Premed · Premed · Genetics
Lecture 19: Population Genetics and Hardy-Weinberg Equilibrium
Genetics
Learning Objectives
By the end of this lecture, students will be able to:
- Define a population in genetic terms and distinguish between Mendelian genetics and population genetics
- State the Hardy-Weinberg principle and list its five assumptions
- Apply the Hardy-Weinberg equations (p + q = 1; p^2 + 2pq + q^2 = 1) to calculate allele and genotype frequencies
- Identify the five evolutionary forces that disrupt Hardy-Weinberg equilibrium
- Explain how natural selection, genetic drift, mutation, migration, and non-random mating alter allele frequencies
- Apply the Hardy-Weinberg model to estimate carrier frequencies for autosomal recessive disorders
Lecture Content
I. Foundations of Population Genetics
Population genetics is the study of allele frequency distribution and change in populations under the influence of evolutionary forces. A population is a group of interbreeding individuals of the same species sharing a common gene pool, which is the total collection of all alleles at all loci in a population at a given time.
Allele frequency (conventionally denoted p and q for a two-allele system) is the proportion of a specific allele among all alleles at that locus in the population, where p + q = 1. Genotype frequency is the proportion of individuals in a population with a particular genotype and can be observed by counting genotypes directly when phenotypes are distinguishable or through molecular genotyping. Allele frequencies can be calculated from genotype counts: if N is the total number of individuals, then p = [2n(AA) + n(Aa)] / 2N and q = [2n(aa) + n(Aa)] / 2N.
<image>Panel A: Diagram illustrating a gene pool concept — a large circle representing a population with many colored dots (two colors representing two alleles), with the allele frequency calculation shown beside it. Panel B: Worked example showing a population of 1000 individuals with genotype counts (320 AA, 480 Aa, 200 aa), step-by-step calculation of allele frequencies (p = 0.56, q = 0.44), and genotype frequencies. Panel C: Comparison table distinguishing Mendelian genetics (focused on individual crosses, family pedigrees, ratios) from population genetics (focused on allele frequencies in groups, evolutionary change, equilibrium models).</image>
II. The Hardy-Weinberg Principle
Proposed independently by G.H. Hardy (a mathematician) and Wilhelm Weinberg (a physician) in 1908, the Hardy-Weinberg principle states that in a large, randomly mating population with no evolutionary forces acting, allele frequencies and genotype frequencies remain constant from generation to generation. The Hardy-Weinberg equations are: allele frequencies p + q = 1, and genotype frequencies p^2 + 2pq + q^2 = 1, where p^2 is the frequency of AA homozygotes, 2pq is the frequency of Aa heterozygotes, and q^2 is the frequency of aa homozygotes. Equilibrium is reached in a single generation of random mating for autosomal loci.
Five assumptions must hold for a population to be in Hardy-Weinberg equilibrium: no mutation (no new alleles are created or converted), no natural selection (all genotypes have equal fitness), infinitely large population size (no random fluctuation in allele frequency due to genetic drift), no migration or gene flow (no alleles enter or leave the population), and random mating (individuals pair without regard to genotype). Hardy-Weinberg equilibrium serves as a null model: deviations from expected genotype frequencies indicate that one or more evolutionary forces are at work.
III. Applying Hardy-Weinberg to Medical Genetics
One of the most important clinical applications of the Hardy-Weinberg model is estimating carrier frequencies for autosomal recessive disorders. For cystic fibrosis in European-descent populations, the incidence of affected homozygotes (q^2) is approximately 1/2,500. Taking the square root gives q = 1/50 = 0.02, so p = 1 - 0.02 = 0.98, and the carrier frequency (2pq) = 2 x 0.98 x 0.02 = 0.0392, or approximately 1 in 25 individuals. For sickle cell disease in some West African populations, q^2 is approximately 0.04, giving q = 0.2 and a carrier frequency of approximately 0.32. The high allele frequency in this case is maintained by heterozygote advantage (balancing selection), as carriers have increased resistance to malaria.
To test for Hardy-Weinberg equilibrium, a chi-square goodness-of-fit test is used to compare observed genotype frequencies to expected frequencies. A statistically significant deviation indicates that the population is not in equilibrium at that locus.
<image>Panel A: Mathematical derivation of Hardy-Weinberg genotype frequencies using a mating table or Punnett square at the population level — showing sperm (p and q across the top) and eggs (p and q down the side) combining to give p^2, 2pq, and q^2. Panel B: Worked clinical example for cystic fibrosis — flowchart starting from disease incidence (1/2500), calculating q, p, and carrier frequency (2pq = ~1/25), with a population diagram showing relative proportions of AA, Aa, and aa individuals. Panel C: Graph showing the relationship between allele frequency (q on the x-axis from 0 to 1) and genotype frequencies (p^2, 2pq, q^2 plotted as curves), highlighting that heterozygote frequency is maximized when p = q = 0.5.</image>
IV. Forces That Disrupt Hardy-Weinberg Equilibrium
Natural selection is the differential survival and reproduction of individuals based on genotype. Directional selection favors one extreme phenotype and shifts allele frequency in one direction. Stabilizing selection favors intermediate phenotypes and reduces genetic variation. Disruptive (diversifying) selection favors both extremes and can increase variation. Balancing selection maintains multiple alleles, as in heterozygote advantage for sickle cell trait. The selection coefficient (s) quantifies the reduction in fitness of a genotype relative to the fittest genotype.
Genetic drift is the random change in allele frequency due to finite population size, and its effects are strongest in small populations. The bottleneck effect occurs when a drastic reduction in population size leads to loss of genetic diversity, as seen in the cheetah population. The founder effect occurs when a small group establishes a new population with allele frequencies that may not represent the source population, as exemplified by the high frequency of Ellis-van Creveld syndrome in the Amish. Drift can fix or eliminate alleles regardless of their selective value.
Mutation introduces new alleles into the population at typical rates of 10^-4 to 10^-8 per locus per generation. Alone, mutation changes allele frequencies very slowly, but it provides the raw material upon which selection and drift act. Gene flow (migration) is the movement of alleles between populations and tends to homogenize allele frequencies between them. It can introduce new alleles or maintain deleterious alleles through migration-selection balance.
Non-random mating alters genotype frequencies without directly changing allele frequencies. Assortative mating occurs when individuals mate with others of similar (positive) or dissimilar (negative) phenotype. Inbreeding is mating between relatives and increases homozygosity while decreasing heterozygosity. The inbreeding coefficient (F) measures the probability that two alleles at a locus are identical by descent.
<image>Panel A: Five panels illustrating each evolutionary force disrupting HW equilibrium: (1) Natural selection — differential survival shown with color-coded organisms, (2) Genetic drift — simulation graphs showing allele frequency fluctuation in small vs. large populations, (3) Mutation — arrow showing allele A mutating to allele a at a low rate, (4) Gene flow — two populations exchanging individuals via migration arrows, (5) Non-random mating — diagram showing assortative mating and inbreeding increasing homozygosity. Panel B: Comparison of bottleneck effect and founder effect — the bottleneck shows a large population reduced to few survivors then re-expanding with reduced diversity; the founder effect shows a small migrant group establishing a new population with skewed allele frequencies. Panel C: Graph showing the inbreeding coefficient (F) effect on genotype frequencies — as F increases from 0 to 1, heterozygosity (2pq) decreases toward zero while homozygosity increases.</image>
V. Natural Selection in Detail
Fitness (w) is the relative reproductive success of a genotype compared to the most fit genotype. The most fit genotype has w = 1, while less fit genotypes have w = 1 - s, where s is the selection coefficient. Selection against a recessive homozygote (as in genetic disease) assigns fitnesses of AA = 1, Aa = 1, aa = 1 - s. Such selection is inefficient at low allele frequencies because most copies of the a allele are hidden in heterozygotes, which explains why deleterious recessive alleles persist in populations.
Heterozygote advantage (overdominance) occurs when the heterozygote has the highest fitness (AA = 1 - s1, Aa = 1, aa = 1 - s2), leading to a stable equilibrium at which both alleles are maintained. The classic example is sickle cell trait and malaria resistance, where the equilibrium frequency of the sickle allele is q_hat = s1 / (s1 + s2). Mutation-selection balance describes the equilibrium at which the frequency of a deleterious allele reflects the balance between new mutations introducing it and selection removing it. For a recessive lethal allele, q_hat = sqrt(mu/s), and for a dominant lethal, q_hat = mu/s.
VI. Measuring Genetic Variation in Populations
A locus is considered polymorphic if the most common allele has a frequency less than 0.95 (or 0.99, depending on the convention used). Heterozygosity (H) is the average proportion of heterozygous loci per individual. When observed heterozygosity (Ho) is less than expected heterozygosity (He) under Hardy-Weinberg, this suggests inbreeding or population substructure.
F-statistics, developed by Sewall Wright, partition genetic variation within and between populations. F_IS measures inbreeding within subpopulations, F_ST measures genetic differentiation between subpopulations (the fixation index), and F_IT measures overall inbreeding in the total population. F_ST is widely used to measure population structure; typical human F_ST values range from 0.10 to 0.15, indicating that most human genetic variation exists within rather than between populations.
