# Impacts of predation on dynamics of age-structured prey: Allee effects and multi-stability

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## Abstract

With a series of mathematical models, we explore impacts of predation on a prey population structured into two age classes, juveniles and adults, assuming generalist, age-specific predators. Predation on any age class is either absent, or represented by types II or III functional responses, in various combinations. We look for Allee effects or more generally for multiple stable steady states in the prey population. One of our key findings is the occurrence of a predator pit (low-density “refuge” state of prey induced by predation; the chance of escaping predation thus increases both below and above an intermediate prey density) when only one age class is consumed and predators use a type II functional response —this scenario is known to occur for an unstructured prey consumed via a type III functional response and can never occur for an unstructured prey consumed via a type II one. In the case where both age classes are consumed by type II generalist predators, an Allee effect occurs frequently, but some parameters give also rise to a predator pit and even three stable equilibria (one extinction equilibrium and two positive ones—Allee effect and predator pit combined). Multiple positive stable equilibria are common if one age class is consumed via a type II functional response and the other via a type III functional response—here, in addition to the behaviours mentioned above one may even observe three stable positive equilibria—“double” predator pit. Some of these results are discussed from the perspective of population management.

## Keywords

Age-specific predation Functional response Generalist predator Population dynamics Predator pit## Notes

### Acknowledgements

LB acknowledges funding by the Institute of Entomology (Z50070508). We also thank two anonymous reviewers for their stimulating comments.

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