Stochastic stomach theory of fish: An introduction

Fish stomach dynamics is discussed and introduced analytically by a simple individually-based stomach model for total stomach content. The predator encounters food (meals) in a Poisson process, starting to search for a new meal when the stomach is empty. Basic equations for the frequency distributions of stomach content are derived for general classes of meal-size distributions and rate models of gastric evacuation. Probability characteristics in steady state of empty and non-empty stomachs are evaluated from first principles with particular attention to the square root rate model of gastric evacuation. The average rate of food consumption and the functional response are derived from simple renewal theory and from obtaining the average of the gastric evacuation rates. Effects of meal size biased stomach sampling are introduced. As a primer on modelling the stomach content of piscivorous fish, the model is discussed in relation to the empirical distribution of the individual stomach content for more than 4000 North Sea whiting in the length range 20–30 cm. Implications of identical meals and variable meal sizes, exemplified by the log-normal distribution, are considered. Estimated average meal searching time and meal size as well as the average rate of food consumption decrease considerably in the more realistic case of variable meal sizes. The model is able to account for the high frequency of empty stomachs, which occurs simultaneously with a relatively high observed mean stomach content. Need and direction for further developments of fish stomach theory are discussed.