Long- and Short-Term Dynamic Optimization Models with Application to the Feeding Strategy of the Loggerhead Shrike

Two dynamic optimization models, having scale lengths of 1 yr and 1 day, respectively, are used to gain insight into the feeding strategy of the loggerhead shrike. The need for at least two models underscores the fact that no single mathematical model is ever likely to describe all aspects of the feeding behavior of an organism. The long-term optimization model begins with the premise that total prey handling time is minimized, but the model is extended to a multiple objective scheme where handling time and weight are optimized simultaneously. The model indicated that it is optimal for shrikes to exceed 50 g in October and November, fall to about 45 g in December and January, and hover close to 50 g the rest of the year. These results are at least consistent with the small amount of data available on the weight of the shrikes. The model also predicts that the shrike should focus optimally on prey of size classes 5 and 6, in agreement with data. The short-term model attempts to account for the diversity of prey and the occurrence of uneconomical prey in the shrike's diet. If prey are unevenly available during the day, the shrike's hunger threshold frequently may be exceeded when only less preferred prey are obtainable. For 1 day in a given month (September) the number of attacks per day, the frequency of attacks for different periods of the day, and the diversity of prey predicted by the model are in good agreement with corresponding observations.