Optimal course by dolphins 

 for detection avoidance 



Carlos A.M. Salvadd 

 Pierre Kleiber 

 Andrew E. Dizon 



Southwest Fisheries Science Center, National Marine Fisheries Service, NOAA 

 P.O. Box 271, La Jolla, California 92038-0271 



One of the assumptions of line tran- 

 sect sampling is that movement of 

 animals being counted is not in re- 

 sponse to the approaching vessel 

 before the animals are detected 

 (Burnham et al. 1980). By observ- 

 ing from a helicopter the reaction of 

 dolphins to an approaching survey 

 vessel, Au and Ferryman (1982) and 

 Hewitt (1985) demonstrated that 

 dolphin schools can detect the ap- 

 proach and maneuver to attempt 

 to avoid detection. Because it may 

 be that dolphin exhibit forms of 

 optimal behavior (Au and Weihs 

 1980), it is of interest to determine 

 whether there is a direction the 



dolphin should take that maximizes 

 their distance to the vessel at the 

 point of closest approach and, if 

 there is such a direction, to deter- 

 mine whether dolphin use it. If this 

 is so, this may be the way of deter- 

 mining through aerial means when 

 dolphin first react to an approach- 

 ing vessel and whether it is after 

 they are detected by a shipboard 

 observer. 



Since the advent of purse-seine 

 fishing in the eastern tropical Pacif- 

 ic in 1959, dolphin that associate 

 with yellowfin tuna (i.e., primarily 

 Stenella attenuata, S. longirostris, 

 and Delphinus delphis) are chased. 



track of vessel 



Figure 1 



The vessel traveling at speed Vg and the dolphin traveling 

 at V[) as seen in the stationary frame of reference. The direc- 

 tion a is the one chosen by the dolphin. Distance f is the perpen- 

 dicular distance between the initial position of the dolphin and 

 the projected path of the vessel, while a + f is the distance 

 between vessel and dolphin when the dolphin is abeam. 



caught in nets, and sometimes 

 drowned (Perrin 1968, 1969). 

 Stuntz and Perrin (1979) reported 

 that these species of dolphin are 

 more difficult to capture in areas 

 where purse-seine-vessel fishing 

 effort has been greatest, imply- 

 ing that evasive behavior may be 

 learned. It has also been reported 

 by Au and Ferryman (1982) that 

 evasive maneuvers by dolphin upon 

 approach of a vessel sometimes 

 begin at a distance that is approx- 

 imately the shipboard observer's 

 horizon. Because the visual horizon 

 of even a leaping dolphin is shorter 

 than that of a shipboard observer, 

 it is likely that they are reacting to 

 the vessel sound. It is therefore 

 plausible that by experiencing re- 

 peatedly the approach of such ves- 

 sels, dolphin not only have learned 

 to evade but do so optimally by 

 choosing through trial and error the 

 direction of escape, if it exists, in 

 which the noise amplitude increases 

 the least. Because the attenuation 

 of sound is proportional to the dis- 

 tance transversed by it, escaping 

 from a sound source in the direction 

 where the amplitude increases the 

 least is the same direction that max- 

 imizes the distance between a uni- 

 formly-moving source and receiver 

 at the point of closest approach. 



Here, we formulate the following 

 problem: Upon detecting the ap- 

 proach of a vessel, a dolphin at- 

 tempts to avoid detection by re- 

 treating. If the velocity of the vessel 

 is Vb and that of the dolphin is Vp, 

 is there a direction in which a dol- 

 phin can escape to maximize its 

 distance from the vessel at the point 

 of closest approach (Fig. 1)? And if 

 so, what direction is it? We will 

 show that there is such a direction: 

 If a is the angle between Vb and 

 Vd, the angle a = arccos(VDA'^B). 

 where Vg and Vd are, respectively, 

 the speeds of the vessel and the 

 dolphin, will maximize the distance 



Manuscript accepted 5 February 1992. 

 Fishery Bulletin, U.S. 90:417-420 (1992). 



417 



