title: The effects of host-feeding on stability of discrete-time host-parasitoid population dynamic models.
abstract: Discrete-time models are the traditional approach for capturing population dynamics of a host-parasitoid system. Recent work has introduced a semi-discrete framework for obtaining model update functions that connect host-parasitoid population levels from year-to-year. In particular, this framework uses differential equations to describe the host-parasitoid interaction during the time of year when they come in contact, allowing specific behaviors to be mechanistically incorporated. We use the semi-discrete approach to study the effects of host-feeding, which occurs when a parasitoid consumes a potential host larva without ovipositing. We find that host-feeding by itself cannot stabilize the system, and both populations exhibit behavior similar to the Nicholson-Bailey model. However, when combined with stabilizing mechanisms such as density-dependent host mortality, host-feeding contracts the region of parameter space that allows for a stable host-parasitoid equilibrium. In contrast, when combined with a density-dependent parasitoid attack rate, host-feeding expands the non-zero equilibrium stability region. Our results show that host-feeding causes inefficiency in the parasitoid population, which yields a higher population of hosts per generation. This suggests that host-feeding may have limited long-term impact in terms of suppressing host levels for biological control applications.
authors.affiliation: Department of Mathematics, Trinity College, Hartford, CT 06106, United States. Electronic address: brooks.emerick@trincoll.edu.
authors.forename: Brooks
authors.initials: B
authors.lastname: Emerick
authors.affiliation: Department of Electrical & Computer Engineering, University of Delaware, Newark, DE 19716, United States; Department of Biomedical Engineering, University of Delaware, Newark, DE 19716, United States. Electronic address: absingh@udel.edu.
authors.forename: Abhyudai
authors.initials: A
authors.lastname: Singh
mesh_terms: D000818:Animals; D006790:Host-Parasite Interactions; D008962:Models, Theoretical; D011157:Population Dynamics
keywords: Functional response; Host-feeding; Host–parasitoid; Nicholson–Bailey; Semi-discrete model