Uniform persistence for sigmoidal diet selection with keystone prey species

In this paper we discuss uniform persistence (UP) criteria of two prey- one predator systems, where we consider that the predator's diet selection is a sigmoidal function of the most profitable prey type in place of a step function of conventional diet choice theory. We also derive UP results of the system with direct interspecific competition between the prey. The role of the most profitable prey item as a keystone species, the magnitude of its carrying capacity, the ability to withstand predation of both prey species, and the ratios of their profitability values (to predators) are important to whether or not adaptive foraging may promote UP. In general, foraging decision rules play no role in UP if the alternative prey item is the keystone species. The result is also not affected by the effect of direct competitive coexistence or dominance relationship of the prey. In some cases, dominance of one of the prey species provides the most advantageous situation for ensuring UP.