FISHERY BULLETIN: VOL. 80. NO. 2 



moving at 10 kn can always closely approach 

 these dolphins, provided that the schools can be 

 followed. Evidently school speeds greater than 

 that of the ship can be maintained only 

 temporarily. Dolphins that do break into the 

 "running," or leaping swimming mode, must be 

 exceeding a certain "crossover speed." This is the 

 swimming speed above which a leaping locomo- 

 tion becomes more efficient. It is calculated to be 

 somewhat in excess of 10 kn (Au and Weihs 

 1980). Thus several lines of evidence indicate 

 that cruising speeds are <10 kn, as we in fact 

 measured. Dolphins of course are capable of 

 temporary higher speeds than reported here. 

 Top burst speeds as high as 14.5 kn have been 

 measured for Tursiops truncatus (Lang and 

 Norris 1966) and 21.4 kn for S. attenuata (Lang 

 and Pryor 1966). 



Because the faster, leaping locomotion 

 produces much splashing, dolphins that avoid 

 ships by moving away more slowly at cruising 

 speed obviously are more difficult to detect from 

 the ships. The initial avoidance probably pro- 

 ceeds at cruising speed because the dolphins are 

 not yet highly alarmed at the distances at which 

 detection of the ship and evasion begins. 



The evasive behavior of dolphins perhaps has 

 its most important implication relative to school 

 density studies conducted from ships. In par- 

 ticular the line-transect method (Seber 1973; 

 Burnham and Anderson 1976), which can be 

 employed for absolute density estimation of 

 schools, may be affected. An important require- 

 ment of the method is that the schools do not 

 move, or move randomly or little, relative to the 

 speed of the observer. However, schools are 

 evidently capable of avoidance movements at 

 speeds approaching that of the ship. Therefore 

 positions of schools relative to the ship and prior 

 to movement that are required to describe the 

 probability of sighting a school cannot be 

 obtained if there is movement. Only if the school 

 trajectories were known could the observed 

 positions be corrected. The probability of 

 sighting is usually obtained from the distribu- 

 tion of perpendicular distances that are a 

 transformation of the relative positions of 

 sighted schools. Laake( 1978) and Burnham etal. 

 (1980) emphasized that when school movement 

 occurs, both the probability functions describing 

 detectability and the altered animal distribution 

 are completely confounded in the distribution of 

 observed perpendicular distances. School move- 

 ment also violates the critical assumption that 



all schools initially on the track line will be seen. 

 Therefore, line transect methods for absolute 

 density estimation usually cannot be used when 

 avoidance movements occur. 



It is easy, however, to understand how avoid- 

 ance behavior reduces the probability of sighting 

 a school from a ship. Without movement this 

 probability would be (Burnham and Anderson 

 1976) 



ll g(x)dx 



where w is the half width of the swath being 

 searched, which could be the horizon distance, 

 and g(x), the detection function, is the probability 

 of sighting a school that is initially at perpen- 

 dicular distance x from the track line. The 

 function, g(x), is monotonically decreasing from 

 1 on the trackline (#(0) = 1). Therefore, schools 

 avoiding a ship by effectively moving farther 

 abeam must obtain a value to g(x), say g(x) 1 , that 

 is less that that at its initial distance x. These 

 reduced values, g(x) 1 , replace the original values 

 of g(x) at all initial perpendicular distances 

 where avoidance movements began. The area 

 under this altered detection curve (i.e., the plot of 

 g{x) x against x), which determines the new 

 probability of sighting a school from the track, is 

 accordingly reduced. Reasonable models of the 

 detection function and how it is altered by 

 avoidance behavior can be constructed to show 

 that this reduction can be considerable. 



If dolphins do obtain lower g(x) values from 

 their avoidance trajectories, the behavior would 

 be advantageous. This seems entirely possible 

 considering that the schools can cruise at speeds 

 approaching that of many research ships (Table 

 3) and apparently can detect and continue to 

 sense a ship from considerable distance. 

 Evidence of the latter are the distances at which 

 avoidance behavior was apparent (Table 2) and 

 the near simultaneous changes in school course 

 or speed following course changes by the ship. 

 Such changes occurred at 3.5 mi in school 1, at 

 6.0 and 3.3 mi in school 2, at 3.2 mi in school 4, 

 and at 2.4 mi in school 7 (Table 1). 



With significant reduction in sighting prob- 

 ability possible from avoidance, it would be 

 useful to empirically determine the actual 

 probabilities, g(x) 1 , or to model this behavior. We 

 expect, however, that the specifics of avoidance 

 trajectories as well as the probabilities would 



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