Gene frequencies in a cline determined by selection and diffusion.

Abstract

IN 1937 (1) the author studied the distribution of the gene ratio in the simple case of an advantageous gene advancing along a linear habitat under a constant selective advantage. In Nature situations must be more complex than in this simple model; in particular it must often occur that the selective advantage itself varies with position. The interesting case arises in which a gene enjoys a selective advantage in one part of a species' range, while in the remainder it is at a selective disadvantage. On the boundary between these regions selection is neutral between two allelomorphic genes. Cases can be observed in practice in which there is a gradient, or line, in the frequencies of the genotypes determined by a single factor. Generally such cases will be complicated by inequalities of topography, and by consequent irregularities in the population density, and in the gradient of selective advantage. It is to be expected also that the boundary will in general neither be straight (i.e. a great circle of the earth's surface), nor constant in position under the conditions prevailing in different years. Any model worth discussing from a theoretical standpoint will therefore be a drastically simplified one, playing the part of a basis for comparisons by which the real complexities of each situation may be critically demonstrated. The purely genetical complication of non-recognition of genotype, due to dominance, is also ignored. This is chiefly because I should regard the occurrence of true dominance in such cases as a danger-signal suggesting the very different genetic situation of a balanced polymorphism; partly because if on more careful examination it is found that the heterozygote is recognizable this will greatly increase the value of the observations. The problem chosen for discussion, as an extension of my work of 1937, thus differs materially from that considered by Haldane in 1948 (2). Haldane discusses the effects of a discontinuous selective intensity acting on a gene ratio obscured by dominance. The available data, in the common case, Arwill consist of gene frequencies observed at chosen centres of collection. From such data the primary need is to determine the neutral, or 50%, line, and the distances