Hardy and Weinberg Present a Model of Population Genetics Summary

  • Last updated on November 10, 2022

G. H. Hardy and Wilhelm Weinberg formalized the first model for evaluating changes in gene frequency within a population, thus giving birth to the field of population genetics.

Summary of Event

Within a few decades following the publication of On the Origin of Species by Means of Natural Selection: Or, The Preservation of Favoured Races in the Struggle for Life (1859) On the Origin of Species by Means of Natural Selection (Darwin) by Charles Darwin, the theory of natural selection had gained considerable approval in the scientific community and had revolutionized the way biologists viewed the natural world. Darwin’s work provided a comprehensive explanation for both the origin and maintenance of the seemingly endless variation in nature. Stated simply, natural selection Natural selection theory is the differential reproduction of heritable characteristics within a population, which ultimately leads to evolutionary change. Evolution;theory Genetics;population Gene frequency Biology;gene frequency Population genetics Hardy-Weinberg law[Hardy Weinberg law] [kw]Hardy and Weinberg Present a Model of Population Genetics (1908) [kw]Weinberg Present a Model of Population Genetics, Hardy and (1908) [kw]Population Genetics, Hardy and Weinberg Present a Model of (1908) [kw]Genetics, Hardy and Weinberg Present a Model of Population (1908) Genetics;population Gene frequency Biology;gene frequency Population genetics Hardy-Weinberg law[Hardy Weinberg law] [g]England;1908: Hardy and Weinberg Present a Model of Population Genetics[02010] [g]Germany;1908: Hardy and Weinberg Present a Model of Population Genetics[02010] [c]Science and technology;1908: Hardy and Weinberg Present a Model of Population Genetics[02010] [c]Genetics;1908: Hardy and Weinberg Present a Model of Population Genetics[02010] [c]Biology;1908: Hardy and Weinberg Present a Model of Population Genetics[02010] Hardy, G. H. Weinberg, Wilhelm Mendel, Gregor Darwin, Charles

Despite almost immediate acceptance, the theory was incomplete in that it failed to account for a mechanism of heritability and an explanation for how such a mechanism could translate into the kinds of changes in populations and species that Darwin’s theory of evolution originally predicted. The first of these problems was overcome in 1900, when the earlier work of Gregor Mendel was rediscovered independently by several researchers. In his quantitative assessment of breeding experiments on garden peas, Mendel demonstrated that many inherited traits in diploid organisms (those containing two sets of chromosomes) are determined by two factors, which are known now as genes (segments of chromosomes). From the frequency of traits in his populations of pea plants, Mendel reasoned that an organism receives one gene from each parent for all such heritable traits. In addition, he argued that alleles (alternate forms of the same gene) separate independently and randomly from one another when gametes (egg and sperm) form but combine again during fertilization.

Almost immediately following the rediscovery of Mendel’s laws of inheritance, several scientists began to realize the implications of these laws for the study of population genetics and evolutionary change. The first observations were noted by William E. Castle Castle, William E. in 1903, and more complete analyses were presented in 1908 by the English mathematician G. H. Hardy and the German physician Wilhelm Weinberg. These later works, which came to be known collectively as the Hardy-Weinberg law (or equilibrium), eventually became the foundation for the study of population genetics.

The law of population genetics, credited to Hardy and Weinberg, was discovered and published independently, but almost simultaneously, by the two scientists. Weinberg was a physician with research interests in multiple births, medical statistics, and population genetics. Between 1908 and 1910, he published four critical papers relating Mendel’s laws of inheritance to genetic changes in populations. Because of this work, some consider him to be the father of population genetics. Hardy was a prominent mathematician who invested most of his time in the study of pure mathematics, on which he published nearly 350 papers. In late 1908, however, he deviated slightly from his main research interests when he published a short note to the editor of the journal Science, in which he made several observations concerning the relevance of Mendel’s laws to populations that were very similar to those pointed out by Weinberg.

The Hardy-Weinberg law states that, given simple patterns of Mendelian inheritance, the frequency of alleles Alleles in a population will remain constant from generation to generation, assuming that certain ideal conditions are met. In other words, if these conditions hold true, allelic frequencies will not change, the genetic structure of the population will remain constant over time, and evolutionary change will not occur. These ideal conditions are as follows. First, the population must be a large, randomly breeding, or panmictic, population. In other words, all individuals in the population must have equal reproductive success. If this condition is not met, and certain individuals experience greater reproductive success than others, or if nonrandom breeding occurs as a result of small population size, then certain genes will be overrepresented in the next generation and the population’s gene frequencies will change.

G. H. Hardy.

A second necessary condition is that the population must be closed; that is, there must be no immigration or emigration of individuals into or out of the population. Third, there must be no spontaneous changes in alleles (mutations). Finally, there must be no differential success (selection) of certain alleles. Alleles must share equal probability of transmission to the next generation. For example, if some individuals possess alleles or combinations of alleles that, under certain environmental conditions, enhance their chances of survival and subsequent reproduction, then their genes will be represented more than those of others in the next generation, gene and allelic frequencies will change, and the population will adapt to environmental conditions. Such differential success of alleles is the essence of Darwin’s theory of natural selection and the primary mechanism by which evolutionary changes proceed.

Given these conditions, the Hardy-Weinberg law asserts, changes in gene frequency in a population (evolution) will not occur. When any one or more of these conditions are violated, however, gene frequencies will be altered, and evolution will take place. Thus, by demonstrating the conditions necessary for evolution not to occur, Hardy and Weinberg were able to illustrate those factors that actually contribute to evolutionary change. In addition to the qualitative discussion of their argument, Hardy and Weinberg also presented their model in a purely mathematical form. To illustrate this quantitative expression of their model, it is easiest to consider a hypothetical population with a single gene and two alleles, represented by A and a. Recall also that each individual in the population possesses two alleles for this gene. Furthermore, let the frequency (numerical proportion) of the A and a in the population equal p and q, respectively, and assume that p + q = 1. As an example, assume that p and q equal 0.8 and 0.2; that is, the proportion of the A allele in the population is 80 percent and that of the a allele is 20 percent.

Hardy and Weinberg reasoned that if Mendel was correct and these two alleles separate randomly and independently as discrete units during formation of the egg and sperm, the frequency of allelic combinations in the next generation could be predicted mathematically. They stated that if p and q are known, and if all conditions of the model hold true, then the frequency of allelic combinations in the next generation could be calculated easily from p2 + 2pq + q2, where p2 is the frequency of individuals with two A alleles, 2pq is the frequency of individuals with one A and one a allele, and q2 the frequency of individuals with two a alleles. This mathematical expression of allele combinations, or genotypic frequencies, follows from a simple rule of mathematical probabilities, which states that the joint probability of two independent events is equal to the product of their individual probabilities. Thus, in the example above, the probability of acquiring two A alleles (or the proportion of individuals acquiring two A alleles) is equal to 0.8 0.8, or 0.64. Similarly, the probability of acquiring one A allele and an a allele in any order is p q 2, or 0.32. In the absence of nonrandom mating, mutation, immigration, emigration, and selection, these frequencies will remain fixed at these values in all subsequent generations.

This mathematical treatment allowed biologists to predict the frequencies of allelic combinations in a population from the individual allelic frequencies. In a similar way, they could calculate frequencies of each allele by working backward from the allelic combinations. The value of this model, however, is not in its applicability to the real world. In fact, biologists believe that natural populations rarely, if ever, meet all the ideal conditions required by the model. Instead, the Hardy-Weinberg equation is a conceptual model that clearly illustrates how evolutionary change occurs at the population-genetic level. Although this model is limited in that the behavior of some alleles is not governed by Mendelian laws of inheritance, it is an important starting point for the study of population genetics.


The Hardy-Weinberg law was a critical breakthrough in evolutionary biology that effectively linked Mendel’s laws of inheritance with Darwin’s theory of natural selection. It demonstrated clearly how cellular mechanisms of inheritance can translate into the microevolutionary changes that Darwin predicted.

This synthesis was accomplished in two ways. First, by defining the conditions necessary for a population to remain genetically unchanged indefinitely, Hardy and Weinberg were able to specify those conditions that contribute directly to evolutionary change. In the absence of mutation, gene flow in and out of the population, and natural selection, a large, randomly breeding population will remain at equilibrium with respect to its allele or gene frequencies. When any one of these conditions is violated, gene frequencies will change in subsequent generations. Hardy and Weinberg’s model thus helped biologists to understand how changes in gene frequencies can occur and that such changes are, in fact, small-scale evolutionary events. In addition, the equilibrium model helped identify mechanisms of evolutionary change that were not obvious from Darwin’s theory of natural selection. Although most biologists agree that differential reproduction of alleles, or natural selection, is the primary force driving evolution, it became clear from Hardy and Weinberg’s work, and is still widely accepted, that other factors—such as random events and differing degrees of gene flow between populations—contribute also to evolutionary change.

The second important observation to emerge from the Hardy-Weinberg law was that sexual reproduction alone does not result in a reduction in genetic variability or in genetic change. One of the problems that Darwin faced was how to explain the maintenance of genetic variability. Darwin correctly assumed that genetic variability is the essential raw material on which natural selection acts. In the absence of an accurate mechanism of inheritance, however, he had incorrectly assumed that the inheritance process must result in a constant blending of genetic material and a loss in genetic variability as well. His insistence that variability is necessary for natural selection posed a serious problem. From Mendel’s work, it soon became clear that genetic material is transmitted in discrete units and therefore is not mixed during reproduction. A short time later, Hardy and Weinberg demonstrated that, under ideal conditions, gene frequencies and genetic variability will remain fixed indefinitely. Their work finally resolved a major problem in the theory of natural selection.

The synthesis of Mendel’s and Darwin’s work resulted in renewed interest in evolutionary biology and soon gave birth to the new field of population genetics. This field was advanced greatly during the 1920’s with the work of Sir Ronald Aylmer Fisher, Sewall Wright, and John Burdon Sanderson Haldane; it continues to be one of the major fields of biological research.

In addition to its impact on basic research, the Hardy-Weinberg law has had several practical applications. Perhaps the most important of these is its use as a conceptual teaching model. Hardy-Weinberg equilibrium is employed in nearly every college-level biology text as a starting point for discussions on evolution, adaptation, and population genetics. In essence, it is a teaching tool that is as useful for beginning students in the twenty-first century as it was for evolutionary biologists at the beginning of the twentieth century. A second important application derived from the model concerns the manner and degree to which deleterious alleles manifest themselves within a population. The Hardy-Weinberg model shows how lethal alleles, such as those that code for fatal genetic diseases, can be maintained in a population at low frequencies. This simple conceptual model had a tremendous impact on the study of evolutionary biology. Genetics;population Gene frequency Biology;gene frequency Population genetics Hardy-Weinberg law[Hardy Weinberg law]

Further Reading
  • citation-type="booksimple"

    xlink:type="simple">Arms, Karen, et al. Biology: A Journey into Life. 4th ed. Fort Worth, Tex.: Harcourt Brace College Publishers, 1995. A general biology text for the layperson that provides a clear and concise description of the Hardy-Weinberg law and its implications. Well illustrated; includes a glossary of general biology terms.
  • citation-type="booksimple"

    xlink:type="simple">Hanson, Earl D. Understanding Evolution. New York: Oxford University Press, 1981. A basic text on evolutionary biology that devotes considerable attention to population genetics and its relevance to evolutionary processes. Gives thorough coverage to Mendel’s laws of inheritance and the Hardy-Weinberg law. Includes modest historical accounts of other relevant events. Well illustrated, with limited references.
  • citation-type="booksimple"

    xlink:type="simple">Merrell, David J. Ecological Genetics. Minneapolis: University of Minnesota Press, 1981. A college-level text, best used as a reference. One of the first attempts to synthesize ecological processes with those of population genetics. Gives the Hardy-Weinberg law moderate coverage. Includes extensive references and a few diagrams and figures.
  • citation-type="booksimple"

    xlink:type="simple">Mettler, Lawrence E., Thomas G. Gregg, and Henry E. Schaffer. Population Genetics and Evolution. 2d ed. Englewood Cliffs, N.J.: Prentice-Hall, 1988. A modern text on population genetics that assumes a certain basic level of understanding. Provides a complete overview of current research efforts in the field. Well referenced, with short chapter summaries.
  • citation-type="booksimple"

    xlink:type="simple">Provine, William B., comp. The Origins of Theoretical Population Genetics. 2d ed. Chicago: University of Chicago Press, 2001. Provides a comprehensive overview of the history of population genetics, including the Hardy-Weinberg law.
  • citation-type="booksimple"

    xlink:type="simple">Raven, Peter H., et al. Biology. 7th ed. New York: McGraw-Hill, 2004. Comprehensive introductory college text on the science of biology. Covers the basic concepts of genetics and heredity and includes a detailed account of Mendel’s laws of inheritance. Discusses the Hardy-Weinberg law and provides a summary of the kinds of natural events that violate this law and thereby alter population genetics. Illustrations and detailed glossary.
  • citation-type="booksimple"

    xlink:type="simple">Wilson, Edward O., and William H. Bossert. A Primer of Population Biology. Stamford, Conn.: Sinauer Associates, 1971. Intended for the beginning biologist. A small, concise handbook, perhaps one of the best introductory texts on classic population genetics. More than half the book concerns the basis of genetic change in populations. A strong mathematical orientation, but problems are explained clearly. Well illustrated, with suggested readings and a short glossary of technical terms.

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Bateson and Punnett Observe Gene Linkage

Morgan Develops the Gene-Chromosome Theory

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