BREDER: PISH SCHOOLS AS OPERATIONAL STRUCTURES 



Figure U.-A school of Kafsnwnnus pelamia off the Hawaiian Islands, breaking up for surface feeding. Courtesy of the National 



Marine Fisheries Service, Honolulu Laboratory, Honolulu, Hawaii. 



of this Study. Figure 12 is based on Hunter's 

 figure, modified appropriately for this analysis. 

 Although the small group used, six captive in- 



10 CM 



dividuals of Trachurus symmetricus (Ayres), is 

 not large enough to form a well organized school 

 and even has members that do not always stay 

 precisely at the same level as the others, it is 

 exceptionally interesting in that it does display 

 items pertinent to school structure. 



Figure 12 represents the progress of the six fish 

 covering S% s shown on 100 frames of motion 

 picture film exposed at a rate of 12 frames/s. The 

 larger circles indicate the mean values of the eight 

 positions of the snouts of each of the six fish. These 

 means are connected serially by straight lines.^ 

 The small circles indicate the patterns of positions 

 of the six fish's snouts for four of the eight means. 

 Every other one has been omitted because ad- 

 jacent patterns overlap enough to be confusing. 



Figure 13 indicates the manner in which the 

 values are related to the trajectory of the group. 



Figure 12.-Analysis of the location of six Trachurus sym- 

 metricus in a school, shown by successive eight steps in their 

 travel. Based on data of Hunter (1966) and his figure 2. Only the 

 odd-numbered positions have the individual fish positions 

 indicated. To show them all would confuse rather than clarify. 



''Hunter (1966) recognized three turns in his figure 2. For 

 present purposes the sequence is given six turns, as indicated in 

 Figure 12 and Table 1. His three indices, mean separation, 

 distance to nearest neighbor, and angular deviation represent 

 other measures of the same activity, all of which relate to the 

 differences of the mathematical approaches involved. 



479 



