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A stochastic version of the Beddington-DeAngelis functional response: modelling interference for a finite number of predators.

1. The predator-dependent Beddington-DeAngelis functional response model can be considered as an extension of the prey-dependent Holling's type II functional response model, since it includes, apart from the states 'searching for prey' and 'handling prey', a third behavioural state, namely 'mutual interference with competitors'. The model is further based upon the underlying idea of mass action, which means that it is assumed that predator and prey numbers are infinitely large. 2. This latter assumption casts doubt on the applicability of the model to experimental situations, which have been used to estimate the underlying behavioural parameters, because such experiments are usually performed with very few competitors. 3. Therefore, a stochastic version of the Beddington-DeAngelis model is presented which overcomes these problems. A maximum-likelihood procedure for parameter estimation is presented and applied to shore crabs foraging on blue mussels. 4. In passing, a mistake in the derivation of the deterministic Beddington-DeAngelis model is corrected, resulting in a slightly different solution.