Genotype Frequencies flashcards 9-10

Genotype Frequencies Notes

• The transcript discusses three genotypes in a population:

  • Homozygous Dominant: typically written as AA
  • Heterozygous: written as Aa (the transcript garbles this as something like “pedozygos,” but the meaning is one dominant and one recessive)
  • Homozygous Recessive: written as aa
  • Key idea: genotypic frequencies include these three types, not just one or two.

• There are multiple ways to calculate genotype frequencies:

  • Direct counting in a sample (count how many individuals are AA, Aa, and aa).
  • Proportions: divide the counts by the total number of individuals to get frequencies.
  • From allele frequencies: compute p and q and then derive genotype frequencies (if assumptions hold, e.g., HW equilibrium).

• Examples used for practice in the transcript:

  • A pig population with seven individuals is used as a practical example for calculating frequencies.
  • A variety of flower examples are used as additional practice problems.
  • An example problem is provided for you to practice after the lecture segments.

• The goal of knowing genotype frequencies (as stated, though cut off in the transcript):

  • The transcript ends with: “The goal of knowing those frequencies is to…”, indicating an introduction to why these frequencies matter. In typical coursework, the goals include:
  • Predicting phenotype frequencies from genotype frequencies (via dominance relationships).
  • Estimating allele frequencies in a population.
  • Testing for deviations from expected distributions (e.g., Hardy–Weinberg expectations) and assessing evolutionary forces (selection, drift, migration, mutation).
  • Informing breeding, conservation, or medical genetics decisions based on genetic variation.

• Core concepts to be aware of (implicit from the topic):

  • Genotype frequencies must sum to 1:
  • f(AA) + f(Aa) + f(aa) = 1.
  • Allele frequencies relate to genotype frequencies:
  • If we denote the frequency of allele A as p\,$ and allele a as q\,$, then p + q = 1.
  • The relationship between genotypes and alleles:
    • p = f(AA) + \tfrac{1}{2} f(Aa)
    • q = f(aa) + \tfrac{1}{2} f(Aa)

• Hardy–Weinberg reference (often used for comparison):

  • Under Hardy–Weinberg equilibrium, genotype frequencies are given by:
  • f(AA) = p^2
  • f(Aa) = 2pq
  • f(aa) = q^2
  • These hold when the population is large, randomly mating, and not affected by evolutionary forces.

• Worked example (pig population with seven individuals): general method

  • Given counts: let x = ext{# of } AA,
    ewline y = ext{# of } Aa,
    ewline z = ext{# of } aa with x + y + z = 7.
  • Genotype frequencies in the sample:
  • f(AA) = \frac{x}{7}, \quad f(Aa) = \frac{y}{7}, \quad f(aa) = \frac{z}{7}.
  • Allele frequencies derived from sample:
  • p = f(AA) + \tfrac{1}{2} f(Aa) = \frac{2x + y}{14}
  • q = f(aa) + \tfrac{1}{2} f(Aa) = \frac{2z + y}{14}
  • Check that p + q = 1 (as a consistency check).
  • If the population is at Hardy–Weinberg equilibrium, the expected genotype frequencies would be:
  • f(AA) = p^2, \quad f(Aa) = 2pq, \quad f(aa) = q^2.
  • Example numbers (illustrative): suppose the observed counts are AA = 3, Aa = 2, aa = 2. Then:
  • Frequencies: f(AA) = \frac{3}{7}, \quad f(Aa) = \frac{2}{7}, \quad f(aa) = \frac{2}{7}.
  • Allele frequencies: p = \frac{2\cdot 3 + 2}{14} = \frac{8}{14} = \frac{4}{7}, \quad q = 1 - p = \frac{3}{7}.
  • HW expectations: f(AA){HW} = p^2 = \left(\frac{4}{7}\right)^2 = \frac{16}{49}, f(Aa){HW} = 2pq = 2\cdot \frac{4}{7}\cdot\frac{3}{7} = \frac{24}{49},
    f(aa)_{HW} = q^2 = \left(\frac{3}{7}\right)^2 = \frac{9}{49}.
  • Expected counts in a sample of 7 under HW: 7\times f(AA){HW} = \frac{112}{49} \approx 2.29,\quad 7\times f(Aa){HW} = \frac{168}{49} \approx 3.43,\quad 7\times f(aa)_{HW} = \frac{63}{49} \approx 1.29.
  • Interpretation: Compare observed counts (3,2,2) to expected HW counts (~2.29, ~3.43, ~1.29) to assess deviation from HW equilibrium in this small sample.

• Connections to foundational concepts and real-world relevance

  • Relates to Mendel’s principles of segregation (alleles separate into gametes) and independent assortment (though this simple model focuses on a single locus).
  • Builds on Punnett square reasoning for predicting genotype probabilities from allele frequencies.
  • Provides a framework for estimating allele frequencies in populations from observed genotype counts.
  • Practical implications include guiding selective breeding programs, conservation genetics, and understanding disease allele frequencies in populations.

• Practice strategy suggested by the transcript

  • Work through multiple examples with different organism sets (e.g., pigs, flowers) and different total counts (not just seven).
  • Practice both counting-based frequencies and allele-based calculations.
  • After practicing, check results against HW expectations where applicable to reinforce the connection between genotype and allele frequencies.

• Notes on the transcript’s ending

  • The last line is incomplete: "The goal of knowing those frequencies is to". The surrounding context implies understanding, predicting, and applying genotype/allele distributions, but the exact stated goal is cut off. Use standard educational goals as a guide for studying.

• Quick reference formulas recap

  • Genotype frequencies (sum to 1):
  • f(AA) + f(Aa) + f(aa) = 1
  • Allele frequencies:
  • p = f(AA) + \tfrac{1}{2} f(Aa), \quad q = f(aa) + \tfrac{1}{2} f(Aa), \quad p + q = 1
  • Hardy–Weinberg expectations (if applicable):
  • f(AA) = p^2, \quad f(Aa) = 2pq, \quad f(aa) = q^2
  • Sample-based genotype frequencies: for counts x = #(AA), \; y = #(Aa), \; z = #(aa) with total n = x+y+z:
  • f(AA) = \frac{x}{n}, \quad f(Aa) = \frac{y}{n}, \quad f(aa) = \frac{z}{n}
  • p = \frac{2x + y}{2n}, \quad q = \frac{2z + y}{2n}