## The theory of natural selection (part 1) - Why is the Hardy-Weinberg ratio useful?

Three sources of interest in the Hardy-Weinberg ratio:

• Historical and Conceptual interest

It is an important property of Mendelian genetics that variation is preserved and the Hardy-Weinberg theorem gives quantitative demonstration of that fact. The theorem was published in the first decade of the 20th century, as Mendelism was becoming accepted, and it was historically influential in proving that Mendelian inheritance did allow variation to be preserved.

• Deviations direct future research

A second interest of the theorem is as a kind of springboard, that launches us toward interesting empirical problems. If we compare genotype frequencies in a real population with the Hardy-Weinberg ratios, then if they deviate, it suggests something interesting (such as selection or non-random mating) may be going on, which would merit further research.

If Hardy-Weinberg ratios are found, then it is a clear sign that sexual reproduction is taking place. Recent research in dandelions, pictured opposite, has found Hardy-Weinberg ratios, suggesting that they are not, as commonly believed, entirely asexual.

• Theoretical interest

In the general model of population genetics there were five stages, joined by four calculations. The Hardy-Weinberg theorem simplifies the model wonderfully. If we assume random mating, we can go directly from the adult frequencies in generation n to the genotype frequencies at birth in generation n + 1, collapsing three calculations into one. If we know the adult genotype frequencies in generation n (stage 1), we only need to calculate the gene frequencies: the genotype frequencies at birth in the next generation (stage 2) must then have Hardy-Weinberg frequencies, because the gene frequencies do not change between the adults of one generation and the new-born members of the next generation.

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