Hardy Weinberg and Population Genetics

Hardy Weinberg

Population and Gene Pool

• A population consists of members of the same species living in the same area at a given time.
• The gene pool is the set of all genes or genetic variation within a population, usually of a particular species.
• Greater variety in a gene pool enhances a population's ability to survive in a changing environment.
  • Example: Humans vs. bacteria.

Genotype Frequencies

• Genotype frequency is the proportion of a population with a particular genotype.
  • Example: Earlobes
    • In a school population, 144 are EE, 192 are Ee, and 64 are ee. Determine the genotypic frequency for each.

Phenotype Frequency

• Phenotype frequency is the proportion of a population with a particular phenotype.
• Example: Earlobes
  • What is the phenotype frequency of free earlobes?
  • What is the phenotype frequency for attached earlobes?

Allele Frequency

• Allele frequency is the rate of occurrence of a particular allele in a population with respect to a particular gene.
• Diploid organisms have two possible alleles for every gene, so the total number of alleles in a population is twice the number of individuals.

Hardy-Weinberg Principle

• In 1908, Godfrey Hardy and Wilhelm Weinberg introduced a mathematical model for studying population genetics.
• The principle states that allele frequencies in a population will remain constant over time if five conditions are met:
  1. The population is large enough that chance events will not alter allele frequencies.
  2. Random mating.
  3. No net mutations.
  4. No migration.
  5. No natural selection against any of the phenotypes.

Mathematical Equations

• p + q = 1.00
• p^2 + 2pq + q^2 = 1.00

Applying the Equations

• Always start calculations with q^2 (homozygous recessive) because this phenotype is visible and directly countable.

Example Problem

• In a fruit fly population, the frequency of the recessive allele for short wings (l) is 0.30. What are the expected genotype frequencies in the next generation?

Example: Retinal Disease

• The gene for retinal disease, causing blindness, is recessive.
• In Michigan, 9 out of 10,000 people have retinal disease.
• In Wisconsin, 2500 people were surveyed.
• If allele frequencies are the same in Wisconsin as in Michigan, how many people would be expected to have retinal disease in Wisconsin?

Example: Β-Thalassemia

• A program to detect carriers of β-thalassemia (a mild blood disorder) found the incidence of the disease to be 4% in a particular population.
• A recessive allele on an autosomal chromosome causes β-thalassemia.
• What is the frequency of the recessive β-thalassemia allele in the gene pool of this population?
  • Answer: 0.2

Sickle Cell Anemia

• Sickle cell anemia is caused by the sickle cell allele (Hb') of a gene that contributes to hemoglobin (Hb) production.
• Abnormal hemoglobin (hemoglobin-S) causes red blood cells to deform and block capillaries, leading to tissue damage.
• Individuals homozygous for the sickle cell gene rarely survive to reproductive age.
• Heterozygous individuals produce normal hemoglobin and a small percentage of hemoglobin-S and are more resistant to malaria.
• The frequency of the Hb' allele in Africa relates directly to the presence of malaria-causing organisms:
  • Western Africa: 0.15
  • Central Africa: 0.10
  • Southern Africa: 0.05
• What is the frequency of the Hb allele in the human gene pool in western Africa?
  • Answer: B (0.85)

Genetic Diversity and the Hardy-Weinberg Principle

• Genetic diversity is the degree of variation within a species or population.
• The Hardy-Weinberg principle represents an ideal situation that rarely occurs in natural populations.
• It is used to measure the amount of change in allele frequencies over time and is representative of a non-evolving population.
• Changes in frequencies indicate that evolution is occurring.

Processes That Cause Change in Allele Frequencies

1. Mutations

• A change in the DNA of an individual.
  • Example: A mutation may cause resistance to HIV.
• HIV enters white blood cells by attaching to protein receptors CD4 and CCR5. Some people are homozygous recessive for the gene that codes for CCR5 and lack a functional receptor, preventing HIV from entering the cell.
• Inheritable mutations diversify a gene pool, providing a selective advantage in changing environments.

2. Gene Flow

• Net movement of alleles from one population to another due to the migration of individuals.
  • Example: Wolves from one population travel and mate with wolves from a different population, introducing new alleles.
• Gene flow can reduce genetic differences among populations.

3. Non-Random Mating

• Individuals choose mates based on physical and behavioral traits, not randomly.
• Random mating is uncommon due to:
  • Preferred phenotypes.
  • Inbreeding.
• Positive effects of inbreeding:
  • Elimination of harmful recessive alleles if homozygous recessive individuals do not breed.
  • Self-fertilization allows plants to reproduce.

4. Genetic Drift

• A change in allele frequencies due to chance events in a small breeding population.
• Large populations are generally unaffected by genetic drift because chance events are unlikely to affect overall allele frequencies.

5. The Founder Effect

• Founders: A few individuals that form a new population.
• The new population is non-representative of the general population.
• Example: Amish
  • The Amish population grew from 200 founders who came to the U.S. from Germany and Switzerland in the mid-1700s.
  • They live in small rural communities and rarely intermarry outside their population.
  • One founder carried a recessive allele for Ellis-van Creveld syndrome, a type of dwarfism with extra fingers and short limbs.
  • Today, the Amish population has a higher incidence of this syndrome than any other population.

6. The Bottleneck Effect

• Gene pool change that results in a rapid decrease in population size.
• Example: Elephant seals
  • Due to overhunting, the population of elephant seals in 1890 was reduced to 20.
  • Although the population has recovered, they have low genetic diversity.