Using Coxʹs proportional hazard models to implement optimal strategies: An example from behavioural ecology

Simple behavioural rules, or “rules of thumb”, which lead to behaviour that closely approximates an optimal strategy, have generated a lot of recent interest in the field of foraging behaviour. In this paper, we derive rules of thumb from a stochastic simulation model in which the foragers behave optimally. We use a particular biological system: the patch leaving behaviour of a parasitoid. We simulate parasitoids whose patch leaving behaviour is determined by a stochastic dynamic programming (SDP) model, while allowing parasitoids to make mistakes in their estimation of host density when arriving in a patch. We use Coxʹs proportional hazards models to obtain statistical rules of thumb from the simulated behaviour. This represents the first use of a proportional hazard approximation to generate rules of thumb from a complex optimal strategy.