BSCI 222 Principles of Genetics - Lecture Notes

BSCI 222 Principles of Genetics - Prof. Thomas D. Kocher

Lecture 14: Population Genetics

Chapter 25 - Key Topics: (#20, 21, 25, 28, 41)

What Controls the Frequency of Alleles and Genotypes in Populations?

• Focus on how allele and genotype frequencies are maintained and change in populations.

Population Genetics

• Definition: Population genetics is the study of allele frequency distribution and change in a population.
  • Alleles: variants of a gene.
  • Important not to confuse dominance with allele frequency; a dominant allele can exist at low frequencies.
  • Example: If A is dominant over a, then the presence of A in genotype does not mean it is frequent in the population.

Calculating Allele Frequencies from Genotype Frequencies

Given Data:

• AA: 17 individuals
• Aa: 45 individuals
• aa: 38 individuals
• Total: 100 individuals
• Definitions:
  • $p = f_A = \frac{2(17) + 45}{200} = \frac{79}{200} = 0.395$
  • $q = f_a = \frac{2(38) + 45}{200} = \frac{121}{200} = 0.605$
• Genotypic Frequencies:
  • Frequency of AA, $P = f(AA) = 0.17$
  • Frequency of Aa, $H = f(Aa) = 0.45$
  • Frequency of aa, $Q = f(aa) = 0.38$
• Alternative calculation of $p$:
  • p = rac{P + \frac{H}{2}}{1} = 0.17 + \frac{0.45}{2} = 0.395

Hardy-Weinberg Expectations

• Gametes during random mating:
  • Sperm: A (p), a (q)
  • Eggs: A (p), a (q)
• Hardy-Weinberg Principle states that under conditions of random mating, the genotype frequencies can be expressed as:
  • $f(AA) = p^2$
  • $f(Aa) = 2pq$
  • $f(aa) = q^2$
• Generation proportions:
  • Genotypes expected in the next generation: $p^2 ext{(AA)}, 2pq ext{(Aa)}, q^2 ext{(aa)}$

Modified Punnett Square

• A method to work with unequal frequencies of alleles:
  • Layout displays frequencies of alleles, similar to a standard Punnett square but accounts for p and q variants.

Genotypic Proportions vs. Allele Frequency

• Graphic representation varies according to allele frequency, with observations of genotypic proportions:
  • Graph data visualizes frequency of AA, Aa, and aa as allele frequency ranges change.

Hardy-Weinberg Extensions

• For populations with more than 2 alleles:
  • Utilize binomial expansion:
  • $(p + q + r)^2 = p^2 + 2pq + q^2$
  • 3 alleles: $f(A^1) = p$, $f(A^2) = q$, $f(A^3) = r$
    • Genotypic frequencies:
    • $f(A^1A^1) = p^2$
    • $f(A^2A^2) = q^2$
    • $f(A^3A^3) = r^2$
    • $f(A^1A^2) = 2pq$
    • $f(A^1A^3) = 2pr$
    • $f(A^2A^3) = 2qr$

Testing Hardy-Weinberg Expectations

Observed Genotype Frequencies:

• AA: 17
• Aa: 45
• aa: 38

Calculate Expected Frequencies:

• $AA: p^2 \times 100 = (0.395)^2 \times 100 = 15.6$
• $Aa: 2pq \times 100 = 2(0.395)(0.605) \times 100 = 47.8$
• $aa: q^2 \times 100 = (0.605)^2 \times 100 = 36.6$
• Allele Frequencies: $p = f<em>A = 0.395$, $q = f</em>a = 0.605$

Chi-Square Test for Hardy-Weinberg

• Degrees of freedom df = 1 (3 categories - 2)
• Chi-square critical value ($\alpha = 0.05$, df = 1) = 3.84
• Deviations calculated:
  • $Genotype | Observed | Expected | (O-E)^2/E$
  • AA: 17, 15.6, 0.126
  • Aa: 45, 47.8, 0.164
  • aa: 38, 36.6, 0.054
• Total Chi-Square = 0.344
• Results indicate acceptance of null hypothesis; population meets Hardy-Weinberg expectations.

Deviations from Hardy-Weinberg Expectations

Causes:

• 4 Forces that change allele frequencies:
  1. Random Genetic Drift
  2. Mutation
  3. Migration
  4. Selection

Inbreeding:

• Extreme self-fertilization:
  • Example: AA x AA → AA, leading to loss of heterozygosity.

Table 25.2: Generational Increase in Homozygotes in Self-Fertilizing Population

• Data for ten generations starting with equal allele frequencies (p = q = 0.5) showing increasing homozygosity over generations.

Inbreeding Coefficient (F)

• Definition: Probability that two alleles in an individual are identical by descent.
• Calculate with $F = (\frac{1}{2})^n$, where n is the number of individuals in the shared ancestry path, excluding the inbred individual.

Table 25.3: Effects of Inbreeding on Mortality of Japanese Children

• Mortality rates are higher in children of related parents (higher F values).

Inbreeding Depression in Crops

• Graph showing average yield of corn per acre declines with increasing inbreeding coefficient (F).

The 4 Forces that Change Allele Frequency in Populations

1. Random Genetic Drift
   • Fluctuations in allele frequency due to random sampling of gametes each generation.

Models for Random Genetic Drift

• Coin Tossing Example:
  • Represents allele frequency changes through 100 trials, assessing the result of sampling variations.

Effect of Random Genetic Drift

• Variance in allele frequency equals $\frac{p q}{2N}$, where N is the size of the population.

Effective Population Size (Ne)

• Definition: Size of an ideal population with the same genetic properties as actual population.
• Typically smaller than actual census size.
• Formula for Ne with unequal gender numbers: $N<em>e = \frac{4N</em>mN<em>f}{N</em>m + N<em>f}$, where $Nm$ = number of males and $N_f$ = number of females.

Bottlenecks

• Definition: A severe reduction in population size, leading to reduced allelic diversity.
  • Example: Northern elephant seals reduced to ~20 individuals due to hunting, now at 30,000 but with low genetic variation.

2. Mutation

• Definition: A change in DNA sequence, affecting allele frequency.
  • Rate of forward mutation generally exceeds reverse mutation; equilibrium is reached when forward equals reverse mutation rates.

Information Regarding Mutation

• At equilibrium, allelic frequencies remain relatively stable under normal mutation rates.
• Formula for change in allele frequency due to mutation: $\Delta q = \mu p - <br /> u q$.

3. Migration

• Migration influences genetic makeup of populations by introducing new alleles or changing frequencies.
  • Population structure models display how gene flow affects allele frequencies in different environments, such as island and continental models.

Change in Allele Frequency Due to Migration

• Formula: $\Delta q = m(q<em>i - q</em>{ii})$, where m = migrant proportion.
  • For a small migration proportion (e.g., 1%), changes in allele frequency are minor unless involving significant differences in initial frequencies.

Impact of Migration on Hardy-Weinberg Expectations

• Migration can lead to deviations from expected frequencies; significant migration is necessary for noticeable impact.

4. Selection

• Selection acts on genetic traits subject to natural selection pressures.
• Types of selection include directional, stabilizing, and disruptive selection.

Types of Selection and Fitness Relations

• Table displays relationships between various fitness models and outcomes of different alleles in a population.
• Fitness definitions:
  • W₁₁, W₁₂, and W₂₂ relate to the fitnesses of specific genotype combinations.

Relative Changes in Allele Frequencies Due to Selection

• Factors affecting changes in allelic frequency expressed as:
  • $\Delta q = -spq^2$ for recessive traits.

Equilibrium Frequency Under Balancing Selection

• Formulas demonstrate expected equilibrium for alleles under selection, factoring in homozygote fitness levels.
• Typical expectation for recessive traits; more generations result in minimal changes in frequency for recessive alleles.

Summary of Forces Affecting Allelic Frequencies

• Review table encapsulating impacts of mutation, migration, genetic drift, and selection on allelic frequencies within populations, highlighting short and long-term effects.

Conclusion: Exploring Balance of Forces

• Suggestion to simulate evolutionary forces to better understand dynamics of allele frequency changes over time.