How host self-regulation governs hyperparasitoid persistence in a caterpillar-parasitoid-trigonalid system

Species at the highest trophic levels are generally the least resilient to perturbations, yet the factors that determine their persistence remain poorly understood. We ask how the intrinsic self-regulation of a basal host governs the persistence of the trophic levels above it. To address this question, we use a minimal discrete-time model of a host-parasitoid-hyperparasitoid system motivated by the biology of trigonalid wasps, obligate hyperparasitoids that complete development only when their caterpillar host is also attacked by a primary parasitoid. We compare two forms of host self-regulation in the absence of natural enemies: scramble (Ricker) fecundity, appropriate when the parasitoid is the host's principal enemy and which recovers the classical model of Beddington and Hammond as a special case; and contest (Beverton-Holt) fecundity, appropriate when the host is held in check by many additional enemies. Using numerical continuation, Lyapunov exponents, and direct computation of the model's trajectories, we find that the form of host regulation is decisive for persistence at the top trophic level. Under scramble host dynamics, coexistence is extremely fragile with respect to both parameter values and initial conditions. Under contest host dynamics, coexistence is robust across broad parameter ranges and loses stability only gradually, through a supercritical Neimark--Sacker bifurcation and a subsequent torus-doubling route to chaos. Therefore, in at least some trophic networks, the resilience of the highest levels can be determined at the base of the network.