Chapter: Population Genetics 

Introduction

Gregor Mendel's foundational work in genetics demonstrated that understanding evolution requires a quantitative, mathematical approach. This insight became even clearer following the publication of Darwin's On the Origin of Species. In the early 20th century, two scientists—G.H. Hardy, an English mathematician, and Wilhelm Weinberg, a German physician—independently developed a mathematical model to study the genetic consequences of mating within populations. Interestingly, they arrived at the same model without knowing of each other's work. Such simultaneous discoveries are not uncommon in science.

The Gene Pool Concept

Hardy and Weinberg’s model relies on the concept of a gene pool—the collection of all the gametes, or reproductive cells, in a population. Imagine a massive pool containing all the sperm and egg cells produced by individuals in a species. They made a key assumption: all gametes combine randomly. This simplified, idealized condition allows us to make powerful predictions about the frequencies of genotypes in a population.

The Hardy-Weinberg Principle

The Hardy-Weinberg principle explores the behavior of a single gene with two alleles. The frequencies of these alleles are denoted as p for the first allele (A1) and q for the second allele (A2), where p + q = 1. Assuming random mating, the expected genotype frequencies in the next generation are as follows: the frequency of individuals homozygous for A1 (A1A1) will be p²; the frequency of heterozygous individuals (A1A2) will be 2pq; and the frequency of individuals homozygous for A2 (A2A2) will be q². Because these are the only possible genotypes, the sum of their frequencies must also equal one, giving us the equation p² + 2pq + q² = 1.

This simple model yields two important predictions. First, the frequencies of genotypes in a population can be calculated from the frequencies of alleles in the preceding generation. Second, as long as certain conditions are met, the allele frequencies in the population will remain constant from generation to generation. This stability implies that the population is not undergoing evolutionary change.

Example Calculation

Consider a population in which the frequency of allele A1 is 0.7 and the frequency of allele A2 is 0.3. The predicted genotype frequencies would then be: 0.49 for A1A1 (calculated as 0.7 squared), 0.42 for A1A2 (calculated as 2 times 0.7 times 0.3), and 0.09 for A2A2 (calculated as 0.3 squared). To determine the allele frequencies in the next generation, we sum the contributions from each genotype: A1 receives 0.49 from A1A1 individuals and half of 0.42 from the heterozygotes, giving a total of 0.70. Similarly, A2 receives 0.09 from A2A2 individuals and half of 0.42 from the heterozygotes, resulting in a total of 0.30. These allele frequencies remain unchanged, confirming that the population is in Hardy-Weinberg equilibrium.

Assumptions of the Hardy-Weinberg Model

The Hardy-Weinberg principle is best understood as a null model—a theoretical baseline against which real populations can be compared. For the principle to hold, several assumptions must be met: mating must be random, there must be no natural selection, the population size must be large enough to prevent genetic drift, there must be no migration (gene flow), and there must be no mutation introducing new alleles. If any of these conditions are violated, the allele frequencies in the population may change over time, indicating that evolution is occurring.

Types of Natural Selection

Natural selection can operate in several different ways, each with distinct consequences for a population’s genetic makeup. In directional selection, one extreme phenotype is favored over all others, causing the average trait value in the population to shift in a particular direction. A classic example is the evolution of longer necks in giraffes or the phenomenon of island dwarfism observed in certain elephants and human populations. In stabilizing selection, individuals with intermediate phenotypes are favored, which reduces variation in the trait without changing the average. This type of selection is seen in human birth weights, where both very low and very high birth weights are associated with increased mortality. In contrast, disruptive selection favors individuals at both extremes of a trait over those with intermediate values. This increases variation and can even lead to the formation of new species. An example might be rabbits in an environment with both dark soil and snow cover, where black and white fur provide camouflage, but gray fur offers no advantage.

Genetic Drift

Genetic drift refers to random changes in allele frequencies, especially in small populations. Unlike selection, which is non-random, genetic drift is a stochastic process that can lead to the fixation or complete loss of alleles, thereby reducing genetic variation. Two well-known instances of genetic drift are the founder effect and the population bottleneck. The founder effect occurs when a small group of individuals establishes a new population, carrying with them only a subset of the genetic diversity of the original population. This can result in unusual allele frequencies in the descendant population. In a population bottleneck, a drastic reduction in population size—due to events like natural disasters or disease—leads to a loss of genetic diversity and intensifies the effects of drift and inbreeding.

Gene Flow

Gene flow refers to the movement of alleles between populations. When individuals migrate and successfully reproduce in a new population, they introduce their genetic material into the gene pool. This movement can increase genetic diversity within a population and reduce genetic differences between populations. In this way, gene flow acts against the process of speciation by homogenizing genetic variation.

Mutation

Mutations are changes in the DNA sequence that introduce new alleles into a population. While many mutations are neutral or harmful, some can confer advantages that may be selected for in future generations. Mutation is particularly influential in asexual populations, where new genetic variation arises almost exclusively through this process. Over long timescales, mutation serves as the ultimate source of genetic variation in all populations.

Sexual Selection and Dimorphism

Sexual selection arises when individuals differ in their ability to attract mates, and it often results in the evolution of traits that improve mating success. Typically, females are more selective due to their higher reproductive investment, while males compete for access to mates. This can lead to pronounced sexual dimorphism—observable differences in size, coloration, or morphology between males and females of the same species. For example, in many bird species, males display bright plumage and elaborate behaviors to attract mates, while females remain more cryptic.

Conclusion

The Hardy-Weinberg principle provides a powerful framework for understanding genetic stability and change in populations. By identifying the conditions under which allele frequencies remain constant, scientists can better recognize when and why evolution occurs. When real populations deviate from Hardy-Weinberg predictions, it signals the action of evolutionary forces such as natural selection, genetic drift, gene flow, mutation, or sexual selection. Together, these mechanisms shape the genetic composition of populations and drive the evolutionary process over time.