FISHERY BULLETIN: VOL. 74, NO. 3 



are more accessible for study and the data ob- 

 tained from them is readily handled by much 

 simpler geometrical methods. Most of the present 

 knowledge of schools is based on observations and 

 analyses of these sheetlike schools, treated as a 

 geometrical surface. 



Unless there is mention to the contrary, all 

 statements in this study refer to small or moder- 

 ate schools. When schools attain huge dimensions, 

 some of these statements require modification. A 

 fish in the central part of such a school, that may 

 have thousands of others between it and open 

 water in any direction, is locked in a position that 

 permits practically no freedom of movement. Such 

 fish are forced to swerve and swim almost as a 

 single block. Thus the turns discussed in the 

 section Problems of a School Turning are not 

 possible. The section Sizes of Fishes in a School 

 discusses conditions involving the amount of size 

 variation of the individuals found in a school. This 

 reaches its maximum in huge schools where size 

 variations are often large enough to break up a 

 lesser school. 



Problems of a School Turning 



A solitary fish obviously can alter its path from 

 that of a straight line and swim off in any direc- 

 tion. The presence of objects, such as neutrally 

 disposed fishes of the same or other species and 

 same general size, may make little difference 

 except for appropriate course altering. Problems 

 loom as a significant influence only when the 

 density factor becomes relatively large, as in a 

 loose unpolarized aggregation. When fishes 

 become even more crowded by each other, the 

 ability to swim in any direction is severely re- 

 stricted by the mere presence of the bodies of 

 other fishes. In a dense school this manner of 

 restriction becomes intense. Such closely packed 

 and regimented fish can swim serenely, parallel to 

 each other, in a straight line or in large swinging 

 arcs of a radius down to a value of about as little as 

 five to ten lengths of the fishes involved as shown 

 in Table 2A. If, however, a sharp curve of shorter 

 radius is attempted, complications arise (Table 

 2B). Such turns are commonly made by small 

 schools up to sizes that are too large to act as a 

 completely cohesive unit.^° The data shown in 

 Table 2 refer only to these small cohesive groups. 



Table 2.-Data on two types of turns made by fish schools. 



A. Radii ot broad curves in Se/ar crumenophthalmus 

 Fish lengths in cm 



'"See Breder (1967) for a discussion of the vastly greater 

 complexities inherent in the behavior of enormous schools. 



Here some disturbance ahead frequently can set 

 off an activity among the leading fishes in which 

 they turn sharply left or right. These are then 

 followed by the others, making their turns in 

 substantially the same place. Normally the ma- 

 neuver is accomplished with a scarcely apparent 

 and transient slowing of pace. The hydrodynamics 

 of how sharp turns are made by fishes with a 

 minimum of deceleration was discussed in detail 

 by Weihs (1972). 



Some of the angles between the initial and 

 subsequent paths of schools making these sharp 

 turns are given in Table 2B, picked from motion 

 picture sequences. Figure 16A indicates that 

 turning at a certain angle could cause following 

 fishes to approach the tail tips of those just ahead, 

 an accident that appears never to happen. 



There is nothing inherent in the situation of a 

 school swimming ahead that concerns angles of 

 turning. The features of the diagram in Figure 

 16A are meaningless to the fishes until they begin 

 to turn. Let the school swim in a straight line and 

 turn 30° to the right at the center of the diagram. 

 Each fish will come out in an occluded sector and 

 find it being brushed by the tail of the fish ahead. 

 If the Weihs (1973a) diamond is elongate along the 

 axis of travel, the fishes will fall a little short of 

 contact but will swim into the wrong side of the 

 vortices shed by the preceding individual. This is 

 evidently sufficient to initiate avoidance reactions. 



If they turn at 60°, there will be no problem as 

 they will be well separated by the amount in- 

 dicated in Figure 3A. The fishes in turning 

 evidently do so only where there is no danger of 



484 



