FISHERY BULLETIN: VOL. 80, NO. 1 



if individual escape speeds remained constant. 

 However, further analysis reveals that the dif- 

 ference in Xo for a given day/night catch differ- 

 ential could be a function of the relationship 

 between the observed night catch and the true 

 water column abundance. This is clearly evident 

 if we express the ratio of the day catch per vol- 



It could be argued that the day/night catch dif- 

 ferential is due to differences in escape speed of 

 the individuals rather than a change in their re- 

 action distance. To explore this we have also 

 solved Equation (3) for the ratio of day escape 

 speed, ud, to night escape speed, u N , after assum- 

 ing x D = x N . 



+ 



m 



r- -. •-■ 



& 



(5) 



ume sampled {DC) and night catch per volume 

 sampled {NC) in terms of real abundance (^4) and 

 percent capture as expressed in Equation (2): 



DC 



NC 



If we assume that the daytime escape speed, 

 Ud, is equal to the nighttime speed, w,v, and solve 

 for the ratio of the daytime reaction distance, xd, 

 to the nighttime reaction distance, Xn, we have: 



Xd/Xs 



1 - 



We have evaluated this equation assuming a true 

 abundance of 100 individuals per volume, night- 

 time catches of 99, 90, 10, 1, and 0.1 individuals 

 per volume, and daytime catches of 50, 10 and 

 1% of the nighttime catch. The ratios of x D /x Ni 

 plotted as a function of the ratio of NC/A Fig. 

 8a), shows that only very small differences in re- 

 action distance between day and night are re- 

 quired to explain large day/night catch differen- 

 tials when the night catch is 10% or less of the 

 true water column abundance. The fact that we 

 see no significant difference in day/night reac- 

 tion distances suggests our nighttime catches 

 also could be affected strongly by avoidance, and 

 that even at night we have significantly under- 

 estimated the numbers of N. megalops in the 

 water column. 



Note that the ratio of day/night escape speeds is a 

 function of xs and R as well as DC, NC, and A. 

 The escape speed and radius of net were not in 



(3) 



Equation (4) for the ratio of day/night reaction 

 distances. We have evaluated this ratio using the 

 same values noted above. With these results (Fig. 

 8b), we reach a conclusion similar to that for re- 



(4) 



action distance, namely, if reaction distance re- 

 mains constant between day and night, then 

 small differences in escape speed can explain the 

 day/night catch differential when the night 

 catch is 10% or less of the true abundance. 



There is, however, an entirely different expla- 

 nation which may account for this outcome in 

 application of Barkley avoidance theory to our 

 data. In fitting these data to Barkley's plots of 

 percent capture versus the ratio of x /R, two 

 assumptions were required: 1 ) that all changes in 

 size frequency are due to avoidance and 2) that 

 swimming speed is a function of body size. The 

 second assumption can be examined if one has 

 day/night pairs of tows taken at the same station 

 location with the same size of net. With swim- 

 ming speed a function of size, Barkley's model 



86 



