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Many mathematical models use functions the value of which cannot exceed some physically or biologically imposed maximum value. A model can be described as 'capped-rate' when the rate of change of a variable cannot exceed a maximum value. This presents no problem when the models are deterministic but, in many applications, results from deterministic models are at best misleading. The need to account for stochasticity, both demographic and environmental, in models is therefore important but, as this paper shows, incorporating stochasticity into capped-rate models is not trivial. A method using queueing theory is presented, which allows randomness and spatial heterogeneity to be incorporated rigorously into capped rate models. The method is applied to the feeding and growth of fish larvae.

Modelling predation as a capped rate stochastic process, with applications to fish recruitment