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The H.W. equation is a simple extension of the Punnett squares with two alleles assigned frequencies p and q. From the table given above, one can trace genetic reassortment during sexual reproduction and see how it affects the frequencies of the B and b alleles during the next generation. In this table, it is assumed that the union of sperm and egg in these cats is random, so that all combinations of b and B alleles are equally likely.

For this reason, the alleles are mixed randomly and represented in the next generation. Each individual in each generation has a 0.6 chance of receiving a B allele (p = 0.6) and a 0.4 chance of receiving a b allele (q – 0.4).

In the next generation therefore, the chance of combining two alleles is p^{2}, or 0.36 (that is, 0.6 x 0.6), and approximately 36% of the individuals in the population will continue to have the BB genotype.

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The frequency of bb individuals is q^{2} (0.4 x 0.4) and so will continue to be about 16%, and the frequency of Bb individuals will be 2pq (2 x 0.6 x 0.4). or approximately 48%. Phenotypically, 84 black individuals (with either BB or Bb genotypes), and 16 white individuals (with bb genotype) in the population are seen.

The simple relationship has proved extraordinarily useful in assessing actual situations. Consider the recessive allele responsible for the serious human disease cystic fibrosis. This allele is present in North Americans of Caucasian descent at a frequency q of about 22 per 1000 individuals, or 0.022.

What proportion of North American Caucasians, therefore, is expected of express this trait? The frequency of double recessive individuals (q^{2}) is expected to be 0.022 x 0.022, or 1 in every 2000 individuals.

What proportion is expected to be heterozygous carriers? If the frequency of the recessive allele q is 0.022, then the frequency of the dominant allele p must be 1 – 0.022, or 0.978. The frequency of heterozygous individuals (2pq) is thus expected to be 2x 0.978 x 0.022, or 43 in every 1000 individuals.

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Most human populations are large and effectively random-mating and are, therefore, similar to the “ideal” population envisioned by Hardy and Weinberg. For some genes, the calculated predictions do not match the actual values. The reasons they do not tell us a great deal about evolution.

**Why DoAllelle Frequencies Change:**

According to the Hardy-Weinberg principle, both the allele and genotype frequencies in a large, random-mating population will remain constant from generation to generation if no mutation, no migration, and no selection occur.

The stipulations tacked onto the end of the statement are important. In fact, they are the key to the importance of the Hardy-Weinberg principle, because individual allele frequencies are changing all the time in natural populations, with some alleles becoming more common than others.

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The Hardy Weinberg principle establishes a convenient baseline against which to measure such changes. By looking at how various factors alter the proportions of homozygous and heterozygous in populations (usually expressed as the HETEROZYGOSITY, the likelihood that a randomly selected individual will be heterozygous at the gene locus), one can identify the factors affecting particular situation. Many factors can alter allele frequencies.

Only five, however, alter enough the proportions of homozygous and heterozygous to produce significant deviations from the proportions predicted by H.W. principle: mutation, migration (both immigration into and emigration out of a given population); genetic drift (random loss of alleles, which is more likely in small populations), nonrandom mating, and selection (see table below).

Of their only selection produces adaptive evolutionary change because only in selection does the result depend upon the nature of the environment. The other factors operate relatively independently of the environment, so the changes they produce are not shaped by environmental demands.