Inadvertent errors and error-constrained optimization: fallible foraging by bluegill sunfish

When the expected reward rate is continuously reduced by foraging in a patch, foragers may adjust their patch persistence times to maximize the average long-term reward rate. The marginal-value model predicts the optimal persistence time for this situation. But real foragers may be unable consistently to achieve a precise persistence time. If the costs of under- and over-persistence differ, or if the resulting distribution of persistence times is skewed, a sufficiently broad persistence-time distribution can substantially shift the actual optimum. Moreover, this “error-constrained” optimum depends on the variable used by the forager to decide when to leave the patch (e.g., on persistence time per se, cumulative number of prey eaten, or instantaneous feeding rate). Here, we analyze laboratory data from bluegill sunfish (Lepomis macrochirus) foraging on larval-midge prey (Chironomus riparius) in patches of artificial vegetation, and we explore some wider implications of a model that seems to fit the data. The bluegills stayed 4%–157% longer in patches than predicted by the marginal value theorem. This behavior closely matched numerical solutions based on the observed variability of persistence times and the assumption that departures were cued by instantaneous feeding rate. On the other hand, the other two mechanisms that we investigated (i.e., persistence time per se and cumulative number of prey eaten) predict weak to moderate underpersistence relative to the marginal-value predictions, patterns quite unlike those observed. Surprisingly, the instantaneous-rate mechanism yields roughly a 10% lower over-all maximal reward rate than would either of the other two departure-cuing mechanisms. The modeling analysis documents the considerable sensitivity of our results to (1) the departure-cuing mechanism, (2) the shape of the frequency distribution of the departure-cuing variable, (3) the way that the shape of this distribution shifts as its mean changes, and (4) the magnitudes of the foraging parameters.