Hardy Weinberg Equilibrium: Population and Evolutionary Genetics

What is population?

An ecosystem consists of many species. Species is a group of living organism comprising of similar individuals capable of exchanging genes through interbreeding. The individuals of a same species of a particular region are called population.

Population definition: “A group of individuals of a particular species occupying a definite space, in which the individuals interact, interbreed and exchange genetic materials.”

What is Population Genetics?

Apart from its ecological significance, population has a important role in the process of evolution. We generally have a wrong notion that an individual in a population is evolving during the course of evolution of a species. But in reality, not the individuals but the population only can evolve. Thus population forms the basic unit of evolution, not the species. We also know that for the process of evolution to occur in a system, there should be changes in the genetic constitution. Since the population is undergoing evolution and not the individuals, the changes should be in the genetic constitution of the population. There is considerable difference between the inheritance of genes in the population and that in the individuals. Population genetics is the study of distributions and changes of allele frequency and interaction of alleles in a population. Study of population genetics is very essential for understanding the species adaptation and evolution.

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As we mentioned earlier, the process of evolution to occur in a population, the population should face evolutionary forces. A population is usually prone to four main types of evolutionary forces such as:

(1). Natural selection

(2). Genetic drift

(3). Mutation

(4). Gene flow (migration)

For a better understanding of Population Genetics, we should understand the following conceptual terms:

(1). What is Mendelian population?

(2). What is Gene pool

(3). What is Gene frequency or allele frequency?

(4). What is Genotype frequency?

(5). What is Hardy Weinberg Law or (Hardy Weinberg Equilibrium)?

(6). What are the Evolutionary forces in a population?

(1). What is Mendelian Population?

A Mendelian population is a group of interbreeding, sexually reproducing individuals that have a common set of genes (species). Mendelian population is also called as genetic population or random mating population.

Definition: “A community of similar individuals living within a circumscribed area at a given time and capable of interbreeding to produce fertile offspring”.

Mendelian population is characterized by individuals having somewhat similar genetic constitution

(2). What is Gene Pool?

Gene pool is the sum total of genes of all the individuals of a Mendelian Population. A gene pool of a population describes genes present in the population, proportions of different kinds of genes and pattern of distribution of genes in the individuals of the population.

For example if we take the seed shape character of pea plant, we should know the proportion of smooth allele and wrinkled allele. We should also know how these alleles are distributed among the individuals (homozygous and heterozygous).

(3). What is Gene Frequency (allelic frequency)?

Gene frequency or allelic frequency is the proportion of an allele in the gene pool as compared with other alleles at the same locus, with no regards to their distribution in organism. Example, in a hypothetical population with two alleles ‘A’ and ‘a’ on a locus (‘A’ is dominant, ‘a’ is recessive) will have three types of individuals:

¼ homozygous dominant (Genotype AA)

½ heterozygous dominant (Genotype Aa)

¼ homozygous recessive (Genotype aa)

Suppose there are 100 individuals in a population, in which:

40 are homozygous dominant (AA)

40 are heterozygous dominant (Aa)

20 are homozygous recessive (aa)


The frequency of A allele will be = (80 + 40)/200  =  0.6

The frequency ofa allele will be = (40 + 40)/200  =  0.4

Thus the gene frequency (allelic frequency) can be calculated by dividing the number of a particular allele in question with the total number of allele present on that locus in the population.

(4). What is Genotype Frequency?

“Genotype frequency for a particular type of gene combination on the same locus can be determined by dividing the number of individuals with that genotype by the total number of individuals in the population”

(5). What is Hardy Weinberg law (Hardy Weinberg Equilibrium)?

Hardy Weinberg law or Hardy Weinberg Equilibrium is an explanation for how variation is maintained in a population with Mendelian inheritance. This theory is proposed independently by G. H. Hardy (a mathematician) and Wilhelm Weinberg (a physician).

Hardy Weinberg Law of Equilibrium: “The relative frequencies of various kinds of genes and alleles in a large and randomly mating (panmictic) population tend to remain constant from generation to generation in the absence of mutation, selection, migration and genetic drift.”

Hardy-Weinberg law describes a theoretic situation in which a population is undergoing NO evolutionary changes.

Hardy Weinberg Law says that if the evolutionary forces are absent (mutation, selection, drift) in the population, if the population is large and its individuals are in random mating, each parent produce roughly equal number of gametes. The gametes produced by the mates combine at random and the gene frequency remains constant. Then the genetic equilibrium of the gene in question is maintained and the variability present in the population is preserved. In another way, we can say that there is NO evolution in the population.

For an easy understanding we can use an example with real values:

Suppose a Mendelian population with two allele A and a on one locus, the frequency of gametes with gene ‘A’ will be same as the frequency of ‘A’ gene. Similarly the frequency of gametes with ‘a’ will be same as the frequency of ‘a’ gene.

Let us presume that the numerical proportion of different genes in this population is as follows:

                           AA                     Aa                  aa

                          36%                 48%             16%

Since ‘AA’ individuals make up 36% of the total population, they will contribute approximately 36% of all gametes in the population. Similarly, ‘aa’ individuals will produce 16% of all the gametes. Gametes from ‘Aa’ individuals will be of two types, i.e., with gene ‘A’ and with gene ‘a’ roughly in equal proportion. Since ‘Aa’ constitutes 48% of the total population, they will contribute 48% gametes, but out of them 24% will possess gene ‘A’ and the other 24% will have gene ‘a’.

Hence the overall output of gametes can be summarized as follows:

Gene Frequency and Genotype Frequency If the gametes unite at random, total number of different genotypes will be:

Gamete formation in a mendelian population

If the frequency of ‘A’ is represented as ‘p’ and the frequency of ‘a’ is represented by ‘q’ and if there is random union of gametes with genes ‘A’ and ‘a’ at the equilibrium state, the population will contain following frequencies of the genes ‘A’ and ‘a’ generation after generation:

Hardy Weinberg Equilibrium

AA + 2Aa + aa as genotype frequency

p2 + 2pq + q2 as gene frequency

The results could be explained by relying on the theory of probability as follows:

In a population of large size the probability of receiving the gene ‘A’ from both parents will be p X p = p2

Similarly the probability of receiving the gene ‘a’ from both the parents will be q X q = q2

The probability of being heterozygous will be pq + pq = 2pq

The relationship between gene frequency and genotype frequency can be expressed as:          

p2 + 2pq + q2 = 1    

or        (p + q)2 = 1

This relation is known as Hardy-Weinberg formula of binomial expression

From this equation, it is clear that in a large random mating population not only gene frequencies but also genotype frequencies will remain constant.


Hardy–Weinberg genotype frequencies for two alleles: the horizontal axis shows the two allele frequencies p and q and the vertical axis shows the genotype frequencies. Each curve shows one of the three possible genotypes. (source wikipedia)

(6). What are the Significance of Hardy Weinberg’s law (Hardy Weinberg Equilibrium)?

@. Gene & Genotype frequencies of different alleles of a gene in a population remain equilibrium (generation after generation)

@. Mating is a completely random phenomenon in a population

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@. Only large population follow Hardy-Weinberg’s Law of equilibrium

@. Gene frequencies will be unpredictable in small populations

@. All the genotypes in a population reproduce equally successfully

@. The variation in Hardy Weinberg equilibrium is produced by mutation, selection, migration and genetic drift. These are the evolutionary forces in a population. If these evolutionary forces are not there in the population, the population follows Hardy Weinberg equilibrium. That means, a population in Hardy-Weinberg equilibrium do NOT show evolution or in other words, for the process of evolution to occur, the population should not follow Hardy Weinberg Equilibrium.

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