HardyWeinberg Principle of Equilibrium
The HardyWeinberg principle can be used to estimate the frequency of alleles and genotypes in a population.
Learning Objective

Use the Hardy Weinberg equation to calculate allelic and genotypic frequencies in a population
Key Points
 The HardyWeinberg principle assumes that in a given population, the population is large and is not experiencing mutation, migration, natural selection, or sexual selection.
 The frequency of alleles in a population can be represented by p + q = 1, with p equal to the frequency of the dominant allele and q equal to the frequency of the recessive allele.
 The frequency of genotypes in a population can be represented by p^{2}+2pq+q^{2}= 1, with p^{2} equal to the frequency of the homozygous dominant genotype, 2pq equal to the frequency of the heterozygous genotype, and q^{2} equal to the frequency of the recessive genotype.
 The frequency of alleles can be estimated by calculating the frequency of the recessive genotype, then calculating the square root of that frequency in order to determine the frequency of the recessive allele.
Terms

phenotype
the appearance of an organism based on a multifactorial combination of genetic traits and environmental factors, especially used in pedigrees

genotype
the combination of alleles, situated on corresponding chromosomes, that determines a specific trait of an individual, such as "Aa" or "aa"
Full Text
HardyWeinberg Principle of Equilibrium
The HardyWeinberg principle states that a population's allele and genotype frequencies will remain constant in the absence of evolutionary mechanisms. Ultimately, the HardyWeinberg principle models a population without evolution under the following conditions:
 no mutations
 no immigration/emigration
 no natural selection
 no sexual selection
 a large population
Although no realworld population can satisfy all of these conditions, the principle still offers a useful model for population analysis.
HardyWeinberg Equations and Analysis
According to the HardyWeinberg principle, the variable p often represents the frequency of a particular allele, usually a dominant one. For example, assume that p represents the frequency of the dominant allele, Y, for yellow pea pods. The variable q represents the frequency of the recessive allele, y, for green pea pods. If p and q are the only two possible alleles for this characteristic, then the sum of the frequencies must add up to 1, or 100 percent. We can also write this as p + q = 1.If the frequency of the Y allele in the population is 0.6, then we know that the frequency of the y allele is 0.4.
From the HardyWeinberg principle and the known allele frequencies, we can also infer the frequencies of the genotypes. Since each individual carries two alleles per gene (Y or y), we can predict the frequencies of these genotypes with a chi square. If two alleles are drawn at random from the gene pool, we can determine the probability of each genotype.
In the example, our three genotype possibilities are: pp (YY), producing yellow peas; pq (Yy), also yellow; or qq (yy), producing green peas. The frequency of homozygous pp individuals is p^{2}; the frequency of hereozygous pq individuals is 2pq; and the frequency of homozygous qq individuals is q^{2}. If p and q are the only two possible alleles for a given trait in the population, these genotypes frequencies will sum to one: p^{2} + 2pq + q^{2} = 1 .
HardyWeinberg proportions for two alleles
The horizontal axis shows the two allele frequencies p and q and the vertical axis shows the expected genotype frequencies.Each line shows one of the three possible genotypes.
In our example, 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 100 pea plants, 86 might have yellow peas and 16 have green peas. We do not know how many are homozygous dominant (Yy) or heterozygous (Yy), but we do know that 16 of them are homozygous recessive (yy).
Therefore, by knowing the recessive phenotype and, thereby, the frequency of that genotype (16 out of 100 individuals or 0.16), we can calculate the number of other genotypes. If q^{2} represents the frequency of homozygous recessive plants, then q^{2} = 0.16. Therefore, q = 0.4.Because p + q = 1, then 1  0.4 = p, and we know that p = 0.6. The frequency of homozygous dominant plants (p^{2}) is (0.6)^{2} = 0.36. Out of 100 individuals, there are 36 homozygous dominant (YY) plants. The frequency of heterozygous plants (2pq) is 2(0.6)(0.4) = 0.48. Therefore, 48 out of 100 plants are heterozygous yellow (Yy).
The HardyWeinberg Principle
When populations are in the HardyWeinberg equilibrium, the allelic frequency is stable from generation to generation and the distribution of alleles can be determined.If the allelic frequency measured in the field differs from the predicted value, scientists can make inferences about what evolutionary forces are at play.
Applications of HardyWeinberg
The genetic variation of natural populations is constantly changing from genetic drift, mutation, migration, and natural and sexual selection. The HardyWeinberg principle gives scientists a mathematical baseline of a nonevolving population to which they can compare evolving populations. If scientists record allele frequencies over time and then calculate the expected frequencies based on HardyWeinberg values, the scientists can hypothesize the mechanisms driving the population's evolution.
Key Term Reference
 allele
 Appears in these related concepts: Mendel's Laws of Heredity, Population Genetics, and Race and Genetics
 dominant
 Appears in these related concepts: The Conflict Perspective, The Conflict Perspective on Deviance, and Boreal Forests and Arctic Tundra
 equilibrium
 Appears in these related concepts: Homogeneous versus Heterogeneous Solution Equilibria, Diffusion, and Second Condition
 evolution
 Appears in these related concepts: Cultural Evolution, Competition, and The Galapagos Finches and Natural Selection
 frequency
 Appears in these related concepts: Properties of Waves and Light, Characteristics of Sound, and Sound
 gene
 Appears in these related concepts: Genomic DNA and Chromosomes, Genes as the Unit of Heredity, and The Influence of Behavior on Genes
 gene pool
 Appears in these related concepts: The Biological Species Concept, Genetic Drift, and Gene Flow and Mutation
 genetic drift
 Appears in these related concepts: Misconceptions of Evolution, Defining Population Evolution, and Gene Duplications and Divergence
 genetic variation
 Appears in these related concepts: No Perfect Organism, Methods of Reproducing, and Genetic Variation
 genetics
 Appears in these related concepts: Identification of Microbes Based on Molecular Genetics, Introduction to Mendelian Inheritance, and The Influence of Genes on Behavior
 heterozygous
 Appears in these related concepts: The Punnett Square Approach for a Monohybrid Cross, Alternatives to Dominance and Recessiveness, and Sex Determination
 homozygous
 Appears in these related concepts: Complementation, Mendelâ€™s Model System, and Mendel's Law of Dominance
 mutation
 Appears in these related concepts: The DNA Double Helix, Protooncogenes, and Lethal Inheritance Patterns
 natural selection
 Appears in these related concepts: Sociobiology, Charles Darwin and Natural Selection, and Natural Selection and Adaptive Evolution
 population
 Appears in these related concepts: The Functionalist Perspective on Deviance, Quorum Sensing, and Basic Inferential Statistics
 probability
 Appears in these related concepts: Theoretical Probability, Rules of Probability for Mendelian Inheritance, and The Addition Rule
 recessive
 Appears in these related concepts: Garden Pea Characteristics Revealed the Basics of Heredity, SexLinked Traits, and Mendel's Law of Segregation
 sexual selection
 Appears in these related concepts: Mating Systems and Sexual Selection, Nonrandom Mating and Environmental Variance, and Sexual Selection
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