The Evolution of Morph-Ratio Clines

Abstract

Simple mathematical models are proposed to represent morph-ratio clines in which the morphs are determined by pairs of alleles. They demonstrate the effects of natural selection of modifiers on the slope and positions of such clines. A modifier with opposite effects on different genotypes may spread in some parts of a cline but not in others, thereby producing sharp local changes (steps) in the cline. The position of these steps need not be related to any sharp changes in the environment. It is suggested that there is an evolutionary trend towards the steepening of morph-ratio clines, and towards the intensification of any steps that may occur. These results provide an explanation of the "area effects" found in Cepaea and Partula.