5 Genetics and Evolution

5.7 Hardy-Weinberg principle

5.7 Hardy-Weinberg principle

Dr V Malathi

 

The Hardy-Weinberg Law, also known as the Hardy-Weinberg Principle or Hardy-Weinberg Equilibrium was formulated byG.H. Hardy, a British mathematician, and Wilhelm Weinberg, a German physician, in 1908.

It is a foundational concept in population genetics providing  a mathematical framework for understanding how gene frequencies in a population remain constant over generations under certain conditions.

The Hardy–Weinberg principle/ law, states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences.

This condition is called genetic equilibrium.

Key Assumptions of the Hardy-Weinberg Equilibrium

The Hardy-Weinberg equilibrium is based on a set of ideal conditions:

  1. Large Population Size: Genetic drift (random changes in allele frequencies) is minimal in large populations.
  2. Random Mating: Individuals pair by chance, not according to genotype or phenotype.
  3. No Mutation: No new alleles are introduced or altered.
  4. No Migration: No new members enter or leave the population, keeping allele frequencies stable.
  5. No Natural Selection: All genotypes have equal chances of surviving and reproducing.

The Hardy-Weinberg Equation

The Hardy-Weinberg equation is used to predict the genetic variation in a population under these ideal conditions.

Let us assume that there are two alleles for a particular gene in a population, typically represented by:

  • p (frequency of the dominant allele, Y)
  • q (frequency of the recessive allele, y)

Then: According to Hardy-Weinberg equation the sum of the allele frequencies must equal 1

i.e., p + q = 1

Using these allele frequencies, we can predict the genotype frequencies in the population with the formula:

 

p2+2pq+q2=1p^2 + 2pq + q^2 = 1

where:

  • p² = frequency of individuals with the homozygous dominant genotype (YY)
  • 2pq = frequency of individuals with the heterozygous genotype (Yy)
  • q² = frequency of individuals with the homozygous recessive genotype (yy)

Example of the Hardy-Weinberg Principle

Suppose in a population, 80% of alleles for a certain gene are dominant (A), and 20% are recessive (a):

  • p = 0.8
  • q = 0.2

Using the Hardy-Weinberg equation:

  • p² = (0.8)² = 0.64 (64% are AA)
  • 2pq = 2 * 0.8 * 0.2 = 0.32 (32% are Aa)
  • q² = (0.2)² = 0.04 (4% are aa)

This means that in this ideal population, 64% would be homozygous dominant, 32% heterozygous, and 4% homozygous recessive.

while no population can satisfy those conditions, the principle offers a useful model against which to compare real population changes.

 

The Hardy-Weinberg principle is used to predict the genotypic distribution of offspring in a given population. In the example given, pea plants have two different alleles for pea color. The dominant capital Y allele results in yellow pea color, and the recessive small y allele results in green pea color. The distribution of individuals in a population of 500 is given. Of the 500 individuals, 245 are homozygous dominant (capital Y capital Y) and produce yellow peas. 210 are heterozygous (capital Y small y) and also produce yellow peas. 45 are homozygous recessive (small y small y) and produce green peas. The frequencies of homozygous dominant, heterozygous, and homozygous recessive individuals are 0.49, 0.42, and 0.09, respectively. Each of the 500 individuals provides two alleles to the gene pool, or 1000 total. The 245 homozygous dominant individuals provide two capital Y alleles to the gene pool, or 490 total. The 210 heterozygous individuals provide 210 capital Y and 210 small y alleles to the gene pool. The 45 homozygous recessive individuals provide two small y alleles to the gene pool, or 90 total. The number of capital Y alleles is 490 from homozygous dominant individuals plus 210 from homozygous recessive individuals, or 700 total. The number of small y alleles is 210 from heterozygous individuals plus 90 from homozygous recessive individuals, or 300 total. The allelic frequency is calculated by dividing the number of each allele by the total number of alleles in the gene pool. For the capital Y allele, the allelic frequency is 700 divided by 1000, or 0.7; this allelic frequency is called p. For the small y allele the allelic frequency is 300 divided by 1000, or 0.3; the allelic frequency is called q. Hardy-Weinberg analysis is used to determine the genotypic frequency in the offspring. The Hardy-Wienberg equation is p-squared plus 2pq plus q-squared equals 1. For the population given, the frequency is 0.7-squared plus 2 times .7 times .3 plus .3-squared equals one. The value for p-squared, 0.49, is the predicted frequency of homozygous dominant (capital Y capital Y) individuals. The value for 2pq, 0.42, is the predicted frequency of heterozygous (capital Y small y) individuals. The value for q-squared, .09, is the predicted frequency of homozygous recessive individuals. Note that the predicted frequency of genotypes in the offspring is the same as the frequency of genotypes in the parent population. If all the genotypic frequencies, .49 plus .42 plus .09, are added together, the result is one

“Hardy-Weinberg Principle of Equilibrium” by Libre Texts Biology is licensed under CC BY 4.0

Applications of the Hardy-Weinberg Principle

  1. Detecting Evolutionary Forces: Deviations from Hardy-Weinberg equilibrium in a population indicate the role of evolutionary forces  for example like  selection or mutation.
  2. Estimating Carrier Frequency: The proportion of a recessive allele for genetic disorders in a population can be calculated
  3. Population Genetics Studies:The principle offers a useful model against which to compare real population changes. It serves as a null hypothesis in studies analyzing changes in allele frequencies over time.

Limitations of the Hardy-Weinberg Principle

  • The principle holds good only under specified conditions (no evolution, no gene flow, etc.),
  • These conditions  are rarely met in real populations.
  • Factors like natural selection, gene flow, and genetic drift often disrupt Hardy-Weinberg equilibrium in natural populations which leads to changes in allele frequencies.

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5.7 Hardy-Weinberg principle by Dr V Malathi is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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