300 CHEMICAL SENSES 



locomotor responses of Scyliorhinus, Mustelus, and Diplodus, the frequent 

 references by earlier workers to responses involving turning movements, and 

 the theoretical implications of the weak feedback control of turning-related 

 locomotor variables strongly suggest that perception of biologically signifi- 

 cant odors modulates mainly a turning control mechanism and thus changes 

 the locomotor pattern. These effects were apparent whether or not the fish 

 received directional cues from the stimulus source. They occurred even when 

 the odor was admitted with the general water supply, thus equally affecting 

 all 16 compartments of the monitor tank (Kleerekoper 1967b). None of the 

 responses mentioned were observed in anosmic fish. That such modulation 

 of turning behavior can also be effected by changes in water flow rates will 

 be demonstrated below. 



Oriented Locomotion 



In a different experimental arrangement, the locomotor patterns of Gingly- 

 mostoma cirratum were cinematographically analyzed, in response to a dis- 

 crete source of water to which extract of fish flesh had been added (Kleere- 

 koper 1967a, b). The locomotor pathways of the shark, as it approached the 

 source, frequently had spiral configurations, many of which were analyti- 

 cally shown to be parts of logarithmic spirals (Kleerekoper et al. 1973). In 

 such an equiangular spiral, the lengths of radii of 90° have a ratio of 1:0.618 

 (Thompson 1942). In various organisms, suppression of sensory input of a 

 single modality brings about spiral movements of the helical type. This has 

 been shown for amoeba (Nageli 1860; Jennings 1901; Schaeffer 1920, 

 1926), ciliates (Bullington 1925), tadpoles (Streeter 1906), dogfish (Lee 

 1894), and others, including man (Schaeffer 1928). In nurse sharks with two 

 functional nostrils, the best logarithmic spiral fits were obtained in animals 

 stimulated with odor diffusing into stagnant water. In such conditions, cen- 

 tripetal movements along the spiral predominated, in contrast to locomotion 

 in the absence of olfactory stimulation or when one nostril was occluded. 

 The records showed that such centripetal locomotion led the animals to the 

 odor source. 



The orientation mechanism instrumental in this behavior is suggested by 

 the consideration that an animal approaching a target in a direct path, which 

 always deviates with a constant angle from a straight line connecting the 

 animal with the target, must follow a logarithmic spiral. In other words, 

 locomotor orientation using a directional sensor system based solely on a 

 bilateral input of constant differential magnitude will manifest itself in a 

 logarithmic spiral locomotor pathway. The differential input may originate 

 in the bilateral olfactory sacs; provided that the difference in strength of the 

 stimulus affecting them is constant, the means of orientation by this prin- 

 ciple are present. It was proposed that this is, indeed, the mechanism em- 

 ployed by the nurse shark, in the strong gradient prevailing in the experi- 

 ments described. Bilaterally different olfactory stimulation must depend on 

 the slope of the odor concentration gradient, which is steep in the vicinity of 

 the source but rapidly flattens, through dilution and dispersion, as the 



