GENOTYPIC PROPORTIONS IN HYBRID ZONES

We study a hybrid zone between two populations of a diploid organism. The populations differ at one locus. Homozygotes have equal fitnesses and the heterozygote fitness is reduced by beta + delta (beta is the b irth rate deviation and delta is the death rate deviation). The popula tions extend along a one dimensional continuous habitat, and migration occurs by diffusion of individuals. The model is formulated as a set of simple continuous time demographic models without age structure for the three genotypes, and the system is transformed into three new var iables, the total population size N, the gene frequency p, and the dev iation from Hardy-Weinberg proportions F. The gene frequency in a stea dy state dine always follows a hyperbolic tangent closely. Analysis of the asymptotic behavior of the dine far from the hybrid zone suggests a qualitative prediction of the shape of N, p and F over the zone. Fo r weak selection the shape is determined by a central steepness of roo t(beta+delta)/4D, as observed by Bazykin in 1969, where D is the diffu sion coefficient. For strong selection the dine is less steep than the Bazykin dine, and the form is dominated by the migration process. The steepness at the center of the dine is close to root b/4D where b is the birth rate of homozygotes.