Analytical Approaches in Genetics

Punnett Squares

  • Diagrams predicting genotypic and phenotypic frequencies from a cross.
  • Parental alleles arranged on top and side; progeny genotypes at intersections.
  • Progeny genotypes are the product of parental alleles.

Monohybrid Cross

  • Dominant alleles: capital letters; recessive alleles: lowercase letters.
  • Homozygous: Both alleles are the same.
  • Heterozygous: Alleles are different.
  • Monohybrid: Cross studying one trait.
  • P generation: Parents being crossed.
  • F generation: Offspring (filial). Denoted with numeric subscripts (e.g., F1, F2).
  • Example:
    • Grandparents (P), Parents (F1), You (F2).
  • Mendel's pea plants: purple (dominant, P) or white (recessive, p).
  • Crossing homozygous purple (PP) with white (pp) yields F1 heterozygotes (Pp).
  • F1 generation all purple due to dominance.
  • Crossing two F1 (Pp) results in:
    • 25% PP.
    • 50% Pp.
    • 25% pp.
  • Phenotype ratio is 3:1 (purple: white).
  • Crossing heterozygotes results in
    • 1:2:1 genotypic ratio (homozygous dominant: heterozygous: homozygous recessive).
    • 3:1 phenotypic ratio (dominant: recessive).
  • Theoretical probabilities are more accurate with larger sample sizes.

Test Cross

  • Determines unknown genotype by crossing with homozygous recessive.
  • If all offspring display dominant phenotype, unknown is likely homozygous dominant.
  • If 1:1 distribution of dominant to recessive phenotypes, unknown is likely heterozygous.
  • Also called a back cross.

Dihybrid Cross

  • Punnett square extended to two genes.
  • Mendel's Second Law (Independent Assortment): Inheritance of one gene is independent of another (for unlinked genes).
  • Example: Flower color and plant height.
    • Purple (dominant, P), white (recessive, p).
    • Tall (dominant, T), short (dwarf, t).
  • Crossing two plants heterozygous for both traits results in 9:3:3:1 phenotypic ratio:
    • 9 tall and purple.
    • 3 tall and white.
    • 3 dwarf and purple.
    • 1 dwarf and white.
  • 3:1 phenotypic ratio holds for each trait (12 tall : 4 dwarf, 12 purple : 4 white).

Sex-Linked Crosses

  • Females (XX) can be homozygous or heterozygous.
  • Males (XY) are hemizygous for X-linked genes, making sex-linked traits more common in males.
  • X and Y symbolize normal chromosomes; superscripts denote defective alleles (e.g., X^h for hemophilia).
  • Hemophilia is a common example of a sex-linked trait.

Gene Mapping

  • Genes arranged linearly on chromosomes.
  • Crossing over during prophase I swaps alleles between homologous chromosomes.
  • Genes closer together are less likely to be separated during crossing over.
  • Recombination frequency (σ) is proportional to distance between genes.
  • Strength of linkage based on recombination frequency:
    • Tightly linked: close to 0%.
    • Weakly linked: approaching 50% (independent assortment).
  • Genetic map: relative distances between genes.
  • 1 map unit (centimorgan) = 1% recombination chance.
  • If two genes are 25 map units apart, expect 25% recombination.
  • Recombination frequencies can be added to approximate gene order.

Hardy-Weinberg Principle

  • Allele frequency: How often an allele appears in a population.
  • Example: 75 dominant alleles out of 100 = allele frequency of 0.75.
  • Evolution results from changes in gene frequencies over time.
  • Hardy-Weinberg equilibrium: Gene frequencies are not changing; no evolution.

Five conditions for Hardy-Weinberg equilibrium:

  1. Very large population (no genetic drift).
  2. No mutations affecting the gene pool.
  3. Random mating (no sexual selection).
  4. No migration.
  5. Genes are equally successful at being reproduced.

Hardy-Weinberg Equations:

  • Define: p = frequency of dominant allele (T); q = frequency of recessive allele (t).
  • Equation 1: p + q = 1 (combined allele frequency is 100%).
  • Equation 2: (p + q)^2 = 1^2 expands to p^2 + 2pq + q^2 = 1.
    • p^2 = frequency of homozygous dominant genotype (TT).
    • 2pq = frequency of heterozygous genotype (Tt).
    • q^2 = frequency of homozygous recessive genotype (tt).
    • p^2 + 2pq = frequency of dominant phenotype.
  • Equation 1: Allele frequencies.
  • Equation 2: Genotype and phenotype frequencies.
  • Equations demonstrate if evolution is occurring.
  • Example: Tall allele (T) frequency p = 0.8. Short allele (t) frequency q = 0.2.
  • F1 cross of heterozygotes: 64% TT, 32% Tt, 4% tt.
  • Genotype frequencies:
    • 64% TT = 64% T and 0% t.
    • 32% Tt = 16% T and 16% t.
    • 4% tt = 0% T and 4% t.
  • Allele frequencies:
    • 80% T and 20% t.
  • Allele frequencies are unchanged in Hardy-Weinberg equilibrium.