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Food sharing and time budgeting in predator-prey interaction

Abstract:

A time-dependent predator-prey system is introduced where food sharing among predators leads to a dynamically stable endemic. The predator population is split into the adult and juvenile sub-population. Food sharing refers to the process in which food is delivered from adults to juveniles. The populations differ in their ability to procure food and reproduce as young predators are assumed to lack the skills required to hunt and are not mature enough to reproduce. Aggregation of predators facilitates the disbursement of captured prey. A set of first principles formalize the behavioral activities of aggregation and food sharing. The effects of these activities are related to population level actions by behavioral response maps. Particularly, the absence of food sharing is modeled as to inflict juveniles faster decease along with hampered regeneration, as a consequence. Analysis of the model without considering adults’ stinginess presents forward bifurcations in the direction of increasing search rate and assimilation efficiency as well as of decreasing handling and sleeping time. Perturbation of assimilation efficiency also leads to a discontinuity-induced Hopf bifurcation, where the predator and prey population oscillate around the activation-deactivation of additional deaths in the juvenile population due to a certain proportion of sharing actuator. The disparate time scales from the prey and predator dynamics also bring forward a slow-fast system with two distinct critical manifolds. The prey-extinction critical manifold repels biologically relevant trajectories, yet any trajectory transferred to it by means of a disease or eradication will converge to the total extinction. The prey-persistence critical manifold attracts and leads trajectories to a stable endemic. This indicates that food abundance and food sharing increase the chance of having a stable endemic irrespective to the variation of the prey-predator lifespan ratio.