Weinberg's Phenotypes

In the 19th century, naturalist Charles Darwin formulated his theory of evolution. He also stated that the offspring of parents had mixtures of physical characteristics taken from the parents. This was proved incorrect by Gregor Mendel who discovered that offspring received particles from their parents that made up their physical traits. In 1908, German physician Wilhelm Weinberg found a way to connect evolution to genetic probability through the use of a formula. That same year, only six months later, English mathematician G.H. Hardy came up with the same formula and ideas. Neither of the men were aware of the other's works. In the past, it was known most as Hardy's Law because Hardy published his works in English, while Weinberg's was only
available in German. Today, it is most commonly known as the Hardy Weinberg Equation. It is also known as the Hardy Weinberg Principle, Law, Theorem, etc. The equation is used to describe the frequency of different genes, known as genotypes, in a (large)population in the absence of other evolutionary influences. Assuming everything is at a equilibrium, the frequency of the genes will always remain constant. Geneticists use the data taken from the equation and compare it to real life situations, where an absence of evolutionary influences are almost impossible. For example, if a certain number of people in a population have cystic fibrosis, scientists can use the data from that number and compare it to the numbers of a population that has the same number of people with cystic fibrosis, but at a Hardy-Weinberg equilibrium.

The Hardy Weinberg Equation compares the genotypes in a population.
A person's genotypes is their genes, which make up their DNA. Alleles are the types of genes, come in pairs in a gene, and are responsible for a person's phenotypes(Wanjie 29). Phenotypes are the physical characteristics of a person. Alleles are either characterized as dominant or recessive. The dominant allele presides over the recessive allele, making the recessive allele "hidden". Because the recessive allele is covered, that person's phenotype will only show the dominant allele. If a person has both recessive alleles, then that person will show the recessive allele. For example, blue eyes are recessive to brown eyes. A person that has two alleles for brown eyes will definitely have brown eyes. If a person has one allele for blue eyes and one for brown eyes, then that person will have brown eyes because the brown eye allele is dominant over the blue eye allele. If a person has two blue eye alleles, then that person will have blue
eyes.

The Hardy Weinberg equation contains at least two variables, depending on the genes in the situation.
Most of the time, only two genes are represented, therefore the equation has two variables. The variable p represents the frequency of the dominant allele, while the variable q represents the frequency of the recessive allele. In the Hardy Weinberg equation, p+q must always equal 1. Given the statement: You will have the dominant allele or the recessive allele. In probability, "or" means to add, therefore p+q=1. You have two alleles, thus given the previous statement, you have (p+q) and (p+q). "And" means to multiply, therefore (p+q)(p+q)=1,
or p² + 2pq + q² = 1. "p²" represents the frequency of homozygous dominant(containing both dominant alleles). 2pq represents the frequency of heterozygous(containing one recessive and one dominant allele). Heterozygous people can also be called heterozygotes. "q²" represents the frequency of homozygous recessive(containing both recessive alleles).

Before beginning with Hardy Weinberg problems, many assumptions must be made. The assumptions ensure a stable and constant frequency, known as a equilibrium, from one generation to the next. The following seven conditions represent a Hardy Weinberg Equilibrium.(anthro.palomar.edu)
1. The population is very large
2. Natural selection is not occurring
3. Mutation is not occurring
4. All members of the population choose to reproduce
5. Mating is completely random
6. Everyone produces the same number of offspring
7. There is no migration from population to population
Because many of the assumptions do not occur in real life, it is almost impossible to reach Hardy Weinberg equilibrium. Geneticists use the equation as a control group in which results from real life populations can be compared to.

Many people, when solving Hardy Weinberg problems, tend to find one variable, substitute it into the equation, and then find the other variable. This common mistake may lead to confusion when solving for the different genotypes, so it is crucial to remember that p+q always equals 1.
Before approaching a Hardy Weinberg problem mathematically, it is important to understand what the question is asking for(homozygous dominant, recessive, heterozygous) and thoroughly analyze the information that is given to you. More than often, the information given contains the number of subjects that show the recessive trait. Recessive genes can easily be counted because you can definitely be sure that both alleles are recessive. From there, you can find the frequency of the recessive allele, q. The frequency of the recessive allele is a ratio of the number of recessive alleles to the total number of people.

Five percent of the population on earth has blue eyes. Blue eyes are recessive to any other eye color. What is the frequency of the recessive allele? What percent of the population is heterozygous for this trait?(Assume the population is in Hardy Weinberg equilibrium).
This is one of the simpler questions; they give you enough information to quickly find one variable, in this case, q. Because blue eyes are recessive and five percent of the population has blue eyes, that means five percent of the population is homozygous recessive(having both recessive alleles). In the equation, q² represents the individuals that are homozygous recessive.
Using this information, we can conclude that q²=5%. When given a percentage, always change the percent to a decimal. q²=0.05, take the square root of both sides to solve for q, and q=0.22(rounded to the nearest hundredth). p is 1-q, or 1-0.22, which is 0.78. We can now answer the first question; the frequency of the recessive allele is 0.22. The second question is asking for the percent of the population that is heterozygous for the trait of recessive blue eyes, meaning they have an allele for blue eyes and an allele for non-blue eyes. To find the percentage, the second part of the equation, 2pq, must be used. Since p and q have already been found, simply substitute in the values to get approximately 0.34, or 34%.

The Hardy Weinberg equation is one of the most used tools in the field of genetics. One of its main uses is to prove the occurrence of evolution.