The intimate connection between natural selection and heredity is indicated by Prof. Dobshansky's definition of evolution as essentially just a change in gene frequencies, for natural selection is the agency that causes gene frequencies to change. Just as mutations are the raw material of evolution, selection is the force that preserves good genes, eliminates bad genes, and produces the changes that lead to the formation of races, and eventually species.

The problem of the action of selection on gene frequencies can be treated, with suitable simplifying assumptions, mathematically, and many years ago Prof. J. B. S. Haldane published a series of papers on this subject (tab. I). The rate at which gene frequencies would change under the action of slow selection is shown in fig. 1. It will be seen that selection acts more slowly, at first, on recessive genes than on dominants, but in the long run the frequencies change from nearly zero to nearly one, or vice versa. Deleterious genes are often never completely eliminated, because they are continually recruited by recurring mutations.

That selection is effective in bringing about considerable changes in organisms is shown by the achievements of domestic plant and animal breeders. The results of selecting for long shanks in chickens are shown in fig. 2, and for a larger number of abdominal chaetae in fruit flies in fig. 3. Though it is not shown here, selection for a lower number of chaetae is also effective.