โฑ๏ธ **2 min read**

#mutations

#hardy-weinbergequilibrium

#phenotype

#genotype

table of contents

written by

samantha himegarner

published on april 5, 2020

Last updated on May 31, 2020

The Hardy-Weinberg Equilibrium is a model in which allele frequencies will *not *change if these five conditions exist:

There is

**no mutation**. (That way no new alleles are added to the gene pool).There is

**no type of selection acting upon the population.**(Yup, this includes all kinds of selection: sexual, artificial, and natural. The idea is that the allele frequency isnโt changing at all, and therefore, no favorable traits.)There is

**no gene flow.**(There can not be any movement between populations or any kind of outside reproduction.)**Population size is infinite.**(That way the population wonโt be affected by a natural disaster, as shown in genetic drift scenarios.)**Mating is random.**(Again, no sexual selection or preference.)

Of course, each of these five things are impossible for a natural situation. A population will never be infinite, and mutation is not something that can be controlled! Thatโs why this simply acts as a model to calculate genotypic ratios under these assumptions (which, of course, are false).

The calculated ratios under this control population can serve as a null hypothesis for evolution. The allele frequencies in a population are calculated from the genotypic ratios. Hereโs how:

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Although this equation may look like a lot, it actually isnโt too bad. If you think about it, we only have two variables! The โpโ in the equations can represent the frequency of allele 1 in the population, and the โqโ will represent the frequency of the second allele. These numbers will be decimals, as they will represent the percentage of the population that has each phenotype (which is why it adds up to 1!).

For the first equation, **p2 **represents the frequency of a **homozygous dominant** genotype, **2pq **represents the frequency of a **heterozygous genotype**, and **q2 **represents the frequency of the **homozygous recessive** genotype.ย
Keeping all that in mind, the first thing to do in the process of calculating is to determine the frequency of the recessive genotype. This is the only genotype that can be determined from the phenotypic ratios (a dominant phenotype could be either homozygous dominant or heterozygous).

The frequency of the recessive genotype will be equal to q2. Therefore, q can be found by taking the square root of that number. Then, subtract this number from 1 to find p, or the frequency of the dominant phenotype in a population.

Once the variable p is found, it can be put into the first equation to find the genotypic ratios of a population.

Image courtesy of Giphy.

For example, if there is a population of 100 birds, 84 of them have white feathers and 16 of them have grey feathers. Hereโs how we would solve:

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