FISH SCHOOLS AS OPERATIONAL STRUCTURES 



Charles M. Breder, Jr. 



ABSTRACT 



The interaction of a space lattice, vortex trails, and the lubricity of fish surface mucus is shown to be 

 important to the operation and structure of fish schools and significant in terms of locomotor eflSciency. 

 This is independent of the various interpretations of possible survival values, protection from 

 predation, and similar ideas-all of which are extremely difficult to prove, even if valid. 



A single type of space lattice is shown to approximate the arrangement of fishes in a school on the 

 basis of geometrical reasoning. This is supported by empirical data. 



The vortex trails left by each fish, when the fishes are deployed according to the "fish school" lattice, 

 lead each following fish into a series of vortices at a point where the water flow is traveling in the 

 direction in which they are swimming. 



The lubricity of the mucus-water mixture that the fish ahead leaves in its vortices decreases the drag 

 on the following fish. 



The advantages of the regimented life in a school, as against the freedom of action common to the 

 more or less solitary life, are evidently related to the effectiveness of the drag-reducing mucus in the 

 vortices. The fishes with the least effective mucus appear to take advantage of the schooling life while 

 those with the most effective mucus are more likely to be solitary. 



The past decade has witnessed^a considerable 

 increase in output of papers addressed to a better 

 understanding of the numerous phenomona pre- 

 sented by fish schools. These documents have 

 covered a wide variety of the inherent problems. 

 Nonetheless, there remain some basic questions 

 that have proved peculiarly elusive, such as the 

 nature of the evident regularity of the positional 

 relationships of individuals in well organized 

 schools and the nature of influences that hold the 

 school members in their regular patterns. A fish 

 school is considered here as a group of polarized 

 individuals that operates as a unit between the 

 times of its resolution and eventual dissolution. 

 Initially, the activity of the fishes crowding 

 together in their polarized pattern creates the 

 structure of which they form components. Once 

 established, the school efficiently regulates the 

 locomotor activities and general comportment of 

 the organized fishes. 



The primary purpose of this paper is to show 

 that both the geometrical pattern of the space 

 lattice approximated by schooling fishes and the 

 surface mucus on their bodies are mutually im- 

 portant elements in the formation and mainte- 

 nance of fish schools. The physical bearing of these 

 two elements is direct and important, each in its 



own right, to an understanding of any theory that 

 attempts to explain the origin of schooling without 

 recourse to theoretical interpretations. 



How much of the schooling phenomenon ob- 

 served in modern fishes is a result of interactions 

 between the swimming capabilities of the fishes 

 and the physical restrictions imposed by their 

 environment, as compared with other biological 

 needs, is not readily determined. However, the 

 experiments described here are in some cases 

 suggestive. These experiments, primarily under- 

 taken to establish data relevant to the basic 

 purposes of this study, in each case, have been 

 carried only as far as was necessary to make a 

 point. Many of them could be extended into much 

 greater refinement with the promise of worth- 

 while further elucidation. 



This work leads to a number of lines of possible 

 approach to the problems of school organization. 

 Some of the newer items discussed have had the 

 benefit of recent studies-remote from schooling 

 problems and in some instances remote from 

 biology. This is especially marked in those studies 

 that are dependent on developments in hydro- 

 dynamics during the last decade. 



FISH SCHOOLS AS SPACE LATTICES 



'Mote Marine Laboratory, 9501 Blind Pass Road, Sarasota, FL 

 33581. 



Manuscript accepted Februarj* 1976. 

 FISHERY BULLETIN: VOL. 74, NO. 3, 1976. 



To further the understanding of the physical 

 organization displayed by schools of fishes, a study 



471 



