Gaining ecological information about Bayesian foragers through their behaviour. I. Models with predictions

A forager that is optimising its behaviour oil the basis of some information is likely to reveal that particular information through its behaviour. We investigated the cases of completely informed and Bayesian foragers searching for food with a clumped distribution (the negative binomial distribution) between patches. Two different currencies were analysed: maximised intake rate and minimised predation risks. Predictions were made concerning two foraging variables: the average giving-up density of food items in the patches and the average patch residence time. We present how these variables correlate with each other and with a fitness variable (depending on the currency) when each of the model parameters is varied. The model is based on nine ecological parameters: (1) the foragers searching efficiency, (2) its metabolic rate during foraging and predator scanning, (3) its metabolic rate during the travel between patches, (4) the mean density of food items in patches, (5) the contagiousness (skew) of the prey density distribution, (6) the energy content of a food item, (7) predation rate during foraging; (8) predation rate during predator scanning, and (9) predation rate during travelling between patches. The values of the model parameters are selected to be representative for a lesser spotted woodpecker, Dendrocopos minor, foraging in its territory. Four qualitatively unique foraging and fitness variable relationships were found. Hence, empirically found relations between these variables can be used to infer the ecological factors causing the variation in foraging behaviour and fitness. The model is applied in a companion paper to pinpoint the most important inter-territorial ecological factor in the lesser spotted woodpecker, and how much this factor contributes to the reproductive success in this species.