FISHERY BULLETIN: VOL. 70, NO. 1 



Testing of the theory requires some knowledge 

 of a species' escape speed as a function of size 

 or stage of development and its reaction distance 

 for one or more net designs under various cir- 

 cumstances, so that particular groups of animals 

 in a sample can be associated with the proper 

 values of xo and Ue in the theory. If the theory 

 is known to be valid in a given instance, Xo can 

 be determined once Ue is known. 



The theory was evaluated against four se- 

 lected sets of catch data. Since not enough was 

 known about the swimming ability of the species 

 in question, assumptions had to be made about 

 swimming speed as a function of size for each 

 one. Aside from the major premise used in de- 

 riving the theory, that animals which can escape 

 will do so, other assumptions made in carrying 

 out analyses of catch data were: that reaction 

 distance is essentially constant for any one spe- 

 cies under a given set of circumstances (one net, 

 towed at one speed, at one time of day) and that 

 the size-frequency curve for a species is deter- 

 mined entirely by mesh losses, avoidance, and the 

 population structure — the number of animals in 

 each size class interval in the population. 



The theory was first applied to daytime catches 

 of Stolephorus purpureus with a 1-m net. Simul- 

 taneous measurements made with a plankton 

 purse seine provided information on the popu- 

 lation structure. This nearly ideal set of data 

 permits direct calculation of the sampling effi- 

 ciency of the 1-m net, so that an absolute test 

 of the present theory could be made. First, the 

 bias due to population structure was removed, 

 by dividing the catch in each class interval by 

 the population in that class interval; this pro- 

 cedure also converts the catch into values of Pc 

 for fish large enough to be completely retained 

 by the meshes, as equation (3) demonstrates. 

 The adjusted catch curve (the solid line la- 

 beled Cl/Nl in Figure 4) can be directly com- 

 pared with theoretical curves from Figure 3 

 (showing Pc for various values of relative reac- 

 tion distance, Xo/R), when the length class in- 

 tervals have been converted to speed class inter- 

 vals by assuming that the fish swim 10 body 

 lengths per second. Agreement between theory 

 and observation appears to be good, with some 

 exceptions. These may be due to sampling var- 



iance, population variance, or failure of one or 

 more assumptions used in matching 5. piirpureiis 

 to the theoretical parameters. In the latter case, 

 the anomalies could be accounted for by incom- 

 petent avoidance behavior and school response 

 instead of individual reaction to the net. 



In the second example, the theory was used to 

 evaluate catches of anchovy by two different 

 nets, a 1-m net and an IKMT, towed at the same 

 nominal speeds. Since population abundance 

 was not determined for anchovy, an additional 

 assumption had to be made: that the catch 

 length-frequency curves were determined pri- 

 marily by avoidance and mesh losses, as in the 

 case of Hawaiian anchovy, where catches de- 

 crease 1,000-fold while the population decreases 

 only by a factor of 10 in the same size interval. 

 With this assumption, catch speed-frequency 

 curves must also be curves of relative Pc as a 

 function of size, or speed. Fitting the observed 

 values to the theoretical Pc curves (Figure 5) 

 yields a unique value for population density in 

 each class interval, numerically equal to the 

 catch at Pc = 1.0. For the anchovy, population 

 densities of 75 and 60 animals per 100 ml wet 

 plankton were obtained for the two samples an- 

 alyzed by this method. In this case agreement 

 between theory and observation, and between 

 samples, seems excellent. Except for night tows 

 with the 1-m net, values of Pc do not exceed 0.40 

 for the 1-m net and 0.12 for the IKMT. The 

 only significant deviations from theory occur at 

 smaller class intervals, where mesh losses are 

 important. Mesh retention can be estimated 

 quantitatively by extrapolating the theoretical 

 curve toward smaller class intervals, for com- 

 parison with observed catches, as illustrated on 

 the right-hand panel of Figure 5. 



The third example makes use of length-fre- 

 quency data for Bathylagus stilbius caught with 

 an IKMT towed at two different ranges of speed. 

 In this case, no satisfactory fit could be achieved 

 for all larger class sizes of both sets of tows, 

 when treated as a unit. If instead the analysis 

 is performed using only one class interval at a 

 time from the two sets of tows, as shown in Fig- 

 ure 7 and Table 1, the cause of the difficulty 

 becomes clear. The estimated population den- 

 sities have almost as great a range as do the 



818 



