BREDER: FISH SCHOOLS AS OPERATIONAL STRUCTURES 



increasing specific and detailed control of their 

 movements. Thus, from a purely empirical begin- 

 ning these studies have gradually developed into 

 the present traffic theory, most of which has 

 developed in the last 10 yr. Introductions to its 

 considerable literature are given by Ashton (1966) 

 and Gazis (1967). 



Some of the similarities and differences 

 between cars and fishes in the attainment of an 

 organization of free-flowing traffic is indicated by 

 the following comparative listing of the two types 

 of redundant units. 



Fish 



1. Fishes, schooling or not, 

 operate freely in three 

 dimensions, but most 

 free-swimming fishes, 

 especially those that 

 form schools, operate 

 mostly parallel (al- 

 though not necessarily 

 close) to a usually hor- 

 izontal surface, either 

 the surface of the water 

 or the bottom. These 

 two mark the vertical 

 limits within which the 

 fishes must stay. Hor- 

 izontal boundaries may 

 vary from too close for 

 schools to exist to prac- 

 tically limitless ex- 

 panse, in the strictly 

 physical sense. School- 

 ing fishes can go in any 

 direction but only with 

 their school. 



2. Other strictures are 

 those with which only 

 schooling fishes are 

 constrained. Here fishes 

 all swim in a common 

 direction, mostly in 

 parallel paths, and in 

 single files. Collisions 

 are rare or absent, their 

 avoidance evidently be- 

 ing rooted in their 

 highly developed sen- 

 sory mechanisms: vi- 

 sion, lateral line and 

 cupulae'- senses, and 

 hearing. There is no 

 provision for "night 

 driving" except in 

 species carrying their 

 own illumination. 

 Others loosen their 



A u to7nobiles 

 Cars, in traffic or not, 

 are confined to a sur- 

 face, which is not 

 necessarily a plane and 

 is often a warped sur- 

 face, where the extent 

 of warping eventually 

 limits the possibility of 

 use by cars. Cars must 

 stay on their roads but 

 do not necessarily stay 

 with their fellows. They 

 may strike out alone 

 wherever there are con- 

 nections with other 

 roads, except where ac- 

 companied by restric- 

 tive road signs forbid- 

 ding a given maneuver 

 or by the general rules 

 of behavior. 



Other strictures are 

 those with which only 

 cars, especially in traffic 

 are constrained. These 

 controls are maintained 

 by laws to run in an in- 

 dicated direction in sin- 

 gle files or in parallel 

 paths, depending on the 

 width of the road and 

 its indicated number of 

 lanes. Collisions occur 

 with monotonous fre- 

 quency. The protections 

 are only the sense or- 

 gans of vision and 

 hearing. Night driving 

 illumination is normally 

 present. 



ranks or break up on 

 nights sufficiently dark 

 to eliminate vision. 

 3. Fishes form well- 

 defined patterns; for 

 hydrodynamic reasons 

 they are quadrilaterals. 



Cars form "diamonds," 

 or if the road has less 

 than three one-way 

 lanes, parts thereof. 



In both cases there are valid reasons for not 

 following closely behind the unit directly ahead 

 and for not traveling in tandem positions. The 

 resulting staggered deployment permits passing 

 and lane shifting with a minimum of confusion. It 

 is this arrangement of units and their possible 

 movements that is largely responsible for the 

 irregularities in any instantaneous structure of 

 the swimming patterns. 



In the case of a traffic jam of cars or the 

 equivalent conditions of pods^^ of fishes, the 

 pattern formed by units is nearly obliterated. 



The shape of the diamond formed by four cars is 

 related to the speed of travel and is determined by 

 the rules of the road covering the increase in 

 distance to be given the car ahead with an increase 

 in speed. Also the rules require the passing car to 

 speed as fast as practicable in passing the slower 

 car. Thus, the faster the traffic, the farther the 

 hexagon or diamond departs from the regular, 

 attenuating along the axis of travel. 



That the fish and a car with its human driver are 

 closely comparable should be clear from the 

 preceding and the following outline indicating 

 that the relations between the two dynamic sys- 

 tems do in fact constitute an isomorphism. Two 

 central nervous systems, one of a fish whose body 

 is vehicle, power plant, and pilot, and the other, 

 that of a human who is the pilot, enveloped in a 

 capsule comprising the vehicle and power plant, 

 operationally calls for the same kinematic pattern 

 and trajectories of behavior. As these are both 

 systems with feedback in which all essential 

 variables are evident, the canonical representation 

 and the ordinary algebraic forms of equations can 

 be calculated. This will not be done here as it would 



In fishes, the same results are obtained by those 

 ahead leaving both advantageous and disadvan- 

 tageous water movements in which the followers, 

 by taking the path of least resistance, fall au- 

 tomatically into positions that mark out the 

 diamond. The lengthening of the figures as the 

 fishes' speed increases is very slight as compared 

 with that of the distance increase with cars. 



^See Cahn (1967) for a survey of the function of these systems. 



'^This term has been defined by Breder (1959). 



487 



