Why is Hardy Weinberg equilibruum an ideal model and not representative of every natural population?

Hardy Weinberg equilibrium describes when evolution by natural selection doesn't occur.  In the equation (p + q)^2 = 1, p and q being the proportions of the population having either allele (usually one is assigned to be dominant, the other recessive in a similar fashion to a Punnett square cross) if evolution does not occur p and q should remain constant through out various generations.  We can observe deviancy from this equation and the change through various generations with the concept.  

Some conditions include: no mutation; infinitely large population; random mating; no selection (all equal fitness/chance at reproduction); no migration (out being a loss of a genotype, in being the introduction of a new genotype--both unacceptable).  Mutation you can never stop, even if you do control the other conditions in a laboratory setting.  Mutation occurs constantly, even with minute little changes in DNA sequence.  

By stating when evolution doesn't occur, we can better understand the mechanisms by which it does occur.

Microevolution is a change in a population's alleles over a period of time.

It is very difficult to detect changes that occur on the microscopic level. These changes must manifest themselves in the organisms phenotype. Since individuals do not evolve, one must keep a close eye on the individuals population to detect any change in genotypic modification. Biologists have a way to help them detect such changes; it is called the Hardy -Weinberg theorem.

Hardy-Weinberg Theorem:

This idea was developed to determine if a population was evolving. The authors of the theorem set up a series of parameters, which do not exist in nature, to be followed when determining the allele frequencies of any population. These guide lines are as follows:

The population must be very large in size.
It must be isolated from other populations. ( no gene flow)
No mutations.
Random mating.
No natural selection.
Since these characteristics cannot be eliminated from nature what is the purpose of these restrictions? To answer this question let us take a look at the mathematics behind this idea.

Let us take a look at a population with alleles for large and small ears. Let us use L for the dominant allele, large ears, and l for the recessive allele small ears. If we look at that population of people, we can determine the number of individuals with large and small ears. Since each group is a result of the following genotypes: LL, Ll, and ll, we have three groups of possible combinations. These alleles make up the gene pool for that trait. The Hardy -Weinberg theorem states that : p + q =1

p = the dominant allele

q = the recessive allele

1 = the gene pool of that trait.

So all the L alleles added to all the l alleles = 100% of the genes for that trait in that population.

If we expand that formula by multiplying it by itself we produce the expanded formula:

p2 + 2pq + q2 = 1
 

The p2 = the genotype LL, the 2pq = the genotype Ll, and the q2 = the genotype ll

If the large ear allele has a .8 frequency in the population, the l allele must have a .2 frequency since .2 + .8 = 1. If we substitute these frequencies into the expanded formula we can determine the percent of each of the three phenotypes in a given population.

p2 = .64 , 2pq = .32, and q2 = .04 = 1
--64%-----32%---------- 4%----------= 100%

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If we know the percent of the homozygous recessive organisms, we can take the square root of the decimal value and determine the frequency. With that value we can determine the frequency of the dominant allele by subtracting it from 1. So as one can see,the formula can be used if the % is given or the frequency.

This first calculation will act as a base and any changes that occur to the frequencies of further calculations may indicate that evolution is occurring in that population.