In-Depth Notes on Population Genetics

Introduction to Population Genetics

  • Definition: Population genetics focuses on genetic variation within populations, including its extent, reasons for existence, and changes over generations.
  • History: Emerged in the 1920s and 1930s, foundational figures include Sir Ronald Fisher, Sewall Wright, and J. B. S. Haldane.

Key Concepts

  • Gene Pool: The complete set of alleles within a population, which population geneticists study for variations and generational changes.

Defining Populations

  • Population: A group of individuals of the same species that interbreed in a shared region.
  • Local Populations: Smaller groups within larger populations that breed more frequently with each other than with the overall population, typically separated by geographic barriers.

Population Changes

  • Changes in a population can occur in:
    • Size
    • Geographic location
    • Genetic composition
  • Population geneticists create mathematical theories to predict shifts in gene pools based on these changes.

Genetic Variation

  • Monomorphic Genes: Genes existing primarily as a single allele.
  • Polymorphic Genes: Genes that exhibit multiple alleles; they show genetic variation.
    • Phenotype Frequency: Frequency of a specific phenotype in a population.

Allele and Genotype Frequencies

  • Fundamental calculations:
    1. Allele Frequency:
      extAlleleFrequency=extNumberofcopiesofanalleleextTotalnumberofallelesforthatgeneext{Allele Frequency} = \frac{ ext{Number of copies of an allele}}{ ext{Total number of alleles for that gene}}
    2. Genotype Frequency:
      extGenotypeFrequency=extNumberofindividualswithaparticulargenotypeextTotalnumberofindividualsext{Genotype Frequency} = \frac{ ext{Number of individuals with a particular genotype}}{ ext{Total number of individuals}}
Example Calculation of Genotype Frequency
  • In a frog population of 100:
    • 64 dark green (genotype D D G G)
    • 32 medium green (genotype D L G G)
    • 4 light green (genotype L L G G)
  • Light Green Genotype Frequency:
    \frac{4}{100} = 0.04 ext{ (4%)}
Example Calculation of Allele Frequency
  • For a frog population:
  • Calculation of L G allele frequency:
    • Total alleles = 200 (100 frogs × 2 alleles)
    • Contribution from genotypes:
    • Dark green: 128 (from 64 D D G G)
    • Medium green: 32 (from 32 D L G G)
    • Light green: 8 (from 4 L L G G)
  • Frequency of allele L G:
    \frac{(2 \cdot 4) + (1 \cdot 32)}{200} = 0.2 ext{ (20%)}

Hardy-Weinberg Equilibrium

  • Definition: A principle that describes the stability of allele frequencies in a population under specific conditions.
  • Equation: p+q=1p + q = 1
    • Where:
    • pp = frequency of the dominant allele
    • qq = frequency of the recessive allele
  • Conditions for Equilibrium:
    1. No mutations
    2. No genetic drift (large population)
    3. No migration
    4. No natural selection
    5. Random mating

Practical Application of Hardy-Weinberg

  • Example with allele frequencies: If p=0.8p = 0.8 and q=0.2q = 0.2, then:
    • Frequency of homozygous dominant (D D G G):
      p^2 = (0.8)^2 = 0.64 ext{ (64%)}
    • Frequency of heterozygous (D L G G):
      2pq = 2(0.8)(0.2) = 0.32 ext{ (32%)}
    • Frequency of homozygous recessive (L L G G):
      q^2 = (0.2)^2 = 0.04 ext{ (4%)}

Assessing Hardy-Weinberg Equilibrium

  • Use Chi-square tests to compare observed and expected genotype frequencies. This determines whether the population adheres to the Hardy-Weinberg equilibrium, indicating evolutionary changes if not.

Genetic Drift

  • Definition: Random fluctuations in allele frequencies, which may lead to the loss or fixation of alleles over generations.
  • Population Size Effect: Smaller populations are more susceptible to genetic drift.
Simulation of Genetic Drift
  • Example simulation shows varying fixation or loss rates of allele A across populations of different sizes.

Mutation Rates

  • Expected Number of New Mutations: extExpectedmutations=2Nμext{Expected mutations} = 2Nμ
    • Where μμ is the mutation rate and NN is population size.

Fixation and Loss Probabilities

  • Probability of Fixation:
    Pfixation=12NP_{fixation} = \frac{1}{2N}
  • Probability of Elimination:
    P<em>elimination=1−P</em>fixationP<em>{elimination} = 1 - P</em>{fixation}

Conclusion: Population Dynamics

  • The effects of genetic drift are amplified in smaller populations due to:
    • Bottleneck Effect: A sharp reduction in population size can lead to significant genetic drift.
    • Founder Effect: A small number of individuals create a new population, potentially differing in genetic makeup from the original population.