 9/16 (Round, Yellow); 3/4 × 1/4 = 3/16 (Round, Green); 1/4 × 3/4 = 3/16 (Wrinkled, Yellow); 1/4 × 1/4 = 1/16 (Wrinkled, Green).
• This reproduces the 9:3:3:1 phenotypic ratio for the dihybrid cross.

Branch Diagrams for Expected Progeny (Dihybrid Context)

• Example branch results for a cross: 3/4 Yellow and 1/4 Green; 3/4 Round and 1/4 Wrinkled.
• Combinations yield probabilities such as:
  • Round, yellow: $frac{9}{16}$
  • Round, green: $frac{3}{16}$
  • Wrinkled, yellow: $frac{3}{16}$
  • Wrinkled, green: $frac{1}{16}$
• For a different parental cross, e.g., Rr Yy × Rr yy, branch diagrams yield:
  • 3/8 R_ Yy
  • 3/8 R_ yy
  • 1/8 rr Yy
  • 1/8 rr yy

Punnett Squares for Specific Crosses

• Parental cross Rr Yy × Rr yy leads to progeny with phenotypes/ genotypes distributed as:
  • 3/8 R_ Yy
  • 3/8 R_ yy
  • 1/8 rr Yy
  • 1/8 rr yy
• Genotype labels for the gametes include: RY, Ry, rY, ry; corresponding offspring genotypes appear in the Punnett square outcomes.

Chromosome Behavior and Meiosis: Linking to Independent Assortment

• Relationship between Mendel’s Principle of Independent Assortment and meiosis:
  • During meiosis, chromosome replication occurs, homologous chromosomes pair and separate during Anaphase I, and sister chromatids separate during Anaphase II.
  • The orientation of chromosome pairs on the metaphase plate is random, leading to independent assortment of alleles at different loci.
  • Example: Across two genes on different chromosomes, all four gamete combinations (e.g., RY, Ry, rY, ry) can be produced, contributing to the 9:3:3:1 ratio in dihybrid crosses.
• Visual cue: a diagram shows replication, Anaphase I, Anaphase II, and the separation of alleles contributing to diverse gamete genotypes.

Genetic Symbols and Nomenclature

• In plants:
  • Dominant alleles are represented by uppercase letters (e.g., A).
  • Recessive alleles are represented by lowercase letters (e.g., a).
  • Sometimes more than one letter is used for a gene (e.g., Ppd gene).
• In animals:
  • Wild-type or most common allele is often designated by a plus sign (+) (e.g., cn+ for brick-red eye color in Drosophila; cinnabar color may be cn).
  • Genotypes are written with a slash between alleles in diploids (e.g., cn+/cn).

Dihybrid Cross in Depth

• Mendel’s second law: The alleles at different loci separate independently of one another.
• Classic dihybrid cross: Round yellow (RRYY) × Wrinkled green (rryy) → F1 = RrYy; self-fertilization yields F2 with 9:3:3:1 phenotypic ratio.
• The mechanism is the independent segregation of two genes during gametogenesis, combined with random fertilization.

Applying Probability to Genetic Problems (Worked Concepts)

• When crossing Aa × Aa, the probability of offspring being RR is $frac{1}{4}$, Aa is $frac{1}{2}$, and aa is $frac{1}{4}$.
• The overall probability of a given dihybrid phenotype requires multiplying the probabilities for each trait (multiplication rule) and then summing when there are multiple genetic routes (addition rule).

End-of-Chapter Problems (Recommendations)

• Practice problems include: 2, 3, 5, 6, 9, 10, 14, 15, 17* (omit c), 18, 19, 20, 22, 25, 28, 30(a), 33, 34.
• These reinforce monohybrid and dihybrid crosses, test crosses, backcrosses, and probability rules.

Quick References and Summary Points

• Key terms: gene, allele, locus, genotype, phenotype, heterozygote, homozygote.
• Core principles: Law of Segregation, dominance, and independent assortment.
• Common crosses: monohybrid (one trait), dihybrid (two traits), testcross, backcross.
• Tools: Punnett square, branch diagrams, probability rules (multiplication and addition).
• Real-world relevance: inheritance patterns, genetic variation, and how meiosis generates the allele combinations that Mendel described.

Notation Recap

• Genotypes: $RR, Rr, rr$
• Phenotypes: Round vs Wrinkled; Yellow vs Green (example traits)
• Ratios: $3:1, 9:3:3:1, frac{1}{2}, frac{1}{4}$, etc. $ext{(all expressed with TeX: }$3:1$,$9:3:3:1$,$ frac{1}{2}$,$ frac{1}{4}$$
• Gametes: carry one allele from each gene, e.g., RY, Ry, rY, ry for two genes.