Dying on the way: the influence of migrational mortality on clines

Migrational mortality is introduced into the classical single-locus model for migration and selection. Genotype-independent migration follows selection, which may be soft or hard. For soft selection, the effect of mortality on the backward migration matrix is the same as in the Malécot model; for hard selection, some neutral results still hold, but some do not. For two diallelic demes, mortality can increase or decrease the stringency of the condition for protecting an allele from loss. In the discrete-space, continuous-time limit, mortality increases the diagonal elements of the migration rate matrix and decreases its off-diagonal elements. Were it not for the same result in the Malécot model, it would be surprising that mortality does not alter the general diffusion limit for multiple alleles, arbitrary multidimensional migration, and arbitrary selection.