FISHERY BULLETIN: VOL. 70, NO. 3 



escape speed, shape, size, and condition are need- 

 ed to assign animals to different components 

 when analyzing' towed-net samples by means of 

 the present theory. Such data could perhaps 

 best be obtained by taking stereoscopic photo- 

 graphs of animals' reactions to the approach of 

 a sampler. In practice, however, it may be pos- 

 sible to assign animals to operationally defined 

 components post facto, based on analyses of 

 catch data with the present theory. An example 

 of this is to be found in Table 1, where Bathy- 

 lagus stilbius ranging from 52 to 92 mm in length 

 were found to have essentially identical proba- 

 bilities of capture and were apparently all re- 

 tained by the meshes, thus meeting the criteria 

 for a single component. 



Inequations (2) and (3) the major unknowns 

 are the losses and the probability of capture. 

 Neither can be formulated precisely until be- 

 havior of many animals, before and after en- 

 tering nets of varied designs, has been studied. 

 However, losses can be estimated to some degree 

 from the difference between observed and the- 

 oretical catches ; and probability of capture can 

 be calculated for a limiting case, minimum prob- 

 ability of certain capture for individual en- 

 counters. This approach makes use of the ge- 

 ometry of the "lethal cone" (Figure 2). The 

 minimum probability of capture, Pc, is: 



Area of "lethal cone" cross section 



p _ at distance Xo 



^ ~ Area of the sampler mouth opening 



= (r/Ry. 

 From Figure 2, 



(4) 

 Substituting Z from equation (1) into (4) gives 



2 



Pc = 



c 



Xo 



which may also be written 



=) 



(5) 



Pc = 



(■ 



XoUe 



R 



^U^- 



w 



1 



(6) 



Where Pc is probability of capture, Xo is the 

 mean reaction distance, R is the radius of the 

 net's opening, U is the net's speed, and We is the 

 animals' mean escape speed. These results can 

 also be derived from equations (4) , (5) , and (7) 

 of my earlier analysis (Barkley, 1964). 



DISCUSSION 



To examine avoidance as a function of towing 

 speed, Gilfillan (reported by Clutter and Anraku, 

 1968) assumed that the product XoUe is a con- 

 stant, K. Starting with an apparent "effective" 



Figure 2. — Definition sketch for calculating P(., the minimum probability of capture. P(. is the 

 ratio of the area of the "lethal cone" (shaded) to the area of the net's mouth opening, at the 

 mean reaction distance Xq for one component of the catch. 



802 



