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Hardy-Weinberg Equilibrium Equation

Evolution is not only the development of new species from older ones, as most people assume.  It is also the minor changes within a species from generation to generation over long periods of time that can result in the gradual transition to new species.

 

This definition of evolution was developed largely as a result of independent work in the early 20th century by Godfrey Hardy, an English mathematician, and Wilhelm Weinberg, a German physician.  Through mathematical modeling based on probability, 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, and the population geneticists who followed them came to understand that

evolution will not occur in a population if seven conditions are met:

1.   mutation is not occurring

2.  natural selection is not occurring

3.  the population is infinitely large

4.  all members of the population breed

5.  all mating is totally random

6.  everyone produces the same number of offspring

7.  there is no migration in or out of the population

 

 

 

Godfrey Hardy and Wilhelm 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.

In the equation 1 is equal to the total population representing a trait (100%)

 

p² + 2pq + q² = 1

 

p is the frequency of the dominant allele for a trait

p = all of the alleles in individuals who are homozygousdominant (AA) and half of the alleles in people who are heterozygous (Aa)

q is the frequency of the recessive allele for a trait

q = all of the alleles in individuals who are homozygous recessive (aa) and the other half of the alleles in people who are heterozygous (Aa)

 

p² is the predicted frequency of homozygous dominant (AA) people in a population

2pq is the predicted frequency of heterozygous (Aa) people

q² is the predictedfrequency of homozygous recessive (aa)

 

p + q = 1

Because there are only two alleles in this case, the frequency of one plus the frequency of the other must equal 1

 

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

(p + q)² = 1

or

p² + 2pq + q² = 1

~THE HARD MATH~

If you want to try out the math yourself or learn more visit

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