Premed · Premed · General Biology 2
Lecture 3: Population Genetics and Hardy-Weinberg
General Biology II — Organismal, Evolution & Ecology
Learning Objectives
By the end of this lecture, students will be able to:
- Define a population in genetic terms and explain the concept of a gene pool
- State the Hardy-Weinberg principle and its five assumptions
- Use the Hardy-Weinberg equations to calculate allele and genotype frequencies
- Identify the conditions under which evolution occurs (violations of Hardy-Weinberg equilibrium)
- Explain the four mechanisms of evolution: mutation, gene flow, genetic drift, and natural selection
- Distinguish between genetic drift and natural selection as agents of evolutionary change
Lecture Content
I. Populations and Gene Pools
A population, in genetic terms, is a group of individuals of the same species living in the same area and interbreeding. The gene pool encompasses the total collection of all alleles present in that population at a given time. Population geneticists quantify the genetic composition of populations using two key measures. Allele frequency is the proportion of a specific allele relative to all alleles at that locus in the population, calculated as the number of copies of that allele divided by the total number of alleles at the locus. For a diploid organism with N individuals, there are 2N alleles at each locus. Genotype frequency is the proportion of individuals carrying a particular genotype. The central insight of population genetics is that tracking how allele and genotype frequencies change over time is, by definition, the study of evolution.
II. The Hardy-Weinberg Principle
Proposed independently by the mathematician G.H. Hardy and the physician Wilhelm Weinberg in 1908, the Hardy-Weinberg principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of evolutionary influences. This principle serves as a null hypothesis -- a baseline against which real populations can be measured to detect whether evolution is occurring.
For a locus with two alleles, A and a, let p represent the frequency of allele A and q represent the frequency of allele a. Since these are the only two alleles, their frequencies must sum to one: p + q = 1. The Hardy-Weinberg genotype frequency equation follows from the random combination of alleles: p^2 + 2pq + q^2 = 1, where p^2 is the frequency of homozygous dominant individuals (AA), 2pq is the frequency of heterozygotes (Aa), and q^2 is the frequency of homozygous recessive individuals (aa).
This elegant mathematical relationship holds only when five stringent assumptions are met. There must be no mutation introducing new alleles, no gene flow through immigration or emigration, an effectively infinite population size so that random sampling error (genetic drift) is negligible, completely random mating with no preference based on genotype, and no natural selection so that all genotypes have equal fitness. If any of these conditions is violated, allele frequencies will change -- and evolution, by definition, is occurring.
<image>A diagram illustrating Hardy-Weinberg equilibrium across two generations. Panel A: A gene pool represented as a jar of colored marbles — dark (A allele, frequency p = 0.6) and light (a allele, frequency q = 0.4). Panel B: Random combination of alleles produces genotypes in the next generation: p² = 0.36 (AA), 2pq = 0.48 (Aa), q² = 0.16 (aa), shown as a Punnett square. Panel C: Bar graphs showing that allele frequencies (p = 0.6, q = 0.4) remain unchanged across generations when all five assumptions are met. Genotype frequencies also remain stable at their expected proportions.</image>
III. Applying Hardy-Weinberg: Problem Solving
The Hardy-Weinberg equations find their most practical application in medical genetics, where they are used to estimate carrier frequencies from disease prevalence data. Consider cystic fibrosis, an autosomal recessive disorder that affects approximately 1 in 2,500 Caucasians. Since affected individuals are homozygous recessive, q^2 = 1/2500 = 0.0004. Taking the square root gives q = 0.02, and since p + q = 1, p = 0.98. The carrier frequency -- heterozygous individuals who carry one copy of the disease allele without showing symptoms -- is 2pq = 2(0.98)(0.02) = 0.0392, or approximately 1 in 25 people. This surprisingly high carrier frequency explains how a rare disease can persist in a population.
To test whether a population is actually in Hardy-Weinberg equilibrium, researchers observe genotype frequencies, calculate expected frequencies using the Hardy-Weinberg equations, and compare the observed and expected values using a chi-square test. A statistically significant deviation indicates that one or more of the five assumptions is being violated. The equations can be extended to loci with three or more alleles (where p + q + r = 1, and genotype frequencies are found by expanding the squared sum), and to X-linked loci where males, being hemizygous, have allele frequencies that directly equal genotype frequencies.
IV. Agents of Evolutionary Change
A. Mutation
Mutation is the ultimate source of all new genetic variation -- without it, evolution would eventually grind to a halt as selection exhausted the existing supply of alleles. However, mutation alone changes allele frequencies only very slowly, with typical mutation rates ranging from 10^-5 to 10^-9 per gene per generation. Most mutations are neutral or deleterious; genuinely beneficial mutations are rare. Mutation's primary evolutionary role is therefore to create the raw material upon which other evolutionary forces -- particularly natural selection and genetic drift -- can act. The types of mutations relevant to population genetics include point mutations (substitutions), insertions and deletions, gene duplications that provide raw material for new gene functions, and chromosomal rearrangements.
B. Gene Flow (Migration)
Gene flow is the transfer of alleles between populations through the migration of individuals or their gametes. Its most consistent effect is to homogenize allele frequencies between populations, reducing genetic differences that might otherwise accumulate through drift or local selection. Gene flow can introduce entirely new alleles to a population and can counteract the divergent effects of natural selection and genetic drift. When humans migrate between previously isolated populations, for example, gene flow reduces the genetic differentiation that had built up during their separation.
C. Genetic Drift
Genetic drift refers to random changes in allele frequencies that occur by chance in finite populations. Because it arises from the statistical sampling error inherent in reproduction -- not every allele in the parental generation will be equally represented among surviving offspring -- drift is more pronounced in small populations than in large ones. Unlike natural selection, drift is non-adaptive: the allele frequency changes it produces are random with respect to fitness. Over time, drift can lead to the fixation of an allele (frequency reaches 1) or its complete loss (frequency reaches 0), and it consistently reduces genetic variation within a population.
Two special cases of genetic drift deserve attention. The founder effect occurs when a small group of individuals colonizes a new area, carrying with them a gene pool that is a non-representative sample of the source population. The Amish communities of Pennsylvania, for example, descended from a handful of founding families, some of whom happened to carry the allele for Ellis-van Creveld syndrome -- a condition now found at unusually high frequency in Amish populations. Similarly, the Afrikaner population of South Africa shows elevated frequencies of Huntington disease traceable to its small founding population.
The bottleneck effect occurs when a catastrophic event -- a natural disaster, epidemic, or habitat destruction -- dramatically reduces population size. The survivors carry only a subset of the original population's genetic diversity, and allele frequencies may shift dramatically by chance. The northern elephant seal was hunted to approximately 20 individuals in the nineteenth century; though the population has since recovered numerically, it retains extremely low genetic diversity. Cheetahs show similarly depressed genetic variation, likely the legacy of a population bottleneck roughly 10,000 years ago.
<image>A comparison of genetic drift in large versus small populations. Panel A: A large population (N = 500) — five computer-simulated allele frequency trajectories over 100 generations, all fluctuating slightly around p = 0.5, none reaching fixation or loss. Panel B: A small population (N = 25) — five simulated trajectories showing dramatic random fluctuations, with several alleles reaching fixation (p = 1.0) or loss (p = 0). Panel C: Illustration of the bottleneck effect — a large diverse population (many colored dots) passes through a narrow bottleneck (natural disaster), resulting in a small surviving population with reduced color diversity, which then expands into a larger but less diverse population.</image>
D. Non-random Mating
Non-random mating does not directly change allele frequencies, but it alters genotype frequencies in ways that can have significant evolutionary consequences. Assortative mating, in which individuals preferentially mate with others of similar (positive assortative) or different (negative assortative) phenotype, changes the distribution of genotypes. Positive assortative mating increases homozygosity. Inbreeding -- mating between close relatives -- has a similar effect, increasing homozygosity across the entire genome. This matters because it exposes deleterious recessive alleles in the homozygous state, leading to inbreeding depression: a measurable reduction in fitness due to the expression of harmful recessives. The inbreeding coefficient (F) quantifies the probability that two alleles at a locus are identical by descent. Sexual selection, by contrast, is a form of non-random mating that does change allele frequencies and is therefore a special case of natural selection rather than merely a violation of the random mating assumption.
V. Interactions Between Evolutionary Forces
In real populations, multiple evolutionary forces operate simultaneously, and their interactions shape the genetic trajectory of populations. Mutation introduces new variation, while natural selection and genetic drift determine the fate of that variation. Gene flow and genetic drift have opposing effects: gene flow homogenizes populations by spreading alleles between them, while drift causes populations to diverge through random fluctuations. Natural selection and genetic drift can work in the same or opposite directions, and the relative strength of each depends on population size -- in large populations, selection dominates over drift, but in small populations, drift can overpower even moderately strong selection.
Balancing selection maintains genetic variation within populations through mechanisms that prevent any single allele from reaching fixation. Heterozygote advantage (overdominance) occurs when heterozygotes have higher fitness than either homozygote. The classic example is sickle cell anemia in malaria-endemic regions: individuals heterozygous for the sickle cell allele (HbA/HbS) are resistant to malaria without suffering the severe anemia that afflicts HbS homozygotes. Frequency-dependent selection creates a fitness advantage for rare phenotypes. In negative frequency-dependent selection, the rarer a phenotype becomes, the higher its fitness, which maintains polymorphism. Scale-eating cichlids in African lakes illustrate this principle -- left-mouthed and right-mouthed morphs are maintained in roughly equal frequencies because prey fish learn to avoid whichever morph is currently more common, giving the rarer morph a feeding advantage.
<image>A diagram illustrating heterozygote advantage using the sickle cell anemia example. Panel A: A map of Africa showing the geographic overlap between malaria prevalence (shaded red) and high frequency of the sickle cell allele (HbS, shaded blue), with overlapping regions highlighted. Panel B: A table showing the three genotypes (HbA/HbA, HbA/HbS, HbS/HbS), their phenotypes (normal, sickle cell trait, sickle cell disease), their malaria resistance (susceptible, resistant, resistant but severe anemia), and their relative fitness in malaria-endemic regions (lower, highest, lowest). Panel C: A graph showing that the equilibrium frequency of HbS is maintained by balancing selection where it confers heterozygote advantage against malaria.</image>
