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Evolution in Action
Hardy-Weinberg Principle
Random Mating
Peccaries are not jealous or possessive animals. Unlike a lot of large mammalian species, any male may mate with any female, a condition known as random mating.

So long as there are approximately equal numbers of males and females in the mating group, the frequencies of b genes (which produce a softer covering bristle on the peccary) and the frequencies of the B genes (which produce the tougher bristle coat on the peccary) will be the same in the male sperm, and the female eggs.

In this example it is assumed that the frequency of the b gene/allele is 0.2 and the frequency of the B gene/allele is 0.8

At the time of conception, when the next generation of baby peccaries is produced, any male sperm can fertilize any female egg cell and start the new peccary on its journey in life. It is possible, therefore, to calculate not only the genotypes of the next generation of baby peccaries, but how many peccaries will be born with those genotypes.

This can be done using a Punnett Square (to determine the different genotypes), and then multiplying together the frequencies of the alleles used to produce those genotypes (to determine how many peccaries are born with each genotypes).


0.8B 0.2b
Sperm 0.8B 0.64BB 0.16Bb
0.2b 0.16Bb 0.04bb

Genotype BB will have a frequency of 0.64
Genotype Bb will have a frequency of 0.32
(from 0.16Bb + 0.16Bb)
Genotype bb will have a frequency of 0.04

Every generation of new peccaries that are born will be 64% BB, 32% Bb, and only 4% bb. This calculation can be performed over and over again, in every generation, for hundreds and thousands of generations, and the answer is always the same: 64% BB, 32% Bb, and only 4% bb.

The ratio of the genotypes (and thus the ratio of the phenotypes) in every batch of baby peccaries born, will always be the same as those of the previous generations, and the same as the ones that follow. This is a very stable, unchanging situation and has been called genetic equilibrium.

If a population is stable, then the gene pool and the ratio of the genes within it will be stable and unchanging.

Allele pool equation G.H. Hardy, a Cambridge professor, was one of the first people to realize that populations are genetically stable in theory. Challenged by geneticist R.C. Punnett (of the Punnett Square fame) to prove this, Hardy wrote out the allele pool equation on the back of a beer mat (a coaster for pints of beer) while the two scientists were having lunch one day in an English pub.

Hardy's equation said that p + q = 1, by which he meant that the sum of the frequencies of all the alleles in a gene pool equals 1.

Chewing on the end of his pencil, Hardy took this equation one step further. He then wrote, p2 + 2pq + q2 = 1, which is what you get when you multiply the simpler equation with itself.

This second equation is another way of representing the outcome of the Punnett Square, and the calculations of genotype frequencies, shown above. It is a mathematical way of determining the ratios of genotypes and phenotypes in every subsequent generation of baby peccaries.

These equations of Hardy's demonstrate that all populations are genetically stable, even over thousands of generations, and hundreds of thousands of years. It was quite an assertion.

Hardy was reluctant to have the "Hardy equation" published, despite its obvious significance to the study of evolution. Punnett eventually persuaded him, but by then a similar conclusion had been drawn by G. Weinberg in Germany, and W.E. Castle in America.

This "law" of evolution became known as the Hardy-Weinberg principle, and Castle's contribution was completely ignored.

© 2001, Professor John Blamire