You have landed on the right page to learn about Hardy-Weinberg Principle. Are all the fields- genetics, population ecology and evolution- related to each other? Can any relation be established between them, and if yes, how? The Hardy Weinberg principle is the link and connects Mendelian genetics to evolution via population ecology. It sounds interesting, right?

Hardy Weinberg Principle mathematically explains the occurrence and consistency of gene frequency for a particular gene. The principle states that the allelic frequency and gene pool remain constant throughout generations. Genetic equilibrium is the term for this process. Furthermore, the allelic frequencies add up to 1. Read this article to learn how genetics, population ecology and evolution is interconnected with the help of Hardy Weinberg’s Principle. Continue reading to know more.

Theory of Hardy-Weinberg Principle

Hardy-Weinberg equilibrium is one of the key concepts in Population genetics. Population genetics is the branch of genetics that studies the frequencies of different genes and the trend of their changes in various conditions. This is an amalgamation of population ecology and genetics. It also involves the examination and modelling of allele frequencies in a population. Genes and alleles differ in populations, and their dispersion gives rise to variations. The variations result due to the presence of alleles in the organism. Alleles are the alternate forms of genes. They occupy the same locus on homologous chromosomes. In a population of sexually reproducing organisms, the allelic frequencies change over generations due to interbreeding. In \(1908,\) G.H. Hardy and W. Weinberg, in their independently published papers, refuted the view that dominant alleles would automatically tend to increase in frequency. Their papers laid the foundation of population genetics.

So what does Hardy Weinberg principle tell us? Hardy Weinberg equation and its application form an important part of population genetics. But before we go into details of it, let’s recall the vocabulary used to understand it.

Terms Used In Hardy-Weinberg Principle

1. Allele: the two (or more) alternative forms of a gene that occupy identical loci (positions) on homologous chromosomes.
2. Dominant allele: the allele that gets expressed in homozygous and heterozygous conditions. It is an allele that expresses its trait even in the presence of an alternative allele, i.e., in heterozygous condition. Alternatively, one of the two alleles that express in \({F_1}\) is called dominant.
3. Recessive allele: the allele that is not expressed in the presence of an alternative allele or in heterozygous condition.
4. Gene locus: A locus is the specific physical location of a gene or other DNA sequence on a chromosome.
5. Gene pool: the total genetic information encoded in the sum of all genes in a Mendelian population. Or the total number of genes of all individuals in a Mendelian population.
6. Genetic diversity: diversity in the alleles of genes and their frequencies within a population is referred to as genetic diversity.
7. Speciation: formation of new species from the pre-existing ones is known as speciation. Many factors are responsible for speciation.
8. Genetic drift: chance elimination of genes of a certain trait when a section of the population migrates or dies due to natural calamities.
9. Gene flow: transfer of alleles from one population to another.
10. Population or Mendelian population is a group of individuals of the same species who arely and naturally inbreeding in a given area at a given time.
11. Gene frequency is the proportion of an allele in relation to all the (total) alleles of a gene present in a Mendelian population.

Statement of Hardy-Weinberg Principle

The Hardy-Weinberg principle, also called the Hardy-Weinberg equilibrium, law, model, or theorem states that allele frequencies in a population will remain constant in the absence of any evolutionary forces.
Or in other words, in a large, non-evolving population of sexually producing individuals, gene or allelic frequencies remain constant from generation to generation irrespective of their phenotypic expressions.

Mathematical Expression of Hardy-Weinberg Principle

Assuming that a gene has two alleles, \(A\) and \(a\). If \(p\) is the frequency of occurrence of the dominant allele \(\left( A \right)\) and \(q\) is the frequency of occurrence of the recessive allele (\(a\)) in the parental generation, then:

1. The genotype frequencies expected as per Hardy-Weinberg principle in the offspring are \({\left( {p + q} \right)^2} = {p^2} + 2\,pq + {q^2} = 1.\)
2. This represents the gene frequency of the total population.
3. Here, \({p^2}\)is the frequency of occurrence of individuals with homozygous dominant alleles \(\left( {AA} \right).\)
4. \(2\,pq\) is the frequency of occurrence of individuals with heterozygous alleles \(\left( {Aa} \right).\)
5. And, \({q^2}\) is the frequency of occurrence of individuals with homozygous recessive alleles \(\left( {aa} \right).\)

This can also be explained using the Punnett square as:

Assumptions of Hardy-Weinberg Principle

The conclusions of the Hardy-Weinberg equation relies on certain assumptions about the population. The factors which control this equilibrium are:

1. Random mating.
2. No mutation in the population.
3. The population is fairly large.
4. Change in allelic frequency due to chance or accident is negligible.
5. Natural selection is non-operative.
6. Organisms are diploid and only sexually reproducing.

When the assumptions are violated, deviations from the Hardy-Weinberg equilibrium takes place.

Factors Affecting Hardy-Weinberg Equilibrium

Several factors affect the Hardy-Weinberg equilibrium, like:

1. Mutation, which causes the change in both gene and allele frequencies.
2. Genetic drift, which leads to the loss of genes or alleles from a population by chance.
3. Genetic recombination occurs during meiosis during sexual reproduction.
4. Migration, including immigration and emigration.
5. Natural selection.

Significance of Hardy-Weinberg Principle

Hardy Weinberg Principle has a number of evolutionary implications such as:

1. The Hardy-Weinberg model enables us to compare a given population’s actual genetic structure over time with the genetic structure we would expect if the population were in Hardy-Weinberg equilibrium (i.e., it is not evolving).
2. This principle allows us to understand and predict the complex genetic behaviours of genes and alleles in a random mating population, like that of the human population.
3. The fate of an allele or a gene in a population can be determined using this principle. For example, according to the Hardy–Weinberg principle (random pairing of alleles), alleles that are rare in a population (low starting frequency) are most often paired with alleles of another type, resulting in a heterozygous genotype. Thus, rare alleles tend to get removed from the population by natural selection. According to some scientists, this is a result of underdominance.

Applying Hardy-Weinberg Equation

Let’s solve an example to see how actually the Hardy-Weinberg equation is applied to solve the problem:

Part A: In Lizards, green scales \(\left( G \right)\) are dominant over blue scales \(\left( g \right).\) There are \(210\) individuals with the genotype \(GG,\,245\) individuals with the genotype \(Gg\) and \(45\) individuals with the genotype \(gg.\) Find the frequency of the dominant and recessive alleles and the frequency of individuals with dominant, heterozygous, and recessive traits.

Solution:
Step 1: Add the number of all types of individuals to know the population size.
Therefore \(210 + 245 + 45 = 500\)
So population size is \(500\)

Step 2: Let’s calculate the gene frequency of recessive allele
Therefore,
Allelic frequency of recessive alleles \( = \frac{{{\rm{Number}}\,{\rm{of}}\,{\rm{individuals}}\,{\rm{having}}\,{\rm{recessive}}\,{\rm{allele}}\,{\rm{(gg}}}}{{{\rm{Total}}\,{\rm{number}}\,{\rm{of}}\,{\rm{individuals}}\,{\rm{in}}\,{\rm{the}}\,{\rm{population}}}}\)
\({q^2} = \frac{{45}}{{500}},\)
\({q^2} = 0.09,\)

Step 3: To find \(q,\)
\(q = 0.09\)
\(q = 0.3\)

Step 4: Use the first Hardy-Weinberg equation \(\left( {p + q = 1} \right)\)to solve for \(p\)
Therefore, \(p = 1 – q,\)
\(p = 1 – 0.3\)
\(p = 0.7\)

Step 5: Now that we know the allele frequencies, let’s calculate the allele frequencies of all the genotypes in the population. To know this we must calculate \({p^2}\)
Therefore \({p^2} = 0.7 \times 0.7\)
\({p^2} = 0.049\)

Step 6: Use the equation \({p^2} + 2\,pq + {q^2} = 1\) to know the gene frequencies of other genotypes
Thus, \({p^2} = 0.049,\)
\({q^2} = 0.09,\)
\(2\,pq = 2 \times 0.3 \times 0.7,\)
\(2\,pq = 0.42\)
Therefore:
The frequency of the dominant alleles: \(p = 0.7\)
The frequency of the recessive alleles: \(q = 0.3\)
The frequency of individuals with the dominant genotype: \({p^2} = 0.49\)
The frequency of individuals with the heterozygous genotype: \(2\,pq = 0.42\)
The frequency of individuals with the recessive genotype: \({q^2} = 0.09\)

Summary

The Hardy Weinberg principle says that a randomly mating population remains in the equilibrium state for the allelic frequencies. This equilibrium or principle relies on assumptions that the population has no external force acting on it. Such an external force could be natural selection, mutation, gene flow, genetic drift, sexual selection, selective mating etc.

Any deviations from equilibrium are indicative of evolutionary forces acting in different time scales. The Hardy Weinberg Principle can be generalized and applied to genes with more than two alleles.

Frequently Asked Questions

Q.1. Why is Hardy-Weinberg equilibrium important?

Ans: The Hardy-Weinberg principle is important for two reasons. First, it tells us how to calculate the allelic frequencies in a population. Secondly, any deviations from the equilibrium give us insights into evolutionary forces acting on the population.

Q.2. How to calculate the allelic frequencies using Hardy-Weinberg Principles?
Ans: The Hardy-Weinberg principle gives a mathematical model to calculate the allelic frequencies. For two alleles at a locus, we use the binomial expansion of \({\left( {p + q} \right)^2}\) which is \({p^2} + \)\(2\,pq + {q^2}.\) Since only two alleles are considered, \(p + q = 1.\) Here, \(p\) is the frequency of the dominant allele and \(q\) is the frequency of the recessive allele.

Q.3. What does the Hardy-Weinberg principle say?
Ans: The Hardy Weinberg principle states that allele frequencies in a population will remain constant in the absence of any evolutionary forces.

Q.4. What are the \(5\) assumptions of Hardy Weinberg equilibrium?
Ans: The Hardy Weinberg Principle relies on the following \(5\) assumptions.
1. Random mating
2. No mutation
3. No gene flow or migration
4. Large population size
5. No natural selection

Q.5. Explain Hardy-Weinberg Principle with an example.

Ans: The Hardy Weinberg principle states that the genetic frequencies of alleles in a population will remain constant in the absence of any disturbing factors. The allelic frequencies for a population can be mathematically calculated, and one can expect the frequencies of different genetic combinations. Any deviations from the equilibrium state are indicative of evolutionary forces acting on the population.