15.1 Hardy-Weinberg equilibrium and population genetic models

Population genetics models help us understand how genes change in groups over time. The Hardy-Weinberg equilibrium principle is a key concept, showing when gene frequencies stay stable across generations.

These models consider factors like genetic drift, selection, and migration. By studying these forces, we can predict how populations might evolve and use this knowledge for conservation and managing genetic diseases.

Hardy-Weinberg Equilibrium Principle

Calculating Allele and Genotype Frequencies

Top images from around the web for Calculating Allele and Genotype Frequencies

• 

  Genetic aspects of populations, Hardy-Weinberg equilibrium - WikiLectures View original

  Is this image relevant?

• 

  Hardy-Weinberg Principle of Equilibrium | Biology for Majors II View original

  Is this image relevant?

• 

  Hardy–Weinberg principle - Wikipedia View original

  Is this image relevant?

• 

  Genetic aspects of populations, Hardy-Weinberg equilibrium - WikiLectures View original

  Is this image relevant?

• 

  Hardy-Weinberg Principle of Equilibrium | Biology for Majors II View original

  Is this image relevant?

1 of 3

Top images from around the web for Calculating Allele and Genotype Frequencies

• 

  Genetic aspects of populations, Hardy-Weinberg equilibrium - WikiLectures View original

  Is this image relevant?

• 

  Hardy-Weinberg Principle of Equilibrium | Biology for Majors II View original

  Is this image relevant?

• 

  Hardy–Weinberg principle - Wikipedia View original

  Is this image relevant?

• 

  Genetic aspects of populations, Hardy-Weinberg equilibrium - WikiLectures View original

  Is this image relevant?

• 

  Hardy-Weinberg Principle of Equilibrium | Biology for Majors II View original

  Is this image relevant?

1 of 3

• The Hardy-Weinberg equilibrium principle maintains that allele and genotype frequencies remain constant across generations without evolutionary influences
• Use the Hardy-Weinberg equation, [p^2 + 2pq + q^2 = 1](https://www.fiveableKeyTerm:p^2_+_2pq_+_q^2_=_1), to calculate genotype frequencies
  • $p$ represents the frequency of the dominant allele
  • $q$ represents the frequency of the recessive allele
• Calculate allele frequencies using the formulas:
  • $p = (2AA + Aa) / 2N$
  • $q = (2aa + Aa) / 2N$
    • $AA$, $Aa$, and $aa$ represent the genotype counts
    • $N$ is the total number of individuals in the population
• The sum of allele frequencies for all alleles at a given locus must equal 1 ([p + q = 1](https://www.fiveableKeyTerm:p_+_q_=_1) for a two-allele system)

Applications and Testing

• Estimate the frequency of carriers (heterozygotes) for recessive genetic disorders in a population using Hardy-Weinberg equilibrium
• Determine if observed genotype frequencies deviate significantly from expected frequencies under Hardy-Weinberg equilibrium using the chi-square goodness-of-fit test
  • Example: Compare observed genotype counts for a gene with two alleles to expected counts calculated using Hardy-Weinberg proportions
• Apply Hardy-Weinberg equilibrium to population data to:
  • Assess the genetic structure of populations (allele and genotype frequencies)
  • Identify potential deviations from equilibrium that may indicate evolutionary forces at work
  • Estimate the prevalence of genetic disorders in populations

Assumptions and Limitations of Hardy-Weinberg

Key Assumptions

• The Hardy-Weinberg equilibrium model assumes:
  • Large population size to minimize the effects of genetic drift
  • Random mating within the population (no assortative mating or inbreeding)
  • No migration of individuals or alleles into or out of the population
  • Absence of mutation, which can introduce new alleles or modify existing ones
  • No selection acting on the alleles under consideration
• Violations of these assumptions can lead to changes in allele frequencies and deviations from Hardy-Weinberg equilibrium

Consequences of Assumption Violations

• Small population sizes can result in genetic drift, causing random changes in allele frequencies over time
• Non-random mating (assortative mating or inbreeding) alters genotype frequencies and leads to deviations from Hardy-Weinberg expectations
  • Example: Inbreeding increases the frequency of homozygotes and decreases the frequency of heterozygotes
• Migration introduces new alleles or changes the frequencies of existing alleles, disrupting equilibrium
  • Example: Gene flow between populations can homogenize allele frequencies and reduce genetic differentiation
• Mutations create new alleles or modify existing ones, affecting allele frequencies over time
• Selection (natural or artificial) favors certain alleles, leading to changes in allele frequencies across generations
  • Example: Directional selection increases the frequency of advantageous alleles, while balancing selection maintains multiple alleles in a population

Hardy-Weinberg as a Null Model

• The Hardy-Weinberg equilibrium model assumes no evolution occurs in the population
• Serves as a null model to test for the presence of evolutionary forces
  • Deviations from expected Hardy-Weinberg proportions suggest the action of evolutionary processes
  • Allows researchers to identify populations or loci under selection, experiencing migration, or subject to other evolutionary forces

Evolutionary Forces on Allele Frequencies

Genetic Drift and the Wright-Fisher Model

• Genetic drift is modeled using the Wright-Fisher model, which assumes:
  • Finite population size
  • Discrete generations
  • Random sampling of alleles from one generation to the next
• The strength of genetic drift is inversely proportional to the effective population size ($N_e$)
  • Smaller populations experience greater drift and more rapid changes in allele frequencies
• The fixation probability of an allele due to genetic drift equals its initial frequency in the population
  • Example: If an allele has an initial frequency of 0.2, it has a 20% chance of eventually reaching fixation (frequency of 1) by drift alone

Selection and Relative Fitness

• Selection is modeled using the relative fitness of genotypes, a measure of a genotype's contribution to the next generation
• Directional selection occurs when one allele is favored over others, increasing its frequency over time
  • Example: Antibiotic resistance alleles in bacteria are favored under antibiotic exposure, leading to increased resistance in the population
• Balancing selection maintains multiple alleles in a population through mechanisms such as:
  • Heterozygote advantage: Heterozygotes have higher fitness than either homozygote (e.g., sickle cell anemia and malaria resistance)
  • Frequency-dependent selection: The fitness of an allele depends on its frequency in the population (e.g., rare color morphs in prey populations)

Mutation and Migration Models

• Mutation is incorporated into population genetic models by considering:
  • The rate at which new alleles arise
  • The fitness effects of those mutations
• The infinite alleles model assumes each mutation creates a unique allele, while the infinite sites model assumes each mutation occurs at a different nucleotide site
• Migration is modeled using:
  • The island model, which considers the exchange of alleles between subpopulations
  • Isolation-by-distance models that account for the geographic distribution of populations and the effect of distance on gene flow
• Population genetic models can incorporate multiple evolutionary forces simultaneously to study their combined effects on allele frequencies over time

Population Genetic Simulations and Implications

Predicting Evolutionary Trajectories

• Population genetic simulations predict the trajectory of allele frequencies under different evolutionary scenarios
• Estimate the fixation time (average number of generations until an allele becomes fixed or lost) using simulations and compare to theoretical expectations
  • Example: Simulate the fixation time of a beneficial allele under different population sizes and selection coefficients
• Demonstrate the potential for genetic drift to cause population differentiation, especially when migration rates are low or populations are small
  • Example: Simulate the divergence of allele frequencies between isolated populations of varying sizes over multiple generations

Maintaining Genetic Variation

• Explore the maintenance of genetic variation in a population through simulations incorporating:
  • Balancing selection
  • Mutation
  • Migration
• Illustrate the concept of selection-drift balance, where the effects of selection and drift on allele frequencies are in equilibrium
  • Example: Simulate a population under weak selection and varying population sizes to identify the conditions under which selection can effectively counteract drift

Population Structure and Genetic Diversity

• Investigate the role of population structure and gene flow in shaping patterns of genetic diversity using simulations that model different migration rates and population sizes
• Identify the conditions under which certain evolutionary outcomes are more likely to occur, such as:
  • The fixation of beneficial alleles
  • The maintenance of polymorphisms
  • Example: Simulate the spread of a beneficial allele through a metapopulation with varying levels of connectivity and subpopulation sizes

Conservation and Management Implications

• Predict the effects of population fragmentation, bottlenecks, or inbreeding on genetic diversity using population genetic simulations
  • Example: Simulate the loss of genetic diversity in a small, isolated population over multiple generations and compare to a larger, connected population
• Inform conservation strategies by modeling the potential consequences of different management actions on population genetic parameters
  • Example: Simulate the effects of translocation or supplementation on the genetic diversity and adaptive potential of a threatened population