CHEMORECEPTION: LOCOMOTION AND ORIENTATION 297 



in the same species (Kleerekoper et al. 1974). With the analytical techniques 

 well in hand, and the principle established in a teleost, quantitative analysis 

 of the locomotor behavior of an elasmobranch, Ginglymostoma cirratum, 

 was undertaken. Although this research is continuing, the results to date will 

 now be discussed in some detail, based on published (Matis, Kleerekoper, 

 and Childers 1974; Matis, Kleerekoper, and Gruber 1975) and still un- 

 published data (Gerald et al., in press). 



The goldfish studies had demonstrated that locomotor behavior can be 

 accurately described through the quantification in time and space of a num- 

 ber of key variables. Seventeen such variables were defined: (1) number of 

 right turns, (2) number of left turns, (3) number of combined turns, (4) 

 radian accumulation of right turns, (5) radian accumulation of left turns, (6) 

 radian accumulation of combined turns, (7) difference between right and left 

 radians, (8) mean size of right turns, (9) mean size of left turns, (10) mean 

 size of combined turns, (11) mean difference between right and left turn 

 size, (12) ratio of left turns to combine turns, (13) ratio of left radians to 

 combined radians, (14) ratio of straight path to turns, (15) distance travelled 

 (cm/s), (16) mean step length, (17) mean velocity (cm/s). 



For each experiment, the record of photocell responses to the presence of 

 the shark was converted into time series of 15-min intervals, and the data for 

 each interval transformed into the 17 variables. It had been established that 

 the time series of these variables have distinct patterns of serial correlation 

 over time (Matis et al. 1973). The strength and the varying periodicity of the 

 oscillations of the 17 series suggested the existence of a complex multivariate 

 interrelationship that determines the constraints on locomotor behavior. 

 These studies were expanded, including additional data, and it was demon- 

 strated that only seven of the time series are sufficient for maximum loco- 

 motor predictability and could form the basis for a satisfactory locomotor 

 control model (Matis, Childers, and Kleerekoper 1974). 



Against this background of information on the goldfish, studies of the 

 locomotor behavior of the nurse shark were initiated, with the immediate 

 object of constructing a refined locomotor control model for a representa- 

 tive elasmobranch. To this effect, the time series behavior of the 17 loco- 

 motor variables was analyzed based on a large data set acquired in six experi- 

 ments with three nurse sharks (Matis et al. 1975). The analytic approach had 

 three objectives: to determine the frequency of serial correlation in the data, 

 to calculate the proportion of residual variation remaining after fitting a 

 first-order autoregressive equation, and to analyze the proportion of residual 

 variation to ascertain whether it differed between experiments and variables. 

 It was found that in this elasmobranch, as in the previously studied teleost, 

 definite serial correlation occurs in the locomotor variables of all the animals 

 and that the strength of this correlation varies among the sharks, and within 

 the same shark between different experiments. The degree of serial correla- 

 tion varies among the 17 variables, reflecting the strengths of the feedback 

 structures by which they are controlled. 



It is not yet clear to what the variations in the strength of the correlations 

 must be attributed. However, it is speculated that the feedback mechanism 



