FISHERY BULLETIN: VOL. 70, NO. 3 



with dividers), setting the upper point at 1.0 

 (1009f ) and reading the fraction or percentage 

 retained at the lower point. 



Let us now consider catches obtained with one 

 type of gear at two different speeds. 



Aron and Collard (1969) made carefully con- 

 trolled IKMT tows at two different speed ranges, 

 at night, using telemetering flow and depth 

 meters to insure that the amount of water sam- 

 pled was the same for all tows and that sampling 

 was done at the desired depths. The speed of 

 their net varied between about 1.0 and 1.7 m/sec 

 and about 1.6 and 2.3 m/sec during the two sets 

 of tows; I have assigned values, corresponding 

 to modal speeds, of 1.2 and 2.0 m/sec to these 

 tows for calculating values of UeJlJ. 



The assumption made thus far that Ue = lOL, 

 cannot be used for the species enumerated by 

 Aron and Collard because of their large size 

 (up to 102 mm) ; escape speeds of 10 body 

 lengths per second yield values in excess of the 

 net's speed. Either fish that big should not have 

 been captured, or their escape speed must be 

 considerably less than 10 lengths per second. 

 Accordingly, it was assumed that Ue = 5L (with 

 units of cm/sec and cm). 



As was noted earlier, the effect of different 

 choices of escape velocity to length ratios is to 

 shift the observed points along the Ue/U axis 

 of Figure 3, with proportional changes in re- 

 sulting values of Xo/R. If a set of observed 

 points fall precisely on the theoretical curve 

 Xo/R — 4, for example, a twofold change 

 in the assumed escape velocity results in points 

 falling equally precisely on the curves for 

 Xo/R = 8 or 2, depending on whether the escape 

 velocities are halved or doubled. Values of Pc 

 are not affected by the choice of velocity to length 

 ratios. 



Obviously, relative values of reaction distance, 

 Xo, can be estimated from the present theory, 

 but absolute values can only be determined if in 

 addition the animal's actual escape velocities are 

 known, preferably as a function of size. Thus, 

 from Figure 5 we can conclude with some as- 

 surance that anchovy react to the IKMT at dist- 

 ances some 2.5 times as great as they do to the 

 1-m net. But the reaction distances themselves, 

 8.3 m for the IKMT and 3.3 m for the 1-m net. 



can only be correct if anchovy do in fact swim at 

 an average speed of 10 body lengths per second 

 when trying to avoid the net. 



Of the species enumerated by Aron and Col- 

 lard, Bathylagus stilhius seemed most amenable 

 to analysis with avoidance theory, because the 

 length-frequency curves for this species were 

 somewhat smoother, and differed more with 

 speed of tow, than was the case for other species. 

 Figure 6 shows the speed-frequency curves for 

 this species, assuming that Ue = 51. and that 

 U = 120 and 200 cm/sec, respectively. A fairly 

 good fit could be obtained for Pc at Xo/R ~ 3.8 

 for the faster tow and for part of the slower tow. 

 For the fit shown in Figure 6, No, the abundance 

 at zero length, is 1,400 animals per class interval 

 (Aron and Collard, 1969, give catches as total 

 numbers caught during all 34 tows made in Jan- 

 uary 1966). An alternative choice of No, 340 

 animals per class interval, produces a good fit 

 with Xo/R = 2.4 for the larger animals caught 

 by the slower tows but does not fit any of the 

 other data. In short, there is no way to fit the 

 length-frequency data for B. stilhius to the the- 

 ory under the assumptions used up to now. 



The assumption most likely to be violated is 

 that population size at different lengths has neg- 

 ligible Influence on the size-frequency curve 

 (Nl c^ No). This assumption when valid makes 

 it possible to fit data from a series of length 

 classes using a single value for A^o, as was done 

 for anchovy (Figure 5). If Nl varied signifi- 

 cantly with length for B. stilhius, only identical 

 length classes can be compared between the two 

 sets of tows at different speeds. Figure 7 illu- 

 strates this procedure for the 62- and 97-mm 

 length classes, where theoretical curves for Pc 

 at Xo/R = 2.8 and 1.8, respectively, fit the data 

 for these two size classes. Values of A'^o thus 

 obtained were 900 individuals per class interval 

 for 62-mm fish and 26 individuals per class in- 

 terval for 97-mm fish. This 35-fold difference 

 in apparent abundance is comparable in mag- 

 nitude to differences in catch rates, 285 to 8 (48- 

 fold) for the faster tows and 57 to 1 for the 

 slower tows. It therefore seems likely that the 

 shape of the length-frequency curves for B. stil- 

 hius was determined in large part by the popu- 

 lation structure; avoidance apparently played 



810 



