FISHERY BULLETIN: VOL. 74, NO, 3 



with considerably less alacrity. Once the 

 behavioral differences between the two types of 

 turn are understood, they can be seen in the field if 

 one happens to be looking directly at the point of 

 turning before it begins. This is easier to see in a 

 relatively large school than in a small one because 

 the larger the number of individuals involved the 

 more prolonged the turning maneuver becomes. 

 Also, it is most noticeable where the sudden 

 appearance of something large and "threatening" 

 produces an apparent "panic situation." Instead of 

 what seems to be the beginning of a tight turn, as 

 previously discussed, the action is most often seen 

 as an attempt to retreat over their forward path. 

 Here there develops a "logjam" and confusion. The 

 immediate response is for the clump of fishes to 

 spread out into a more or less circular area, out of 

 which the school is seen to beat a hasty retreat. 

 Figure 18 shows such a performance which theo- 

 retically, at least, could move off in any direction 

 but, so far as our observations go, has usually been 

 close to the opposite direction of the abandoned 

 advance. The conventions of Figure 17 have been 

 used and the same number of frames cover this 

 sequence. The seeming difference of speed is 

 simply that badly frightened fish move faster than 

 relatively placid ones and therefore make up much 

 of the time lost in the greater length of their 

 confusion-imposed travel. This area sometimes 

 develops a central clear spot devoid of fishes, and a 

 true "fish mill"^^ is transiently developed. 



The angular measurements between the track 

 of a school before the turn and after it can only be 

 precise in photographs taken wnth the camera 

 pointed straight down. This is nearly impossible 

 with feral fishes because such schools simply move 

 away from anything directly overhead. The pho- 

 tographs on which Table 2 are based are those 

 which approach that position as nearly as possible. 

 This departure from the vertical naturally tends to 

 slightly blur the accuracy of the angles and thus 

 serves to produce a greater spread in the apparent 

 angles. This effect has less influence on the mean 

 values of each clustered group. To help counter this 

 source of error, a transparent dial was prepared 

 with the sectors shown in Figure 16. Hand held, it 

 can be tipped at an angle appropriate to the 

 angular amount of departure from the vertical 

 with which the eye or camera viewed the scene. A 



( 



^ 



_/ 



"A term used by Parr (1927) to cover the case of a fish school 

 swimming in a more or less circular path, where every fish is 

 following those ahead of it. The clear center that these mills 

 sometimes develop has been discussed by Breder (1951). 



Figure 18.-A slower turn of the school shown in Figure 17, with 

 confusion at the turning point. The directions of the two paths, 

 into and away from the melee, are indicated by arrowheads. 



variety of items shown in such a film helped 

 establish the needed correction with sufficient 

 accuracy for present purposes. Although little use 

 could be made of it in the direct observations 

 because of the rapidity of the action, it was 

 invaluable in studying strips of motion picture 

 film. Small cues that helped establish the proper 

 angle of tilt of the viewing dial included prin- 

 cipally the amount of the sides of the fishes that 

 could be seen plus other objects incidentally in- 

 cluded in the photographs. 



Absolute turns enforced on schools of Mugil 

 cephalus Linnaeus and Pollachius virens (Lin- 

 naeus) by the end of an aquarium were studied by 

 Radakov (1972). These are in contrast to the 

 preceding studies of turning in open water where 

 the actual cause of the turn was often obscure, but 

 irrelevant to the mechanics of turning. The 

 aquarium studies show nothing like the "sharp 

 turns" but are close to, if not identical with, the 

 present "slower turns" where the school breaks 

 down and reforms on the retreat path. Here and in 

 Radakov's (1972) work, there is considerable mix- 

 ing and the place of individual fishes in the school 

 after these turns may be grossly altered. In the 

 confines of an aquarium there is practically no 

 choice of turning angle and the complex situation 

 in turning in open water does not exist. 



General Traffic Problems 



Road traffic of automobiles may seem to be very 

 remote from a school of fishes. Close examination, 

 however, reveals that the two have common roots 

 and that, despite their apparent differences, they 

 are isomorphic. Both cars on a road and fishes in a 

 school can be treated as embodiments of math- 

 ematical expressions concerned with mass 

 movements of redundant units. The mathematics 

 of the behavior of automobiles developed along 

 with their proliferation, following the need for 



486 



