Effects of predation pressure on species packing on a resource gradient: insights from nonlinear dynamics

The classical case of three competitors arranged on a resource gradient such that the central competitor will be excluded due to competition from the other two is studied from the point of view of the effects of added predators. The basic formulation is motivated by a desire to understand the effects of asymmetries in multidimensional Lotka-Volterra systems. We first study the effects of perfectly specialist predators and find a rich collection of possible behaviors of the system including (1) extinction of all predators and subsequent extinction of the subordinate competitor, (2) dominant competitors and their predators coexist but the subdominant competitor goes extinct, (3) all species except the predator of the subordinate competitor coexist in coordinated phase-reversed chaos, (4) exclusion of one or more species occurs through an expanding heteroclinic cycle, and (5) all species coexist in an uncoordinated chaos. We then study the effects of five qualitatively distinct forms of polyphagy. In one case, corresponding to the well-known vulnerability to predation versus competitive ability trade-off, it is possible to have the subordinate competitor be the only survivor in the system. The other three cases of polyphagy lead to distortions in the basic pattern seen in the previously analyzed specialist case. Studying this case of ecologically motivated asymmetries in the basic Lotka-Volterra formulation is a step in the direction of fully understanding interacting populations.