Hardy-Weinberg+Principle

**//__A. Introduction__//**
The term evolution is defined as the sum total of genetic changes occurring in an individual that is a member of a gene pool. However, a very simple definition of evolution would describe it as a change in allele frequencies in a gene pool of a population. As time developed, the definition became more precise and easier to comprehend, especially through the independent work of an English Mathematician, Godfrey Hardy and a German Physician, Wilhelm Weinberg. Based on their mathematical studies, they concluded that frequencies of gene pool are stable and that evolution is more likely to occur in all populations. As a result, they made an effort to analyze the net effects of potential evolutionary mechanisms.

__//**B. Genetic Equilibrium**//__
As they described, a non-evolving population has no change in their allele frequencies. Also, they discussed some conditions that must be met in order for the population to remain stable:

1. **No net mutation**: There shouldn’t be any conversion of alleles from dominant to recessive or vice versa. The allele frequencies must not change. Since any mutation could cause a change in allele frequencies or could create a new allele, no mutations should occur.

2. **No natural selection**: Since natural selection favors one phenotype over the other for survival by making a contribution to the next generations by evolution, no natural selection should occur.

3. **Large Population**: In small populations, allele frequencies are more likely to change creating a major impact in the gene pool. Since the effects aren’t seen as significant in a large population, population size should be larger.

4. **Random Mating**: If the mating is nonrandom and the individuals select their mates, then the individuals that have a better ability to adapt will have a reproductive advantage, making evolution possible. Therefore, mating should be random and individuals with different genotypes must mate with one another randomly.

5. **No Migration**: There shouldn’t be any migration into or out of the gene pool as it could alter the allele frequencies of the individuals.

**//__C. Mathematical Relationships__//**
If these processes or mechanisms don’t seem to occur, there will be no evolution taking place and the allele frequency of the gene pool will remain stable. But, they are very unlikely to happen and as a result, evolution is inevitable. To keep track of the genotypic frequencies and the changes, Hardy and Weinberg developed an equation which became known as Hardy-Weinberg Equation: p² + 2pq + q² = 1. In this equation, P stands for dominant allele frequency while q represents the frequency of the recessive allele. To make it even simpler, p represents all the alleles in an individual that is homozygous dominant and half of the alleles in people who are heterozygous. Similarly, q is equal to all the alleles in an individual who is homozygous recessive and half of the alleles in people who are heterozygous. In this equation, p² represents the frequency of homozygous dominant, 2pq represent the frequency of heterozygous while q² represents the frequency of homozygous recessive. Since only two alleles are present in the equation, their sum of their frequencies must be 100%, which brings up another equation: p + q = 1 or p = 1 - q. Once we know the equation and value of q is known, we could plug in the value to find out the frequencies. An interesting thing to know is that the genotypic and the phenotypic frequency of the recessive allele are the same and therefore once we have one, we automatically know the other.

The Hardy-Weinberg Equation allows us to compare the actual genetic structure over time with the ones that we expect to have if the populations were considered to be an ideal Hardy- Weinberg population living under the conditions of genetic equilibrium. It also helps in calculating the allele, genotypic, and phenotypic frequencies of a gene present in a population.