The Dynamics of Animal Grouping

Abstract

Though the term “grouping” is used very ambiguously in this chapter, we mean it to be a phenomenon such as insect swarming or fish schooling in which a number of animals are involved in movement as a group. In this chapter an attempt is made to describe the motion of swarming individuals, and to comprehend the grouping from the standpoint of advection—diusion processes.

The study of animal grouping, both theoretical and observational, has undergone an explosive development in the two decades since the First Edition of this book appeared. To maintain the spirit of this book, and to keep our contribution reasonably concise, we have divided our chapter into two sections. The first includes Okubo’s original chapter, modified slightly by us and according to revisions he noted before his death. The second includes a brief description of some of the ideas and approaches that are new or that have developed significantly in the recent past, especially those that we believe were most influenced by Okubo and his book. We do not attempt in this small space to be comprehensive, but instead, we refer the reader to many other existing reviews. Among these are Okubo’s own excellent review of animal aggregations (Okubo, 1986) and a brief survey of mathematical approaches co-authored with one of us (Grünbaum and Okubo, 1994). Also see Pitcher and Parrish (1993).