Density dependence in a stage structured population is a well-established driver of population cycles or oscillations. However, in a host-parasitoid system not prone to cycles, we observe time series with quasi-cyclic dynamics that are not explained by deterministic models with saturating functional responses. In this study we explore the dual roles of density dependence and demographic stochasticity in driving the competitive interactions between two parasitoid species competing for the same host (the harlequin bug). We modeled the dynamics of this system with a system of delay differential equations (DDE) with various forms of density dependence in functional response. We used parameters estimated from separate lab experiments and investigated the parasitoid dynamics with a pulsed resource supply. We introduced demographic stochasticity using an individual based model, similar to a Gillespie algorithm. We compared the stochastic models with time-series data of six replicate host-parasitoid communities using root mean square error (RMSE) to perform model selection between forms of density dependence and competition in parasitism. We created distributions of parameter estimates including intraspecific and interspecific competition coefficients, attack rates, and handling times.
The period of oscillations in species density was controlled by the interaction between the time between resource pulses and the developmental delay. Oscillations were independent of the actual length of delay, instead strongly driven by the timing of maturation with respect to the resource pulse. We found better fits (smaller errors) to all models with demographic stochasticity, indicating that demographic stochasticity is the key driver of quasi-cyclic dynamics. Consistently, the best fit functional responses and corresponding parameter values revealed strong density dependence in both parasitoid species. Models that included intraguild predation were not consistently chosen, most likely because in this system predation occurs within the host egg, but the observed data consisted only of adults. This mismatch between the data that would be most informative and the data that is available will hinder any type of model selection and parameter estimation. Our results have important applications for host-parasitoid systems in general, but also for natural pest control, given that many insect pests are controlled by parasitoid natural enemies.