In 1908 the English mathematician **Godfrey H. Hardy** (1877 - 1947) and the German Doctor **Wilhem Weinberg** They concluded that if no evolutionary factor acted on a population that met certain conditions, the frequencies of their alleles would remain unchanged over generations.

This principle became known as **Hardy-Weinberg law or theorem or principle of gene balance.**

## Hardy-Weinberg equilibrium conditions

The conditions necessary for a population to remain in gene equilibrium, according to Hardy and Weinberg, are as follows:

**The population must be very large**(theoretically, the bigger the better) so that all possible crossings can occur according to the laws of probability.**Population must be panmitic (**from greek*pan*, all, and from Latin*miscere*, mix), ie the crossings between individuals of different genotypes should occur randomly, without any preference.

A population that has these characteristics, and in which no evolutionary factors occur, such as mutation, selection or migration, will remain in gene equilibrium, that is, the frequencies of alleles do not change over the generations.

## The expression of gene balance

Suppose a population in gene equilibrium, in which the frequencies of alleles **THE** and **The** (non-sex) are respectively 80% and 20% (0.8 and 0.2). Knowing that each gamete carries only one allele of each gene, it can be concluded that 80% of gametes produced by members of this population will carry the allele. **THE**, and 20% will be carriers of the allele **The**.

A homozygous individual **AA** formed when a male gamete carrying an allele **THE** fecundates a female gamete also carrying an allele **THE**. The probability of this event happening is equal to the product of the frequencies with which these types of gametes occur. So the probability of forming an individual **AA** **é** **0.64 or 64%**.

**f _{(}**

_{THE)}x f_{(THE)}= 0.8 x 0.8 = 0.64 or 64%A homozygous individual **aa**, in turn, originates when two gametes meet it. The probability of this event occurring is equal to the product of the frequencies with which these gametes occurred. The probability of forming an individual **aa is 0.04 or 4%.**

**f _{(The)} x f_{(The)} = 0.2 x 0.2 = 0.04 or 4%**

A heterozygous individual **Aa** graduates when a male gamete **THE** fecundates a female gamete **The**, or when a male gamete **The** fecundates a female gamete **THE**. The probability of these events occurring is **0.32 or 32%.**

**f _{(THE)} x f_{(The)} + f_{(The)}x f_{(THE)} = 0.8 x 0.2 + 0.2 x 0.8 = 0.32 or 32%**

If we call p the frequency of the dominant allele, and q the frequency of the recessive allele, we can write that the frequency of individuals AA is equal to p2, the frequency of individuals **aa** is equal to q2, and that of heterozygous individuals **Aa** equals 2pQ. See why:

Allele frequency in male gametes p = f_{(The)} | |||

Female gamete allele frequency |
| P^{2 }= f_{(AA)} | pq = f_{(Aa)} |

qp = f_{(aa)} | what^{2} = f_{(aa)} |

The sum of the frequencies of the different genotypes will be 1 or 100%.

### P2 + 2 why + q2 = 1

### F(AA) f(Aa) + f(aa) f(aa)

The Hardy-Weinberg principle states that for a given pair of alleles with frequencies **P** and **what**, in an equilibrium Mendelian population, the frequency of the different genotypes in each generation will be in accordance with the expression p2 + 2pq + q2 = 1.

## Importance of the Hardy-Weinberg Principle

The Hardy-Weinberg principle sets a theoretical standard for gene behavior across generations. **In practice, it helps us to understand whether or not a population is in equilibrium, drawing attention to the possible evolutionary factors that are at work.**

Geneticist FJ Ayala (1934) of the University of California (USA) compares the Hardy-Weinberg principle with Newton's first law of mechanics, according to which a moving body keeps its velocity constant until no force intervenes. external. Bodies are always subject to external forces, but Newton's law is a theoretical starting point, important for understanding mechanics. The Hardy-Weinberg principle states that in the absence of evolutionary factors gene frequencies remain constant in a theoretical population. There are always evolutionary factors at work in real populations. However, the Hardy-Weinberg law is important because it allows you to determine how much and how a population's balance is being affected by evolutionary factors.