# Definition of Hardy Weinberg Equilibrium

Hardy-Weinberg Equilibrium defined as the totality of the alleles of every gene in a population is the **gene pool** of that population. Each individual carries some of the alleles, but individuals come and go. However, the total gene pool continues as a constant representation of a population. Changes in the specific frequencies of particular alleles constitute the raw material of evolution. At first, modest alteration in allelic frequency does not produce observable changes in a population, but over long periods of time, such changes produce marked alterations in the characteristics of a population.

# Explanation of Hardy Weinberg Equilibrium

A better understanding of the slow way in which shifts in gene (allele) frequencies may generate the patterns of evolutionary change comes from a study of hypothetical populations in which **no such shifts** in gene frequencies occur. Using the genetic principles of Mendel, G. H. Hardy and W. Weinberg determined that the frequencies of alleles and even the ratios of genotypes tend to remain constant from one generation to the next in sexually reproducing populations under certain conditions.

# Conditions of Hardy Weinberg Equilibrium

These conditions include:

- A very large population
- No change in mutation rates
- Complete randomness in mating so that reproductive success is the same for all allelic combinations
- No large-scale migrations into or out of the mating pool

# Calculation of Hardy Weinberg Equilibrium

In such stable populations, gene frequencies follow simple laws of probability.

## Calculation For One Allele

For example, if allele **A** has a frequency of **p** in a population, and allele **B** has a frequency of **q,** and there are no other alleles for this gene, **p** + **q –** 1. The probability that two events will occur at the same time is equal to the probability that the first will occur multiplied the probability that the second will occur. The probability that allele **A** will occur is equal to its frequency **p;** likewise, the probability that **B** will occur is **q.** Thus, in a given population the frequency of homozygous **AA **individuals is equal to the probability that two **A** alleles will be in the zygote at the same time, which is equal to **p** x **p,** or **p ^{2}.** By similar reasoning, the frequency of

**BB**homozygotes is

**q**

^{2}.## Calculation For Two Alleles

Since there are two ways of forming the heterozygote **AB** (the **A** allele from the mother and the **B** allele from the father, or vice versa), the frequency of **AB** in the population is 2**pq** (rather than simply **pq).** The sum of all three genotype frequencies = **p ^{2}** + 2

**pq**+

**q**1. Note that this is a binomial expansion of the term

^{2}=**(p + q)**If there were three alleles in the population, the frequencies of each genotype could be determined from the trinomial expansion

^{2}.**{p**+

**q**+ r)

^{:}, where r is the frequency of the allele C.

# Practical Example Hardy Weinberg Equilibrium

In a population in Hardy-Weinberg equilibrium, with only two alleles for a particular gene, if we know that allele A has a frequency p of 0.3, we can find the frequency of allele B. Since p + q – 1, we know that q = 1 — p = 0.7. Furthermore, we can determine the frequencies of the various genotypes, as follows:

AA = p^{2} = (0.3)(0.3) = 0.09

AB = 2 pq = 2(0.31(0.7) = 0.42

BB = q^{2} = (0.71(0.7) = 0.49

Since allelic frequencies tend to remain constant from generation to generation, departures from this constancy help to expose selection pressures operating in the population.