Under which conditions is character displacement a likely outcome of secondary contact?

Sympatric character displacement is one possible mechanism that prevents competitive exclusion. This mechanism is thought to be behind the radiation of Darwin's finches, where character displacement is assumed to have followed secondary contact of ecologically similar species. We use a model to evaluate under which ecological and environmental conditions this mechanism is likely. Using the adaptive dynamics theory, we analyse different ecological models embedded in the secondary contact scenario. We highlight two necessary conditions for character displacement in sympatry: (i) very strong premating isolation between the two populations, and (ii) secondary contact to occur at an evolutionary branching point. Character displacement is then driven by adaptation to interspecific competition. We determine how ecological and environmental parameters influence the probability of ecological divergence. Finally, we discuss the likelihood of sympatric character displacement under disruptive selection in natural populations.