Hardy-Weinberg equilibrium

Definitions & Key takeaways

The Hardy-Weinberg equilibrium states that the gene frequencies in a population will remain constant from generation to generation if there is no selection, mutation, or migration. This principle can be used to calculate the expected genotype and allele frequencies in a population.

Watch video only
Two scientists - G. H.
Hardy and Wilhelm Weinberg - helped to bridge two major concepts - Mendelian genetics and natural selection. Mendelian genetics state that traits are inherited from one generation to the next through genes, which come in two different versions called alleles.
Alleles can be dominant or recessive, the difference being that it only takes one dominant allele to express a dominant trait, but there need to be two recessive alleles in order to express a recessive trait.
Natural selection, on the other hand, states that organisms that have traits which make them better adapted for their environment are more likely to pass on their genes to their descendents.
Hardy and Weinberg realized that dominant and recessive alleles offer variation in a population and that natural selection would act upon that variation, altering the overall frequency of those traits.
So they took the altering factor - natural selection - off the table and came up with the Hardy-Weinberg principle, or equilibrium, which is a hypothetical state of balance in a population, where the frequency of dominant and recessive alleles remains the same from one generation to the next.
So for a population to achieve this balance there have to be no factors altering its genetic composition. One altering factor is natural selection.
Other factors are mutations - where alleles actually change and become a new variety of a certain trait - and migration - where new and maybe different alleles enter or leave the population causing its composition to change.
Finally, a determining factor is the size of the population - a smaller lot has a greater risk of losing alleles from one generation to the next because some organisms don’t get to reproduce - a process called genetic drift.
If none of these factors affect a population, the genetic pool remains constant. Now let’s say we have a population with a genetic pool that’s large and stable over time.
And let’s assume that we want to study a specific gene that has only two alleles - dominant “A” and recessive “a”. Now, we’ll call the frequency or proportion of the dominant allele - “p” and the frequency or proportion of the recessive allele “q”.
Since these are the only two alleles in the population, p + q has to equal 1. For example, if we know that 75%, or 0.75 of the alleles are dominant, then the remaining 25%, or 0.25 must be recessive alleles, since 0.75 plus 0.25 equals one.
Now, let’s use a Punnett square. There are only two possible alleles that can be found in the male gamete A and a, and the same is true for the female gamete - A and a.
So in this scenario, the chance of having a dominant “A” allele is 0.75, and the chance of having a recessive “a” allele is 0.25.
So in a population the probability of having two dominant alleles or homozygous dominant, means getting a dominant allele from both the male and the female gamete.
This can be calculated as the probability of having a dominant allele from the male gamete, which is p, multiplied by the probability of having a dominant allele from the female gamete, which is also p.
So that’s p x p or p squared. Similarly, the probability of having two recessive alleles or homozygous recessive means getting a recessive allele from both the male and the female gamete, and it works out to q x q or q squared.
Finally, the heterozygous genotype which is one dominant and one recessive allele, can be represented by pq. But if you think about it, there are actually two different ways for the offspring to be heterozygous: One way is to get a dominant allele from the male gamete and a recessive allele from the female gamete.
This can be calculated as the probability of having a dominant allele from the male gamete, which is p, multiplied by the probability of having a recessive allele from the female gamete, which is q.
So that works out to p x q or pq. A second way is to get a recessive allele from the male gamete and a dominant allele from the female gamete.
This can be calculated as the probability of having a recessive allele from the male gamete, which is q, multiplied by the probability of having a dominant allele from the female gamete, which is p.
So that works out to q x p or qp, which is equivalent to pq. So since either way is okay, we add these together and pq + pq = 2pq, and that’s the frequency of the heterozygous genotype.
Since ultimately all of these possibilities have to add up to 1, we get: p2 + 2pq + q2 = 1 Now, in practice, it’s hard to know the exact frequency of the dominant and recessive alleles.
But since two copies of a recessive allele are needed for a recessive phenotype, it’s possible to identify the proportion of recessive phenotypes that are in a population and use that information to calculate allele frequencies.
For example, in pea plants, violet is the dominant trait for flower color and white is the recessive trait for flower color.
Among 100 pea plants, if there are 49 plants that have white flowers, then 49/100 equals q squared. Now we can use that information to calculate the frequency of q which would be √0.49=0.7.
Once you figure out that q = 0.7, then since p+q=1, p must equal 0.3. From there we can simply use the Hardy-Weinberg equilibrium equation: p2 + 2pq + q2 = 1, and since we know the value of p and q, we just have to plug in the numbers.
p2 is 0.32, so 0.09, 2pq is 2 times 0.3 times 0.7, so 0.42 and q2 is 0.72, so 0.49. And of course 0.09 + 0.42 + 0.49 sum up to one.
This means that 0.09, or 9% of the individuals have a homozygous dominant genotype and 0.42, or 42% have a heterozygous genotype.
And that makes sense because the pea plants that have violet flowers will be equal to 9%+ 42%, which is 51% of the population, and together with the 49% that have white flowers, that makes 100%.
Alright, as a quick recap, the Hardy–Weinberg principle states that the genetic features of a population remain the same from one generation to the next as long as the population is in equilibrium.
It is represented by the equation: p2 + 2pq + q2 = 1. And though it is unlikely for a population to reach this equilibrium, the principle can be useful to detect when evolution is happening.