Population Genetics and Hardy-Weinberg Equilibrium

U.S. Crime Rates Since 1990s

  • Both violent and property crime rates in the U.S. have significantly decreased since the 1990s, regardless of whether data is sourced from the FBI or BJS.
  • Trends in violent and property crime from 1993-2022:
    • FBI data on violent crimes per 100,000 people decreased from 747.1 in 1993 to 380.7 in 2022.
    • BJS data on violent victimizations per 1,000 people ages 12+ decreased from 79.8 in 1993 to 23.5 in 2022.
    • FBI data on property crimes per 100,000 people decreased from 4,740.0 in 1993 to 1,954.4 in 2022.
    • BJS data on property victimizations per 1,000 households decreased from 101.9 in 1993 to 35.8 in 2022.
  • FBI figures include only reported crimes, while BJS figures include both unreported and reported crimes.

Concerns About Crime

  • Since 2021, concerns about crime have increased among both Republicans and Democrats.
  • Percentage of people who say reducing crime should be a top priority for the president and Congress:
    • Total: Increased from 47% in 2021 to 58% in 2024.
    • Republicans/Lean Republicans: Increased from 60% in 2021 to 68% in 2024.
    • Democrats/Lean Democrats: Increased from 39% in 2021 to 47% in 2024.

Genetic Diversity

  • When comparing the resilience of Narwhal and Beluga whale populations against a new virus, the population with greater genetic diversity is likely to be better equipped to survive.
  • Narwhals have shown long-term low genetic diversity despite a large population size (Westbury et al, 2019).

Heterozygosity and Inbreeding

  • Observed heterozygosity (HO) is represented by light bars, and the inbreeding coefficient (F{IS}) by dark bars. Grey bars represent heterozygosity measured at intergenic DNA.
  • A higher inbreeding coefficient indicates more inbreeding.
  • Wild cats are predicted to have the largest gene pool compared to purebred or mixed cats, because how much inbreeding coefficient they have.

Announcements

  • ILCS131 Quiz review sessions are scheduled.
  • Important dates to remember:
    • Learning reflection due 2/23.
    • Weekly lecture quiz due 2/23.
    • Homework quiz due 2/23.
    • First exam on 3/5 at 7 PM.
    • Short answer assignment due 2/19.

Evolution

  1. Definitions and preconditions.
  2. Artificial selection: proof of concept.
    • An example.
  3. Phenotypic variation.
  4. Genetic variation.
    • Sources and implications.
    • Heterozygosity.
    • Allele frequency.
  5. Hardy-Weinberg principle.
  6. Mechanisms:
    • Natural selection.
    • Genetic drift/migration.
  • Next topic: Speciation.

Population Genetics

  • Population genetics studies allele frequencies within populations, not just the number of genes.
  • It focuses on the frequency of a specific allele within the entire population.

Alcohol Metabolism and ALDH2

  • Acetaldehyde dehydrogenase (ALDH) converts acetaldehyde (harmful) into acetic acid (less harmful) and is the second step of detoxifying ethanol in the liver.

ALDH Alleles

  • Quick (Q) allele: Efficiently detoxifies acetaldehyde.
  • Slow (S) allele: Less efficient at detoxifying acetaldehyde.

ALDH Genotype and Allele Frequencies

  • Study of 100 males (half with alcoholism, half healthy controls) examined ALDH genotype and allele frequencies.
  • ALDH S allele is associated with reduced detoxification of alcohol.

Example Calculation: ALDH-Q Allele

  • In a study, we will calculate the percentage of total alleles in non-alcoholics that are represented by the ALDH-Q allele.
  • The slide refers to data from Thomasson et al., Am J. Hum Genetics, 1991.

Conclusions from ALDH Data

  • Based on the study data, considerations include:
    • Dominance relationships between ALDHQ and ALDHS.
    • The likelihood of alcoholics having the ALDHS allele.
    • Potential disappearance of the ALDHS allele from the population.

Allele vs. Genotype vs. Phenotype Frequency

  • Allele frequency, genotype frequency, and phenotype frequency are distinct concepts.
  • Example: In non-alcoholics, 88% may have at least one copy of the Q allele, but only 70% of all alleles are Q, while 30% are S.
  • This information does not determine dominance or recessiveness of alleles.

Calculating Allele Frequency

  • For two alleles, frequencies sum to 1 (p + q = 1).
  • Genotype frequencies also sum to 1 (pp + pq + qq = 1).

Butterfly Genotype Frequencies

  • A population of butterflies has genotype frequencies: 0.45 AA, 0.35 Aa, and 0.2 aa.
  • To find the frequency of the "a" allele, use: f(a) = \frac{1}{2} \cdot f(Aa) + f(aa)

Simplified Allele Frequency Calculation

  • Allele frequency = 1/2 (heterozygous) + homozygous for that allele.

Lactate Dehydrogenase (LDH) Polymorphism

  • In a minnow population, 1000 individuals were sampled.
  • Genotype frequencies: AA = 0.08, Aa = 0.28, aa = 0.64.
  • Calculate the allele frequency of the "A" allele.

Butterfly Gene Example

  • If the allele frequency of "a" is 25% and there are 10% heterozygotes in a population of 100 butterflies, determine the number of homozygous AA individuals.

Garden Peas Example

  • Garden peas have a dominant allele for fat, juicy peas (R) and a recessive allele for wrinkled peas (r).
  • The allele frequency of the dominant allele is 30%, and 20% of plants are heterozygotes.
  • Calculate the number of homozygous rr plants in a population of 100.

Winged Lemurs Example

  • A population of winged lemurs has a gene controlling tail rings with two alleles, M and F.
  • Genotype frequencies: MM: 0.5, MF: 0.3, FF: 0.2.
  • Calculate the allele frequency for F.

Calculating Allele Frequency for F

  • Basic formula: f(F) = f(FF) + \frac{1}{2} f(MF)
  • f(F) = 0.2 + \frac{1}{2}(0.3) = 0.35
  • The formula also means that f(M) = 0.65

Pigeon Wing Color Patterns

  • Pigeons have a gene that controls color patterns on their wings, with two alleles: bar (+) and barless (-).
  • Genotype frequencies: ++ = 0.4, -- = 0.4.
  • Calculate the genotype frequency of the "+-" heterozygotes.

Evolution Reminder

  1. Definitions and preconditions
  2. Artificial selection: proof of concept
  3. Genetic Variation
  4. Hardy Weinberg
  5. Mechanisms:
    • Natural Selection
    • Genetic Drift/migration
  • Next: Speciation

Evolution and Allele Frequency

  • Evolution is defined as the change in allele frequency within a population.
  • If allele frequencies are changing, evolution is occurring.
  • The Hardy-Weinberg equation tests whether evolution is happening at a specific locus.

Squirrel Color Variants

  • Eastern gray squirrels exhibit three variants: gray, gray/black, and black, due to varied expression of a single gene.
  • The black allele is currently rare.
  • Heterozygotes have an intermediate phenotype.
  • The question is whether black squirrels will eventually disappear or become more common.

Squirrel Population Example

  • In a large squirrel population without selection or other evolutionary mechanisms, allele frequencies should remain stable, regardless of frequency or dominance.

Squirrel Genotype Frequencies

  • Phenotype frequencies: Grey (bb) = 0.49, Brownish (Bb) = 0.42, Black (BB) = 0.09.
  • From these genotype frequencies, predictions can be made about the next generation.

Random Mating

  • Random mating involves all gametes (with one allele each at a locus) combining randomly.
  • This process is influenced by the frequency of the alleles.

Determining Expected Genotypes

  • Random mating gives all possible genotypes influenced by allele frequencies.

Calculating Allele Frequencies

  • Phenotype: Grey (bb) 0.49, Brownish (Bb) 0.42, Black (BB) 0.09.
  • f(b) = 0.49 + \frac{1}{2}(0.42) = 0.7
  • f(B) = 0.09 + \frac{1}{2}(0.42) = 0.3

Expected Genotype Frequency

  • By using the allele frequencies, you can determine what the expected genotypic frequencies are in the next generation.

Hardy-Weinberg Equilibrium

  1. The null hypothesis states that if alleles are in equilibrium, then no evolutionary forces are acting.
  2. Use allele frequencies to calculate expected genotype frequencies.
  3. If observed genotype frequencies match expected frequencies, the null hypothesis is supported.
  4. This state is called Hardy-Weinberg equilibrium.

Hardy-Weinberg Equilibrium Explained

  • If no factors cause alleles to leave the population, allele frequencies will remain constant from generation to generation.
  • It serves as a test: if observed frequencies match expected frequencies, no evolution is occurring.

Conditions for Hardy-Weinberg Equilibrium

  • If no evolutionary mechanism is operating, genotype frequencies should be in equilibrium.
  • Maggie May Does Not Smoke (mnemonic for conditions):
    • No Mutation
    • No Migration
    • No Drift
    • Non-random mating
    • No Selection
    • Large Population

Two Allele Situation

  • Consider two alleles, p and q:
    • p = frequency of the dominant allele
    • q = frequency of the recessive allele
  • Using decimals for frequency (e.g., 0.25, not 25%).
  • p + q = 1
  • Hardy-Weinberg Equilibrium is a test to see if evolution is occurring at a locus.