  The shape of allele-frequency clines maintained by migration-selection
balance depends not only on the properties of migration and selection, but also
on the dominance relations among alleles and on linkage to other loci under
selection. We investigate a two-locus model in which two diallelic, recombining
loci are subject to selection caused by an abrupt environmental change. The
habitat is one-dimensional and unbounded, selection at each locus is modeled by
step functions such that in one region one allele at each locus is advantageous
and in the other deleterious. We admit an environmentally independent,
intermediate degree of dominance at both loci, including complete dominance.
First, we derive an explicit expression for the single-locus cline with
dominance, thus generalizing classical results by Haldane (1948). We show that
the slope of the cline in the center (at the step) or, equivalently, the width
of the cline, is independent of the degree of dominance. Second, under the
assumption of strong recombination relative to selection and migration, the
first-order approximations of the allele-frequency clines at each of the loci
and of the linkage disequilibrium are derived. This may be interpreted as the
quasi-linkage-equilibrium approximation of the two-locus cline. Explicit
asymptotic expressions for the clines are deduced as $x\to\pm\infty$. For
equivalent loci, explicit expressions for the whole clines are derived. The
influence of dominance and of linkage on the slope of the cline in the center
and on a global measure of steepness are investigated. This global measure
reflects the influence of dominance. Finally, the accuracy of the
approximations and the dependence of the shape of the two-locus cline on the
full range of recombination rates is explored by numerical integration of the
underlying system of partial differential equations.
