Introduction

The Hardy-Weinberg equilibrium principle says that allele frequencies in a population will remain constant in the absence of the evolutionary mechanisms: natural selection, mutation, genetic drift, gene flow, and non-random mating. In fact, we know they are always affecting populations. We have discussed natural selection, mutation, and genetic drift at length so far in this course. Before we can dive into Hardy-Weinberg Equilibrium, we need to dive into gene flow.

Gene Flow

Gene flow refers to the flow of alleles in and out of a population due to the migration of individuals or gametes (Fig 6.1). While some populations are fairly stable, others experience more flux. Many plants, for example, send their pollen far and wide, by wind or by pollinator, to pollinate other populations of the same species some distance away. Even a population that may initially appear to be stable, such as a pride of lions, experience immigration (coming into) and emigration (departing from) as developing males leave their mothers to seek out a new pride with genetically unrelated females. The flow of individuals in and out of populations changes the population’s allele frequencies. When an individual migrates into a new population, it may sometimes carry alleles that were not present in that population before, introducing new genetic variation into that population (Fig 6.1). Alternatively, if an individual emigrates from (leaves) a population where it was the only individual with a particular allele, it can result in its original population losing genetic diversity. Migration between populations causes them to become more genetically similar to each other. For example, alleles that may be present in one population but not the other can become present in both populations when a migrating individual introduces that allele to the new population.

There are many examples of populations evolving through gene flow. An appreciation of gene flow can help us understand the global distribution of HIV resistance in humans. The CCR5 mutation confers resistance to some forms of HIV, yet is not most common in areas with a high prevalence of HIV and AIDS. The mutation is relatively new: biochemical and biogeographic evidence suggest an origin in Northern Europe approximately 1,200 years ago. However, the mutation was distributed globally long before HIV and AIDS were relevant to human health. In fact, the mutation’s distribution pattern mirrors the Viking migration of the 9th through 11th centuries. Thus, we can hypothesize that Vikings carried the mutation with them as they conquered new territories, and passed the mutation to their descendants.

Hardy-Weinberg Equilibrium

In the early twentieth century, English mathematician Godfrey Hardy and German physician Wilhelm Weinberg stated the principle of equilibrium to describe the population’s genetic makeup. The theory, which later became known as the Hardy-Weinberg equilibrium, states that a population’s allele and genotype frequencies are inherently stable; the allele and genotype frequencies will not change unless some kind of evolutionary force is acting upon the population. The Hardy-Weinberg principle assumes an infinitely large population and conditions with no mutations, migration, emigration, or selective pressure for or against genotype. While no population can satisfy those conditions, the principle offers a useful model against which to compare real population changes. The Hardy-Weinberg Equilibrium is a null hypothesis. We can use it to generate predictions about what we would observe if it were true (i.e., if evolution were not happening) and compare those predictions to observed data. For example, if the allele frequency measured in the field differs from the predicted value, scientists can make inferences about what evolutionary forces are at play.

Allele and Genotype Frequency

Working under this theory, population geneticists represent different alleles as different variables in their mathematical models. The variable p represents the frequency of a particular allele (e.g., the Y allele for the trait of yellow peas in Mendel’s peas), while the variable q represents the frequency of another allele for the same trait (e.g., the y allele that confer the color green in Mendel’s peas). If these are the only two possible alleles for a given locus in the population then the frequency of these two alleles will sum to 100%, which can be represented as: p + q = 1. In other words, all the p alleles and all the q alleles comprise all of the alleles for that gene in the population.

Biologists are not interested in just the allele frequency, but also the frequencies of the resulting genotypes, known as the population’s genetic structure. The genotype frequency is important because it determines the phenotype distribution in the population. For genes with a simple dominance structure, if we observe the phenotype, we can know only the homozygous recessive allele’s genotype. We can use calculations to provide an estimate of the remaining genotypes. Since each individual carries two alleles per gene, if we know the allele frequencies (p and q), predicting the genotypes’ frequencies is a simple mathematical calculation to determine the probability of obtaining these genotypes if we draw two alleles at random from the gene pool. In the above scenario, an individual pea plant could be pp (YY), and thus produce yellow peas; pq (Yy), also yellow; or qq (yy), and thus produce green peas (Figure 6.2). In other words, the frequency of pp individuals is simply p²; the frequency of pq individuals is 2pq; and the frequency of qq individuals is q². Again, if p and q are the only two possible alleles for a given trait in the population, these genotypes frequencies will sum to one: p2 + 2pq + q2 = 1.

In our example in figure 6.2, the possible genotypes are homozygous dominant (YY), heterozygous (Yy), and homozygous recessive (yy). If we can only observe the phenotypes in the population, then we know only the recessive phenotype (yy). For example, in a garden of 500 pea plants, 455 might have yellow peas and 45 have green peas. We do not know how many are homozygous dominant (Yy) or heterozygous (Yy), but we do know that 45 of them are homozygous recessive (yy).

Therefore, by knowing the recessive phenotype and, thereby, the frequency of that genotype (45 out of 500 individuals or 0.09), we can calculate the number of other genotypes. If q² represents the frequency of homozygous recessive plants, then q² = 0.09. Therefore, q = 0.3. Because p + q = 1, then 1 – 0.3 = p, and we know that p = 0.7. The frequency of homozygous dominant plants (p²) is (0.7)² = 0.49. Out of 500 individuals, there are 49 homozygous dominant (YY) plants. The frequency of heterozygous plants (2pq) is 2(0.7)(0.3) = 0.42. Therefore, 210 out of 500 plants are heterozygous yellow (Yy).

In theory, if a population is at equilibrium—that is, there are no evolutionary forces acting upon it—generation after generation would have the same gene pool and genetic structure, and these equations would all hold true all of the time. Of course, even Hardy and Weinberg recognized that no natural population is immune to evolution. Populations in nature are constantly changing in genetic makeup due to drift, mutation, migration, selection, and non-random mating. As a result, the only way to determine the exact distribution of phenotypes in a population is to go out and count them. However, the Hardy-Weinberg principle gives scientists a mathematical baseline of a non-evolving population to which they can compare evolving populations and thereby infer what evolutionary forces might be at play. If the frequencies of alleles or genotypes deviate from the value expected from the Hardy-Weinberg equation, then the population is evolving.

References

Adapted from:

Clark, M.A., Douglas, M., and Choi, J. (2018). Biology 2e. OpenStax. Retrieved from https://openstax.org/books/biology-2e/pages/1-introduction

and

Fowler, S., Roush, R., & Wise, J. (2022). NSCC Academic Biology 1050. Nova Scotia Community College. Retrived from https://pressbooks.nscc.ca/biology1050/