Hardy-Weinberg-Equilibrium

I am reluctant to intrude in a discussion concerning matters of which I have no expert knowledge, and I should have expected the very simple point which I wish to make to have been familiar to biologists.

This is how the British mathematician Godfrey Hardy opened his 1908 Science publication (Mendelian Proportions in a Mixed Population), which was an important corner stone for the emerging field of population genetics. In his article Hardy shows that under certain conditions (see below) the frequency of two alleles at a single autosomal gene locus stay constant. Assuming that a population has an allele A with frequency p and an allele a with frequency q then this population will have these three genotypes:

AA with frequency p2
aa with frequency q2
Aa with frequency 2pq

Under the following four assumptions the frequency of p2:2pq:q2 will remain constant in all following generations:

  1. infinitely large population
  2. panmixia (random mating)
  3. no migration
  4. no selection or mutation.

This means, if we were to analyse the allele frequencies of a population and we find that they are not in equilibrium, then one or several of the above assumptions must be violated, i.e. there may be selection against one of the three phenotypes or there is no random mating. This however can only be the starting point of an analysis. In fact in many cases we already know that selection against a phenotype is going on and we don’t have to care for the equilibrium in the first place.

So, what makes the HWE special? I think it is two-fold. Firstly, at the beginning of the 20th century, genetics was still in its infancy. Gregor Mendel just published his work on plant hybridisation and the laws of inheritance he found for certain traits characteristics (1866). His work was rediscovered in 1900 by the botanists Hugo de Vries, Carl Correns und Erich Tschermak, who gained similar results in their own experiments. In combination with Darwin’s work On the origins of species this formed the basis for the study of the inheritance of phenotypic characteristics.

There was a rising interest in understanding inheritance in humans. For example there were the Biometricians, like Francis Galton, who believed in ancestral heredity. The idea was that every ancestor has an equal part in its offspring (i.e. father 50%, grandfather 25%, …). On the opposite side stood the Mendelians, who believed in the ‘pure gametes’ which would only carry one characteristic (one allele) but not two. In fact, only because this is true the above rule as formualted by Hardy can actually work.

However, neither was Hardy the first one to discover this principal nor was he the only one who published it. In fact, it was in the very same year that german doctor Wilhelm Weinberg published his work Über den Nachweis der Vererbung beim Menschenleben (or, On the evidence of heredity in humans). Unfortunately, Weinberg published both in German and in a rather unknown journal. His publication had a very similar fate to the one from Gregor Mendel. It took several years until it was rediscovered. At this point the rule, which both researche had independently formulated, became known as the Hardy-Weinberg-Equilibrium.

And even if their contribution to genetics might be small of substance and most likely meaningless for today’s questions I still think the HWE has its right to persist in curriculums. For everyone who teaches computational modelling this is a classic example of how to conceptualise mechanisms that we find in nature. Though, I wonder how long we can afford to talk about a paradigm that we actually never really use.

 

Further reading

If your fluent in german read this short article by Aichinger and Grimm from 2008 (http://link.springer.com/10.1007/s11825-008-0114-y).

An english review was published by Oliver Mayo, also in 2008 (http://www.journals.cambridge.org/abstract_S1832427400009051)