Mutation and the Hardy-Weinberg principle

Where does variation come from, and how does speciation occur? Mendel had described inherited 'factors', but Darwin either ignored this or said nothing.

In the first decade of the twentieth century, Hugo de Vries, working on evening primrose, brought out the idea of mutation: a large difference arising suddenly in a population.

De Vries held that mutation, not the small heritable variations Darwin described, causes evolution. Mutations are random and directionless; Darwin's variations are small and directional.

For Darwin evolution was gradual; de Vries thought mutation caused speciation in a single large step, which he called saltation. Later, population genetics clarified the picture.

Hardy-Weinberg principle: allele frequencies in a population are stable and constant from generation to generation. The gene pool (all the genes and their alleles in a population) stays constant; this is genetic equilibrium.

The allele frequencies add up to 1. In a diploid, p is the frequency of allele A and q that of allele a, so p + q = 1.

The chance that A appears on both chromosomes is p × p, so AA individuals have frequency p²; aa has q² and Aa has 2pq.

So p² + 2pq + q² = 1, the binomial expansion of (p + q)².

If the measured frequencies differ from these expected values, the difference and its direction show the extent of evolutionary change. A change in allele frequencies, that is a disturbance of Hardy-Weinberg equilibrium, is read as evolution.