The Evolution of Clines at Equilibrium

There are at least five forces that affect the form of a cline: the genetics of the character, genetic drift, population density, the magnitude, direction and type of selection, and the magnitude and direction of gene flow. Arguably, the two most influential of these forces are selection and gene flow. At equilibrium, the width of a cline largely represents a balance between the diversifying effects of selection and the homogenizing effects of dispersal (Figure 3). When selection (s) represents the difference in fitness between genotypes at the center of the cline, and u is the standard deviation of the distance from parents to offspring along a linear gradient (which is broadly proportional to the width of the dispersal cloud around parents and is linearly related to the distance that an offspring moves on average), then the width of the cline at equilibrium is proportional to us_1/2. Thus, narrow clines in highly dispersive organisms will be maintained only when there are high levels of selection, while

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