# Testing a stochastic version of the Beddington–DeAngelis functional response in foraging shore crabs

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## Abstract

Current behaviour-based interference models assume that the predator population is infinitely large and that interference is weak. While the realism of the first assumption is questionable, the second assumption conflicts with the purpose of interference models. Here, we tested a recently developed stochastic version of the Beddington–DeAngelis functional response—which applies to a finite predator population without assuming weak interference—against experimental data of shore crabs (*Carcinus maenas*) foraging on mussels (*Mytilus edulis*). We present an approximate maximum likelihood procedure for parameter estimation when only one focal individual is observed, and introduce ‘correction factors’ that capture the average behaviour of the competing but unobserved individuals. We used the method to estimate shore crab handling time, interaction time, and searching rates for prey and competitor. Especially the searching rates were sensitive to variation in prey and competitor density. Incorporating constant parameter values in the model and comparing observed and predicted feeding rates revealed that the predictive power of the model is high. Our stochastic version of the Beddington–DeAngelis model better reflects reality than current interference models and is also amenable for modelling effects of interference on predator distributions.

## Keywords

Prey Item Prey Density Agonistic Interaction Predator Density Stochastic Version## Notes

### Acknowledgments

We would like to thank Maurice Sabelis for constructive comments and discussion. IMS was financially supported by a research grant from the Netherlands Organization for Scientific Research (NWO).

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