Natural selection occurs where there is heritable variation in a population and where there are differences in survival and fecundity associated with this variation. Thus, in order for natural selection to operate there must not only be phenotypic variation, there must also be an underlying genotypic variation. The relationship between phenotype and genotype can be very complex (see Schlichting and Pigliucci 1998) but we will confine ourselves to simple situations where there is a one-to-one mapping of genotype to phenotype, or to cases of complete dominance. Genotypes, and thereby alleles, leaving the most descendants will tend to increase in frequency in the population through the process of natural selection. You will note that this last statement is not absolute, because if the heterozygous genotype leaves the most descendants, the proportions of the various genotypes may remain constant from one generation to the next (see section 11.2.2).

The various equations that quantify natural selection are largely developed intuitively by the use of empirical examples. For those who are interested, the mathematical details of the derivations are confined to a few text boxes and an appendix, but it is not necessary to be able to derive the equations yourself in order to understand them. Simulations are used to analyse and show the predictions of the equations, but their application to the natural world is left until Chapter 11.