FISHERY BULLETIN: VOL. 76, NO. 2 



fluorescent lights placed around the perimeter of 

 the tank which shone through the walls. This pro- 

 vided even, diffuse light in the tank. The water in 

 the tank was noncirculating. 



Schooling behavior was recorded on Tri-X film 

 using a 35 mm camera with motor drive and a 

 variable setting automatic timer. A mirror was 

 placed above the tank and pictures were taken of 

 the squid by photographing the surface image 

 reflected in the mirror. A black plastic barrier 

 surrounded the experimental tank. A small hole 

 in the barrier allowed observations to be made of 

 the squid without disturbing them. Exact 

 methods, timing of pictures, etc. varied with the 

 experiment and will be described in the appro- 

 priate section. 



After the films were developed, they were 

 analyzed using a Scientific Data Products data 

 tablet (Graf-Pen) coupled with a PDP 11-45 com- 

 puter. The data tablet is a set of microphones 

 placed at right angles which record the sound pro- 

 duced by an electrical spark made by a special 

 marking pen. The x and y coordinates of a point 

 were relayed to the computer by pressing the pen 

 down on the tablet at that point. This device al- 

 lowed the recording of large amounts of squid posi- 

 tion data. In each frame, the tip of the tail, the tip 

 of the outstretched arms, and a point midway be- 

 tween the two eyes were recorded for each squid. 

 Other information, such as the position of 

 barriers, was recorded in the same way. Mea- 

 surements taken from the photographs were sub- 

 sequently converted to real distances by multipli- 

 cation by appropriate scale factors. 



Students of schooling have examined school 

 geometry both as a two-dimensional system on a 

 horizontal plane (Breder 1959; Williams 1964; 

 John 1964; Hunter 1966, 1968; Van 01st and 

 Hunter 1970) and as a three-dimensional struc- 

 ture (Cullen et al 1965; Symons 1971a, b; Pitcher 

 1973). Since squid schools do have a three- 

 dimensional structure in nature, a three- 

 dimensional analysis will eventually be necessary 

 to determine all of the structural details of the 

 school. A three-dimensional analysis, however, is 

 much more difficult than a two-dimensional 

 analysis. It was felt that a two-dimensional 

 analysis would suffice to examine certain aspects 

 of squid schooling behavior. In these experiments, 

 the squid were very nearly confined to a two- 

 dimensional plane by the shallow water depth in 

 the experimental tank. Observations of small 

 schools (up to six squid) in a deeper tank (1 m 



depth) indicated that the two-dimensional struc- 

 ture observed in the experimental tank was not 

 uncommon. 



Three indices were chosen to quantify the angu- 

 lar orientation of individuals in a school, the over- 

 all shape of the school, and the distance between 

 neighboring individuals in a school. These indices 

 were proposed by Hunter ( 1966) and he includes a 

 detailed discussion of their properties. The three 

 indices are: 



1. Mean separation distance: An average of the 

 horizontal distances separating each squid from 

 every other squid in the school. It is influenced by 

 school shape, distance between neighboring squid, 

 and number of squid in the school. Distances be- 

 tween all possible pairs of squid are measured and 

 these values are averaged. Distance is measured 

 between the two closest points on the midline of 

 the bodies ( including outstretched arms) of the two 

 squid. 



2. Mean distance to nearest neighbor: An aver- 

 age of distances from each squid in the school to its 

 nearest neighbor. The measurement is made be- 

 tween the two closest points on the midline of the 

 bodies (including outstretched arms) of the two 

 squid. The same measurement is used twice if two 

 squid are closer to each other than to any other 

 squid. 



3. Mean angular deviation: This is a measure of 

 the differences in orientation among squid within 

 a school. The heading of each squid is determined 

 and the resultant direction of the school is com- 

 puted by assigning each squid a value of one and 

 adding the headings vectorally. The mean number 

 of degrees individual squid deviated from this re- 

 sultant direction of the school was calculated as 

 the index of orientation. 



One difference between squid and most of the 

 schooling fish which have been studied is that 

 squid readily swim both forward and backward. 

 Thus, a squid with an orientation that was 180° 

 out of phase with the rest of the school might still 

 be swimming with the rest of the school. For this 

 reason, one orientation measure was calculated 

 which regarded the squid as a line segment rather 

 than as a directed vector and measured the small- 

 est angular deviation between line segments. 

 Such measurements were rarely different from 

 measurements made considering the orientation 

 of the squid and therefore will not be considered 

 further in this paper. 



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