• In the absence of natural selection, and with random mating in a large population, the genotype frequencies at a locus move in one generation to the Hardy-Weinberg ratio; the genotype frequencies are then stable.

• It is easy to observe whether the genotypes at a locus are in the Hardy-Weinberg ratio. In nature, they will often not be, because the fitnesses of the genotypes are not equal, mating is non-random, or the population is small.

• A theoretical equation for natural selection at a single locus can be written, by expressing the frequency of a gene in one generation as a function of its frequency in the previous generation. The relation is determined by the fitnesses of the genotypes.

• The geographic pattern of melanic and light colored forms of the peppered moth cannot be explained only by the selective advantage of the better camouflaged form. An inherent advantage to the melanic form, and migration, are also needed to explain the observations.

• The evolution of resistance to pesticides in insects is in some cases due to rapid selection for a gene at a single locus.