Hardy-Weinberg Equilibrium Problem | Allele & Genotype Frequencies

The Hardy-Weinberg principle states that allele frequencies remain constant under specific conditions: p² + 2pq + q² = 1. To calculate allele frequencies from phenotype data: identify homozygous recessive frequency (q²), take square root to find q, then p = 1 - q. The ABO blood group system demonstrates multiple alleles (I^A, I^B, i) with genotypes: I^A I^A or I^A i = type A, I^B I^B or I^B i = type B, I^A I^B = type AB, ii = type O. Expected genotype frequencies are p², 2pq, 2pr, 2qr, and r². The chi-square test determines if a population is in Hardy-Weinberg equilibrium: χ² = Σ[(observed - expected)² / expected]. For biallelic systems, df = 1, critical value at p = 0.05 is 3.84.

For genes with more than two alleles, the Hardy-Weinberg equation expands accordingly. For three alleles (p, q, r), the equation becomes p² + q² + r² + 2pq + 2pr + 2qr = 1. Each homozygous term is squared and each heterozygous combination is multiplied by 2. This generalization allows analysis of complex inheritance patterns like human blood groups.

This section covers multiple alleles (more than two alleles for a gene) and the ABO blood group system with three alleles (I^A, I^B, i). It explains codominance between I^A and I^B, and recessiveness of i. The section demonstrates how to calculate genotypes and phenotypes for multiple alleles using the n(n+1)/2 formula.

This section covers the ABO blood group system and multiple alleles. The ABO system has three alleles: I^A, I^B, and i. I^A and I^B are codominant, while i is recessive. The possible genotypes are: I^A I^A or I^A i (blood type A), I^B I^B or I^B i (blood type B), I^A I^B (blood type AB), and ii (blood type O). Multiple alleles refer to a gene that has more than two alleles in a population, increasing genetic diversity. Students learn to apply these concepts to solve blood type inheritance problems.

Human blood groups are a classic example of multiple alleles. The three alleles (IA, IB, and i) determine blood group type. IA and IB are codominant (both expressed when present together, resulting in AB blood group), while i is recessive to both. The possible combinations are: IAIA or IAi = blood group A, IBIB or IBi = blood group B, IAIB = blood group AB, and ii = blood group O. This demonstrates how multiple alleles at a single locus can produce multiple phenotypes.

Population genetics has significant applications in conservation biology, including creating mating matrices to avoid inbreeding and maintain genetic diversity, monitoring populations affected by environmental disasters (like the Mariana dam disaster), tracking changes in genetic diversity over time, and assessing endogamy levels. These applications help conservationists make informed decisions about species management, reintroduction programs, and maintaining genetic health in threatened populations.

Population genetics has diverse applications across fields: (1) Integrated pest management - studying pest population genetics helps develop control strategies, as demonstrated by research on the alfalfa weevil in Argentina; (2) Conservation genetics - analyzing genetic diversity in species like llamas helps ensure sustainable resource management; (3) Pathogen evolution - studying pathogen population genetics (e.g., Sclerotinia in soybeans, E. coli in humans) helps predict and prevent disease outbreaks by understanding evolutionary potential.

This segment covers the application of population genetics to real-world genetic diseases. The instructor explains how to calculate the frequency of individuals affected by recessive genetic disorders, using the example of a disease affecting 1 in 1000 individuals. The calculation shows that if q² = 0.001, then q = √0.001 ≈ 0.0316, meaning the recessive allele frequency is approximately 3.16%. The dominant allele frequency is then p = 1 - q ≈ 0.9684. The heterozygous carrier frequency is calculated as 2pq = 2 × 0.9684 × 0.0316 ≈ 0.0612, meaning approximately 6.12% of the population are carriers. This demonstrates how population genetics principles are applied to understand disease prevalence and carrier frequencies in human populations.

Population genetics studies how genetic variation changes in populations over time, rather than focusing on individuals. A population is defined as a group of interbreeding individuals sharing a common gene pool. Researchers measure genetic diversity through phenotypic traits and genotypic analysis using molecular markers—specific DNA regions showing polymorphism between individuals. Microsatellites (short tandem repeats) are widely used for their high variability. Effective markers should show high polymorphism, codominance, independence from developmental stage, ease of use, and cost-effectiveness. PCR technology revolutionized conservation genetics by enabling rapid DNA amplification. Key parameters analyzed include allele frequencies, genotype frequencies, heterozygosity levels, population structure, and gene flow. Case studies demonstrate both successes and challenges: the Florida panther population was restored through introduction of genetically distinct individuals, growing from near-extinction to 120-230 adults by 2017. Conversely, Puerto Rican primates isolated since 1938 demonstrated that some populations can avoid significant inbreeding through behavioral mechanisms. Hybridization with domestic animals poses serious threats, as seen in Ethiopian wolves facing genetic swamping from village dogs.

Advanced Hardy-Weinberg applications include lethal alleles and heterozygote advantages. When homozygous recessive individuals die before reproducing, allele frequencies decrease but heterozygotes may persist due to selective advantages. For PKU (1 in 10,000 affected), q² = 0.0001 gives q = 0.01, p = 0.99, carrier frequency = 2pq = 0.0198 or 1.98%, yielding ~28 carriers in 14,000 people. Sickle cell anemia demonstrates heterozygote advantage—4% affected (q² = 0.04) gives q = 0.2, p = 0.8, and 32% heterozygotes who show malaria resistance. These examples illustrate how rare recessive alleles persist at low frequencies in populations due to balancing selection pressures.

The Chi-squared test (χ²) is a statistical method used in population genetics to determine whether a population is in Hardy-Weinberg equilibrium by comparing observed genotype frequencies to expected frequencies calculated from allele frequencies; the test uses degrees of freedom (number of classes minus one) and a 5% significance level (critical value 3.84), where a χ² value less than 3.84 indicates the population is in equilibrium and the hypothesis is not rejected.

The Hardy-Weinberg equilibrium is a fundamental principle stating that allele and genotype frequencies remain constant across generations in the absence of evolutionary forces. Three primary statistical methods test for equilibrium: (1) Chi-squared test comparing observed and expected genotype frequencies using Σ[(O-E)²/E], with degrees of freedom calculated as (number of genotype classes) - (number of alleles) - 1; (2) Likelihood ratio test (G-test) comparing likelihoods under full and reduced models using G = 2 × Σ[Oᵢ × ln(Oᵢ/Eᵢ)]; (3) Fisher's exact test for small samples using hypergeometric distribution. For multiple alleles (S alleles), genotype classes are S(S+1)/2, and df = (S-2)(S+1)/2. When HWE is rejected, biologists consider explanations including natural selection, genetic drift, mutation, migration, and non-random mating such as inbreeding.

Chi-squared analysis compares observed F1 generation genotype data with expected values from Hardy-Weinberg equilibrium calculations. The null hypothesis states no significant difference exists between observed and expected data. For three genotype groups (AA, AB, BB), degrees of freedom equals 2, with critical value 5.99 at P=0.05. In spreadsheets, calculate expected frequencies using p², 2pq, and q², then convert to individual counts by multiplying by population size and rounding to whole numbers. Calculate chi-squared components for each genotype using (Observed - Expected)² / Expected, then sum all components for the total chi-squared value.

Degrees of freedom equals number of genotypes minus number of alleles. Use statistical tables to find critical χ² value at α = 0.05 for the calculated degrees of freedom. If calculated χ² < theoretical χ², the population is in Hardy-Weinberg equilibrium (allele frequencies remain constant). If calculated χ² > theoretical χ², the hypothesis is rejected, indicating evolutionary forces are affecting the population.

Degrees of freedom (df) in Chi-square testing represent the number of independent pieces of information available for estimation. It is calculated as: df = number of categories - number of parameters estimated from the data. For genetic crosses with three phenotypic categories (AA, Aa, aa), df = 3 - 1 = 2. The '1' represents the single parameter (total number of trials) that was estimated from the data to calculate expected values. This accounts for the constraint that all expected values must sum to the total observed.