Hardy-Weinberg Theorem

Hardy-Weinberg Theorem

Hardy-Weinberg theorem, an algebraic formula that describes the hereditary equilibrium within a population. Hardy-Weinberg theorem is named for the two scientists Wilhelm Weinberg, a German physician, and Godfrey Harold Hardy, a British mathematician, who derived the principle independently in 1908.

Population, Gene Pool, Allele and Genotype Frequencies

A population is a localized group of individuals belonging to the same species. For now, we will define a species as a group of populations that have the possibility to interbreed in nature. Each species has a geographical variety within which individuals are not expanded evenly, but are usually concentrated in several localized populations.

A population may be isolated from others of the same species, exchanging genetic products just seldom. Such isolation is especially typical for populations confined to widely separated islands, unconnected lakes, or mountain ranges separated by lowlands. Within a population, individuals are concentrated in centers and are more likely to interbreed with members of the same population than with members of other populations.

For that reason, individuals near a population center are, on average, more closely related to one another than to members of other populations.

The total aggregate of genes in a population at any one time is called the population’s gene pool. It includes all alleles at all gene loci in all individuals of the population. For a diploid species, each locus is represented twice in the genome of an individual, who might be either homozygous or heterozygous.

If all members of a population are homozygous for the same allele, that allele is stated to be fixed in the gene pool. More frequently, there are two or more alleles for a gene, each having a relative frequency (percentage) in the gene pool.

Let us consider an example.

Imagine a wildflower population with 2 varieties contrasting in flower color. An allele for pink flowers, which we will symbolize by A, is entirely dominant over an allele for white flowers, represented by a. Suppose these are the only two alleles for this locus in the population. Our imaginary population has 500 plants.

Twenty have white flowers since they are homozygous for the recessive allele; their genotype is aa. Of the 480 plants with pink flowers, 320 are homozygous (AA) and 160 are heterozygous (Aa). Since these are diploid organisms, there is an overall of 1000 copies of genes for flower color in the population.

The dominant allele represents 800 of these genes (320×2 = 640 for AA plants, plus 160×1 = 160 for an individuals). Therefore, the frequency of the A allele in the gene pool of this population is80%, or 0.8.

And since there are only two allelic kinds of the gene, the allele must have a frequency of 20%, or 0.2. Related to these allele frequencies are the frequencies of genotypes. In our model wildflower population, these frequencies are:

AA= 0.64 (64%) (320 out of 500 plants),

Aa= 0.32 (160/500) and

aa = 0.04 (20/500).



Hardy-Weinberg Theorem

The frequencies of genotypes of non-evolving populations are explained by Hardy- Weinberg theorem.

“It states that the frequencies of alleles and genotypes in a population’s gene pool remain constant over the generations unless acted upon by agents other than sexual recombination. So, shuffling of alleles due to meiosis and random fertilization has no effect on the overall genetic structure of a population.”

A general equation called the Hardy- Weinberg equation is used for computing the frequencies of alleles and genotypes in populations at equilibrium.

Estimations of Allelic Frequency

For a gene locus where only 2 alleles occur in a population, population geneticists use the letter P to represent the frequency of one allele and the letter q to represent the frequency of the other allele.

  • P = Dominant allele
  • q= Recessive allele

In the imaginary wild flower population, P= 0.8 and q= 0.2.

Note that P+ q= 1;

  • The combined frequencies of all possible alleles must account for 100% of the genes for that locus in the population.
  • If there are just 2 alleles and we understand the frequency of one, the frequency of others can be calculated:

if P + q = 1, then 1 – P = q or 1 – q + P.

Estimation of Gene frequency

When gametes combine their alleles to form zygotes, the probability of producing an AA genotype is P2. In the wildflower population, P-0.8, and P2= 0.64, the probability of an A sperm fertilizing an A ovum to produce an AA zygote.

The frequency of individuals homozygous for the other allele aa is q2, or 0.2 x0.2= 0.04 for the wildflower population. There are two ways in which an Aa genotype can arise, depending upon which parent contributes the dominant allele. For that reason, the frequency of heterozygous individuals in the population is 2Pq (2×0.8 x0.2= 0.32, in our example). If we have actually calculated the frequencies of all possible genotypes properly, they ought to amount to 1:

P2 + 2pq + q2 = 1

Frequency of AA Frequency of Aa Frequency of aa

For our wildflowers, this is.

0.64 + 0.32 + 0.04 =1

In fact, the Hardy-Weinbergtheorem is a binomial expansion.

(P+ q) 2 = P2 + 2Pq + q2

Factors affecting Gene Frequency

Lots of factors can change gene frequency. Out of these five affect the proportion of homozygotes and heterozygotes enough to produce significant variances from the percentage claimed by the Hardy Weinberg principle. They are as follows.


The ultimate source of all modifications and changes; individual mutations occur so hardly ever that mutation alone does not change allele frequency much.


A really powerful representative of change, migration locally acts to prevent evolutionary changes by avoiding populations that exchange members from diverging from one another. Emigration and migration of members of a population, cause disruption in the gene pool.

3.Genetic drift

It is the change in frequency of alleles at a locus that happens by chance. In small populations, such fluctuations may lead to the loss of particular alleles. This may happen in a little population when a few individuals fail to reproduce and after that genes are lost from the population.

4.Non-random mating

Inbreeding is the most typical kind; it does not alter allele frequency, however, reduces the percentage of heterozygous individuals. Individuals with particular genotypes often mate with one another more commonly than would be anticipated on a random basis. This is called non-random mating, causing the frequencies of specific genotypes to differ significantly from those forecasted by the Hardy- Weinberg principle.


Some individuals leave behind more offspring than others, and the rate at which they do so is affected by their acquired qualities. This is called selection. Selection can be an artificial selection or natural selection. In artificial selection, the breeders pick for the wanted characters. In natural selection, the environment plays this function, thus affecting the proportions of genes in a population.