week 6

4.1 Hardy-Weinberg Equilibrium

  • Population Genetics Foundation

    • Algebraic description of a population's genetic makeup.

    • Developed by R.A. Fisher, S. Wright, and J.B.S. Haldane in the 1920s and 30s.

    • Agreement on evolutionary processes despite disagreements on force importance.

Hardy-Weinberg Equilibrium (HWE)

  • Definitions

    • Species: Group of individuals capable of interbreeding.

    • Population: A group within a species actively interbreeding.

    • Demes: Subdivided, partially isolated populations.

  • HWE Discovery

    • Independently discovered by W. Weinberg and G.H. Hardy in 1908.

    • Applies to diploid, sexually reproducing individuals if conditions are met: random mating, large size, no mutation/migration/selection.

  • HWE Principles

    1. Allelic frequencies at an autosomal locus do not change from generation to generation (allelic-frequency equilibrium).

    2. Genotypic frequencies are determined predictably by allelic frequencies (genotypic-frequency equilibrium).

    3. The equilibrium is neutral and returns after disruption within one generation of random mating.

Calculating Allelic Frequency

  • Method 1: Count Genes

    • Determine frequency of alleles (example: a allele frequency q).

    • Formula: q = (number of a alleles) / (total number of alleles).

Example (Page 2)

  • Dominant Allele Frequency (Pea Population)

    • Genotype counts:

      • Round (RR) = 114

      • Round (Rr) = 76

      • Wrinkled (rr) = 10

      • Total = 200

    • Calculation for p (R alleles):

      • p = f(R) = (2 * 114 + 76) / (2 * 200) = 304 / 400 = 0.76.

    • Calculation for q (r alleles):

      • q = f(r) = (2 * 10 + 76) / (2 * 200) = 96 / 400 = 0.24.

    • Shortcut: p + q = 1, thus q = 1 - p.

Genotypic Frequencies Calculation

  • From genotype frequencies:

    • f(RR) = 114 / 200 = 0.57

    • f(Rr) = 76 / 200 = 0.38

    • f(rr) = 10 / 200 = 0.05

    • Allelic frequencies:

      • p = f(R) = f(RR) + (1/2)f(Rr)

      • q = f(r) = f(rr) + (1/2)f(Rr).

Assumptions of HWE

  • Eight key assumptions:

    1. Organism is diploid.

    2. Organism is sexually reproducing.

    3. Discrete generations (no overlapping).

    4. Mating is completely random.

    5. Population is large to prevent genetic drift.

    6. No migration (alleles must remain in population).

    7. No selection pressure exists (no reproductive advantage based on genotype).

    8. No mutation occurs (alleles should remain unchanged).

Violations of HWE Assumptions

  • Common Violations:

    1. Many plants are polyploid, violating diploid assumption.

    2. Apomixes in plants allow asexual reproduction, impacting sexual reproduction assumption.

    3. Overlapping generations in perennial species affect discrete generations.

    4. Random mating assumptions violated by behavioral influences, location variances, etc.

    5. Small populations lead to genetic drift.

    6. Migration concerns with plant phenotypes affected by environmental pressures.

    7. Selection pressures evident in both natural and artificial selection scenarios.

    8. Mutation is constant and cannot be fully controlled in populations.

Deriving HWE Formula (Page 24)

  • Key Aspects:

    • Genetic make-up through binomial expression.

    • Equilibrium reflected by potential frequencies:

      • f(AA) = p^2, f(Aa) = 2pq, f(aa) = q^2.

Impact of Inbreeding

  • Inbreeding Effects:

    • Self-pollination in plants vs. sibling mating in animals increase homozygous frequency.decrease heterozygous frequency.

    • Positive assortative mating (similar phenotypes mate more often) increases homozygosity, whereas negative assortative mating reduces it.

  • Self-Fertilization:

    • Extreme inbreeding with direct consequences on genetic diversity.

Genetic Drift and Small Populations

  • Genetic Drift:

    • Changes in allelic frequencies due to random sampling effects.

    • Particularly salient in small populations where chance events greatly impact frequencies.

Selection Pressures

  • Selection Pressure Dynamics:

    • Influences from natural selection, impacting reproductive success and allowing beneficial traits to prevail over generations.

Conclusions

  • Hardy-Weinberg Equilibrium serves as a critical foundation for understanding genetic populations.

  • Practical applications in plant and animal breeding require careful consideration of genetic parameters and the impacts of inbreeding, migration, and selection to achieve desired outcomes.