The Hardy-Weinberg principle is like a Punnett square for populations, instead of individuals. A Punnett square can predict the probability of offspring's genotype based on parents' genotype or the offsprings' genotype can be used to reveal the parents' genotype. Likewise, the Hardy-Weinberg principle is a tool we can use to calculate the frequency of particular alleles in a population.

A a

A

a

AA Aa

Aa aa

Aa Aa

aa aa

a a

A

a

The Hardy-Weinberg model enables us to compare a population's actual genetic structure over time with the genetic structure we would expect if the population were in Hardy-Weinberg equilibrium (or not evolving). If genotype frequencies differ from those we would expect under equilibrium, we can assume that evolution is taking place.

Evolution is simply a change in frequencies of alleles in the gene pool of a population. 

Let us assume that there is a trait that is determined by the inheritance of a gene with two alleles--B and b. 

• Alleles:

•Gene Pool:

• Population:

One of two or more forms of a gene that code for different versions of the same trait.

All possible genes and genetic combinations in a population.

A group of organisms from the same species and the geographic location.

B=brown

b=blonde

If the parent generation had 92% B and 8% b and their offspring collectively had 90% B and 10% b, it would be evident that evolution had occurred between the generations. 

This definition of evolution was developed in the early 20th century by Godfrey Hardy, an English mathematician, and Wilhelm Weinberg, a German physician. 

They concluded in 1908 that gene pool frequencies are inherently stable but that evolution should be expected in all populations virtually all of the time.  They resolved this apparent paradox by analyzing the net effects of potential evolutionary mechanisms.

Hardy

Weinberg

Hardy-Weinberg Equilibrium maintains five basic assumptions:

3.  mutation is not occurring

Under these conditions it is obvious that evolution would not occur.  There are no mechanisms of evolution acting on the population, so the process cannot happen--the gene pool frequencies will remain unchanged.

5.  natural selection is not occurring

1.  the population is infinitely large, and that genetic drift is not an issue within the population.

4. all mating is totally random

2.  there is no gene flow, or migration in or out of the population

However, since it is highly unlikely that any one of these seven conditions, let alone all of them, will happen in the real world, evolution is inevitable.

Hardy and Weinberg went on to develop a simple equation that can be used to discover the probable genotype frequencies in a population and to track their changes from one generation to another. 

This has become known as the Hardy-Weinberg equilibrium equation.

p² + 2pq + q² = 1

p is defined as the frequency of the dominant allele

q is the frequency of the recessive allele for a trait controlled by a pair of alleles (A and a)

In other words, p equals all of the alleles in individuals who are homozygous dominant (AA) and half of the alleles in people who are heterozygous (Aa) for this trait in a population.  In mathematical terms, this is

p = AA + ½AaLikewise, q equals all of the alleles in individuals who are homozygous recessive (aa) and the other half of the alleles in people who are heterozygous (Aa).

q = aa + ½Aa

Because there are only two alleles in this case, the frequency of one plus the frequency of the other must equal 100%, so…

p + q = 1

Since p+q=1, then logically p=1-q

There were only a few short steps from this knowledge for Hardy and Weinberg before they realized that the chances of all possible combinations of alleles occurring randomly is

(p + q)² = 1

Or more simply: p² + 2pq + q² = 1

In this equation, p² is the predicted frequency of homozygous dominant (AA) organisms in a population, 2pq is the predicted frequency of heterozygous (Aa) organisms, and q² is the predicted frequency of homozygous recessive (aa) ones!

Tudaaaaaaah!

From observations of phenotypes, it is usually only possible to know the frequency of homozygous recessive organisms, or q² in the equation, since they will not have the dominant trait. 

Those who express the trait in their phenotype could be either homozygous dominant (p²) or heterozygous (2pq). 

This Drosophila melanogaster is white-eyed. The genotype is rr.

The Hardy-Weinberg equation allows us to predict which ones they are.  Since p = 1 - q and q is known, it is possible to calculate p as well. Knowing p and q, it is a simple matter to plug these values into the Hardy-Weinberg equation (p² + 2pq + q² = 1).   This then provides the predicted frequencies of all three genotypes for the selected trait within the population.

This Drosophila melanogaster is red-eyed. The genotype could be RR, or Rr, as red is a dominant trait.

Albinism is a rare genetically inherited trait that is only expressed in the phenotype of homozygous recessive individuals (aa). 

The most characteristic symptom is a marked deficiency in the skin and hair pigment melanin. 

                                       

                                            

This condition can occur among any human group as well as among other animal species.  The average human frequency of albinism in North America is only about 1 in 20,000.

The Hardy-Weinberg equation (p² + 2pq + q² = 1), and the frequency of homozygous recessive individuals (aa) in a population is q².  Therefore, in North America the following must be true for albinism: q² = 1/20,000 = .00005By taking the square root of both sides of this equation, we get:   

q = .007 (rounded)     

In other words, the frequency of the recessive albinism allele (a) is .007 or about 1 in 140.  Knowing one of the two variables (q) in the Hardy-Weinberg equation, it is easy to solve for the other (p).

p = 1 – q

p = 1 - .007

p = .993

The frequency of the dominant, normal allele (A) is, therefore, .99293 or about 99 in 100.The next step is to plug the frequencies of p and q into the Hardy-Weinberg equation:p² + 2pq + q² = 1

(.993)² + 2 (.993)(.007) + (.007)² = 1.986 + .014 + .00005 = 1

This gives us the frequencies for each of the three genotypes for this trait in the population:p² = predicted frequencyof homozygousdominant individuals = .986 = 98.6%

2pq =predicted frequencyof heterozygousindividuals = .014 = 1.4%

q² = predicted frequencyof homozygousrecessive individuals (the albinos) = .00005 = .005%

(AA)

(Aa) (aa)

1. You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following: A. The frequency of the "aa" genotype.

The frequency of the “aa” genotype is given in the problem as 35%!

B. The frequency of the "a" allele.

The frequency of aa is 36%, which means that q2 = 0.36, by definition.

If q2 = 0.36, then q = 0.6, again by definition.

Since q equals the frequency of the a allele, then the frequency is 60%.

C. The frequency of the "A" allele.

Since q = 0.6, and p + q = 1, then p = 0.4;

the frequency of A is by definition equal to p, so the answer is 40%.

D. The frequencies of the genotypes "AA" and "Aa." The frequency of AA is equal to p2, and the frequency of Aa is equal to 2pq.

So, using the information above, the frequency of AA is 16%

(p2 = 0.4 x 0.4 = 0.16)

and Aa is 48%

(2pq = 2 x 0.4 x 0.6 = 0.48)

E. The frequencies of the two possible phenotypes if "A" is completely dominant over "a."

Because "A" is totally dominate over "a", the dominant phenotype will show if either the homozygous "AA" or heterozygous "Aa" genotypes occur.

The recessive phenotype is controlled by the homozygous aa genotype. Therefore, the frequency of the dominant phenotype equals the sum of the frequencies of AA and Aa, and the recessive phenotype is simply the frequency of aa.

Therefore, the dominant frequency is 64% and, in the first part of this question above, you have already shown that the recessive frequency is 36%.

• http://anthro.palomar.edu/synthetic/synth_2.htm• http://media.nasaexplores.com/lessons/04-006/images/9-12_redeyefly.gif• http://www.k-state.edu/parasitology/biology198/hardwein.html• http://en.wikipedia.org/wiki/Hardy-Weinberg_principle