This article investigates models of ecological character displacement in which shifts in the relative resource-exploitation abilities of consumer species are driven by the accumulation of deleterious mutations with resource-specific effects. The models assume a simple ecological scenario in which there are two consumer species and two resource types. A mutation-selection balance determines the value of per-unit-resource consumption rates of each resource by each consumer species. A competitor that differentially reduces the abundance of the less-used resource of the focal consumer produces an increased equilibrium frequency of deleterious mutations affecting this resource. This results in divergent character displacement. If the reduction in the abundance of the less-used resource is sufficient, a process of mutational collapse may occur, in which the focal species becomes specialized on a single resource. Large magnitudes of displacement generally require high genomic deleterious mutation rates and mutations with a high degree of specificity to particular resources.