Hardy-Weinberg law

SIGNIFICANCE: The Hardy-Weinberg law is the foundation for theories about evolution in local populations, often called microevolution. First formulated in 1908, it continues to be the basis of practical methods for investigations in fields from plant breeding and anthropology to law and public health.

Introduction

The Hardy-Weinberg law can be phrased in many ways, but its essence is that the genetic makeup of a population, which meets certain assumptions, will not change over time. More important, it allows quantitative predictions about the distribution of genes and genotypes within and among generations. It may seem strange that theories about fundamental mechanisms of evolution are based on a definition of conditions under which evolution will not occur. It is the nature of science that scientists must make predictions about the phenomena being studied. Without something with which to compare the results of experiments or observations, science is impossible. Sir Isaac Newton’s law of inertia plays a similar role in physics, stating that an object’s motion will not change unless it is affected by an outside force.

After the rediscovery of Mendelian genetics in 1900, some scientists initially thought dominant alleles would become more common than recessive alleles, an error repeated in each generation of students. In 1908, Godfrey Hardy published his paper “Mendelian Proportions in a Mixed Population” in the journal Science to counteract that belief, pointing out that by themselves, and Mendelian inheritance have no effect on an allele’s commonness. Implicit in Hardy’s paper was the idea that populations could be viewed as conglomerations of independent alleles, what has come to be called a “gene pool.” Alleles randomly combine in pairs to make up the next generation. This simplification is similar to Newton’s view of objects as simple points with mass.

Hardy, an English mathematician, wrote only one paper in biology. Several months earlier, Wilhelm Weinberg, a German physician, independently and in more detail had proposed the law that now bears both their names. In a series of papers, he made other contributions, including demonstrating Mendelian heredity in human families and developing methods for distinguishing environmental from genetic variation. Weinberg can justifiably be regarded as the father of human genetics, but his work, like Mendel’s, was neglected for many years. The fact that his law was known as Hardy’s law until the 1940s is an indictment of scientific parochialism.

The Hardy-Weinberg Paradigm

The Hardy-Weinberg “law” is actually a paradigm, a theoretical framework for studying nature. Hardy and Weinberg envisioned populations as collections of gametes (eggs and sperm) that each contain one copy of each gene. Most populations consist of organisms that have two copies of each gene. Each generation of individuals can be regarded as a random sample of pairs of gametes from the previous generation’s pool. The proportion of gametes that contain a particular allele is the frequency of that allele.

Imagine a population of one hundred individuals having a gene with two alleles, A and a. There are three genotypes (combinations of alleles) in the population: AA, aa (both homozygotes), and Aa (heterozygotes). If the population has the numbers of each listed in the table “Genome Frequencies,” then the genotype frequencies can be computed as shown.

The individuals of each genotype can be viewed as contributing one of each of their alleles to the gene pool, which has the composition shown in the table headed “Gene Pool Composition.”

This population can be described by the genotype ratio AA:Aa:aa = 0.36:0.38:0.16 and the allele frequencies A:a = 0.6:0.4. Note that allele frequencies must total 1.0, as must genotype frequencies.

The Hardy-Weinberg Law and Evolution

Allele and genotype frequencies would be of little use if they only described populations. By making a Punnett square of the gametes in the population and using allele frequencies, the table showing predicted genotype frequencies in the next generation will be obtained.

The predicted frequencies of homozygotes are 0.36 and 0.16; the frequency of Aa is 0.48 (adding the frequencies of Aa and aA). These are the same as the previous generation.

Hardy pointed out that if the frequency of A = p and the frequency of a = q, thenp + q = 1. Random mating can be modeled by the equation (p+ q) × (p + q) = 1, or more compactly (p + q)² = 1. This can be expanded to provide the genotype frequencies: p2 + 2pq + q² = 1. In other words, the ratio of AA:Aa:aa = p²:2pq:q². Substituting 0.6 for p and 0.4 for q produces the figures shown in the preceding table, but more compactly and easily. The Hardy-Weinberg concept may also be extended to genes with more than two alleles. Therefore, three predictions may be made for a Hardy-Weinberg population: frequencies of alleles p andq add up to 1.0 and will not change; the frequencies of genotypes AA, Aa, and aa will be p²:2pq:q², will sum to 1.0, and will not change (that is, they are in equilibrium); and if the genotype frequencies are not initially at equilibrium ratios, they will eventually reach equilibrium.

There are within-generation and between-generation predictions. Within any one generation, the ratios of the genotypes are predictable if allele frequencies are known; if the frequency of a genotype is known, allele frequencies can be estimated. Between generations, allele and genotype frequencies will not change as long as the following assumptions are met: (1) there are no mutations, (2) there is no with other populations, (3) mating is totally random, (4) the population is of infinite size, and (5) there is no natural selection. Violations of these assumptions define the five major evolutionary forces: mutation, gene flow, nonrandom mating, genetic drift, and natural selection, respectively.

Despite its seeming limitations, the Hardy-Weinberg law has been crucially useful in three major ways. First, its predictions of allele and genotype frequencies in the absence of evolution provide what statisticians call the “null hypothesis,” which is essential for statistically rigorous hypothesis tests. If measured frequencies do not match predictions, then evolution is occurring. This redefines evolution from a vague “change in species over time” to a more useful, quantitative “change in allele or genotype frequencies.” However, it is a definition that cannot be used in the domain of macroevolution and paleontology above the level of biological species. Similarly, Newton’s definition of a moving object does not apply in quantum physics. Second, Hardy-Weinberg provides a conceptual framework for investigation. If evolution is happening, a checklist of potential causes of evolution can be examined in turn. Finally, the Hardy-Weinberg paradigm provides the foundation for mathematical models of each evolutionary force. These models help biologists determine whether a specific evolutionary force could produce observed changes.

Using the Hardy-Weinberg Law

Sickle-cell disease is a severe disease of children characterized by reduced red blood cell number, bouts of pain, fever, gradual failure of major organs, and early death. In 1910, physicians noticed the disease and associated it with distortion (“sickling”) of red blood cells. They realized that victims of the disease were almost entirely of African descent. Studies showed that the blood of about 8 percent of adult African Americans exhibited sickling, although few actually had the disease. By the 1940s, sickling was known to be even more common in some populations in Africa, India, Greece, and Italy.

In 1949, James Neel proved that the disease was caused by a recessive gene: children for the sickle allele developed the disease and died, while heterozygotes showed the sickle trait but did not develop the disease. Using the Hardy-Weinberg law, Neel computed the among black Americans as follows: letting p equal the frequency of the sickle allele, 2pq is the frequency of heterozygotes (8 percent of adult African Americans). Since p + q = 1, q = 1 – p and 2p(1 – p) = 0.08. From this he computed p = 0.042 (4.2 percent). From the medical literature, Neel knew the frequency of the sickle trait in several African populations and computed the sickle allele frequency to be as high as 0.10. (Since then the frequency has been found to be as high as 0.20.) These are extraordinarily high frequencies for a lethal recessive allele, raising the question of why it was so common.

The Hardy-Weinberg assumptions provided a list of possibilities, including nonrandom mating, mutation, and gene flow. However, mathematical models based on Hardy-Weinberg showed that nonrandom mating distorts genotype frequencies but cannot change allele frequencies, and for the loss of sickle alleles via death of homozygotes to be balanced by new mutations, scientists estimated that the mutation rate from normal to sickle allele would have to be about three thousand times higher than any known human mutation rate, which seemed unlikely. As for gene flow, models showed that gene flow simply reduces differences between local populations caused by other evolutionary forces; thus, gene flow from African populations caused by slavery would explain the appearance of the sickle allele in North America but not the high frequencies in Africa.

Another possibility was genetic drift. Models had shown that deleterious alleles could rise to high frequencies in very small populations (fewer than one thousand). It was possible that the sickle allele had drifted to a high frequency in a human population that had been either started by a small number of founders (the founder effect) or reduced to small numbers by some catastrophe (population bottleneck). If so, the population had since grown far above the size at which drift is significant. Moreover, drift was random; if there had been several small populations, some would have drifted high and some low. It was unlikely that drift would maintain high frequencies of a deleterious allele in so many large populations in different locations. Therefore, the remaining possibility, natural selection, was the most reasonable possibility: the heterozygotes must have some selective advantage over the normal homozygotes.

A few years later, A. C. Allison was doing field work in Africa and noted that the incidence of the sickle-cell trait was high in areas where malaria was prevalent. A search of the literature showed this was also true in Italy and Greece. In 1954, Allison published his hypothesis: in heterozygotes, sickle-cell alleles significantly improve resistance to malaria. This hypothesis has been repeatedly confirmed. Scientists have found alleles for several other blood disorders that also provide resistance to malaria in heterozygotes.

Impact and Applications

The Hardy-Weinberg law has provided scientists with a more precise definition of evolution: change in allele or genotype frequencies. It allows them to measure evolution, provides a conceptual framework for investigation, and continues to serve as the foundation for the theory of microevolution. Beyond population genetics and evolution, the Hardy-Weinberg paradigm is used in such fields as law (analysis of DNA “fingerprints”), anthropology (human migration), plant and animal breeding (maintaining endangered species), medicine (genetic counseling), and public health (implementing screening programs). In these and other disciplines, the Hardy-Weinberg law and its derivatives continue to be useful.

The Hardy-Weinberg law also has implications for social issues. In the early twentieth century, growing knowledge of genetics fueled a eugenics movement that sought to improve society genetically. Eugenicists in the 1910s and 1920s promoted laws to restrict immigration and promote sterilization of “mental defectives,” criminals, and other “bad stock.” The Hardy-Weinberg law is often credited with the decline of eugenics, as it makes clear that if a recessive trait is rare (as most deleterious alleles are), most copies of the recessive allele are hidden in apparently normal heterozygotes, and selecting against affected individuals will be inefficient at best. However, a host of respected scientists championed eugenics into the 1920s and 1930s, long after the implications of Hardy-Weinberg were understood. It was really the reaction to the horrors of the Nazi eugenics program that made eugenics socially unacceptable. Moreover, it is premature to celebrate the end of the disturbing questions raised by eugenics. Progress in molecular biology makes it possible to detect deleterious alleles in heterozygotes, making eugenics more practical. Questions of whether genes play a major role in criminality and mental illness are still undecided. Debate about such medical and social issues may be informed by knowledge of the Hardy-Weinberg law, but decisions about what to do lie outside the domain of science.

Key Terms

• allele frequencythe proportion of all the genes at one chromosome location (locus) within a breeding population
• gene flowmovement of alleles from one population to another by the movement of individuals or gametes
• gene poolthe total set of all the genes in all individuals in an interbreeding population
• genetic driftrandom changes in allele frequencies caused by chance events

Bibliography

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