Abstract
The fruit fly, Drosophila melanogaster, displays a scale-free behavior in foraging, i.e., the dwell time on food exhibits a power law distribution. The scaling exponent is generally believed to be stable and the significance of the exponent itself with respect to the scale-free behavior remains elusive. We propose a model whereby the scaling exponent of the scale-free behavior of an animal depends on the memory of the individual. The proposed model is based on the premise that animal behaviors are associated with internal states of the animal. The changes in the scaling exponent are derived by considering losing memory as increasing uncertainty, which is expressed in terms of information entropy of the internal states. Predicted model behaviors agree with experimental results of foraging behavior in wild-type and learning/memory Drosophila mutants. The concept of changes in the scaling exponent due to the amount of memory provides a novel insight into the emergence of a scale-free behavior and the meaning of the scaling exponent.
