Population Genetics and Hardy-Weinberg Equilibrium

Population Genetics

Genetic Variation and Evolution

Genetic variation within a population is essential for evolution to occur. Without variation, evolution cannot proceed, as alleles must change in frequency over time for evolutionary processes to take place.

• Genetic Variation: Differences in DNA among individuals within a population.

• Gene Pool: The total collection of alleles in a population.

• Allele Frequency: The proportion of a specific allele among all alleles for a gene in a population.

• Population: A group of individuals of the same species living in the same area and interbreeding.

• Example: Caribou populations in the Yukon may share genes but are not totally isolated, leading to genetic mixing.

Measuring Genetic Diversity

Genetic diversity is measured by examining the gene pool and calculating allele frequencies. This helps scientists understand how populations evolve over time.

• Gene Pool Analysis: Describes all alleles present in a population.

• Allele Frequency Calculation: Frequency of an allele = (Number of copies of the allele) / (Total number of alleles for that gene).

• Example: In a flower population, the frequency of an allele for flower color is determined by counting the number of copies of that allele among all flowers.

Hardy-Weinberg Equilibrium

Principle and Assumptions

The Hardy-Weinberg equilibrium describes a state in which allele frequencies in a population remain constant from generation to generation, provided certain conditions are met. This principle serves as a null model for evolution.

• Assumptions:

  • No mutations

  • Random mating

  • No natural selection

  • Extremely large population size

  • No gene flow (migration)

• Implication: If all assumptions are met, evolution does not occur and allele frequencies remain unchanged.

• Violation: If any assumption is violated, evolution may occur and allele frequencies can change.

Calculating Allele and Genotype Frequencies

Allele and genotype frequencies can be calculated using the Hardy-Weinberg equation. This allows prediction of genetic makeup in a population.

• Allele Frequency:

  • Let p = frequency of one allele (e.g., dominant)

  • Let q = frequency of the other allele (e.g., recessive)

  • Since there are only two alleles, $p + q = 1$

• Genotype Frequency:

  • Homozygous dominant: $p^2$

  • Heterozygous: $2pq$

  • Homozygous recessive: $q^2$

  • Sum of genotype frequencies: $p^2 + 2pq + q^2 = 1$

• Example: If the frequency of allele R is 0.8 and allele r is 0.2, then:

  • Homozygous RR: $0.8^2 = 0.64$

  • Heterozygous Rr: $2 imes 0.8 imes 0.2 = 0.32$

  • Homozygous rr: $0.2^2 = 0.04$

Conditions for Hardy-Weinberg Equilibrium

All five conditions must be met for a population to be in Hardy-Weinberg equilibrium. If any are violated, allele frequencies may change, indicating evolution.

Condition	Description
No mutations	Genetic information remains unchanged
Random mating	All individuals have equal chance to mate
No natural selection	No differential survival or reproduction
Large population size	Minimizes effects of genetic drift
No gene flow	No migration of individuals in or out

Applications of Hardy-Weinberg Equation

The Hardy-Weinberg equation is used in medical genetics to estimate carrier frequencies for genetic diseases, such as phenylketonuria (PKU).

• Example: If PKU is caused by a recessive allele, the frequency of carriers can be estimated using $2pq$.

• Application: Helps predict the proportion of individuals who carry or express a genetic disorder.

Causes of Evolutionary Change

When populations do not meet Hardy-Weinberg conditions, evolutionary changes can occur due to:

• Mutation: Introduction of new alleles

• Non-random mating: Certain individuals mate more frequently

• Natural selection: Differential survival and reproduction

• Genetic drift: Random changes in allele frequencies, especially in small populations

• Gene flow: Movement of alleles between populations

Summary Table: Hardy-Weinberg vs. Evolutionary Change

Hardy-Weinberg Equilibrium	Evolutionary Change
Allele frequencies remain constant	Allele frequencies change over time
No evolution occurs	Evolution occurs
All five conditions met	One or more conditions violated

Additional info: The notes include examples and analogies (such as colored balls representing alleles) to illustrate allele frequency calculations and the effects of random sampling. The application to medical genetics (PKU) is also discussed, showing real-world relevance.