FISHERY BULLETIN: VOL. 70, NO. 3 



theless, the plankton net appears to be more effi- 

 cient at night than during the day. The catches 

 of the smaller larvae are closer to the purse seine 

 catches than during the day, and much larger 

 larvae were taken at night — 21.5 mm maximum 

 versus 14.5 mm by day. This suggests that vis- 

 ion plays an important role in dodging. 



It is interesting to note that the maximum size 

 taken by the plankton net at night (21.5 mm) 

 coincides with a change of slope of the day purse 

 seine catches. The plankton observation taken 

 by itself might be interpreted as a size beyond 

 which all larvae can swim out of the net even 

 if they blunder into it. A length of 21.5 mm is 

 approximately the size of metamorphosis and the 

 onset of schooling. This social trait might also 

 adversely affect the day purse seine catches to 

 the extent that a school is more effective than 

 the sum of the individuals in detecting and re- 

 sponding appropriately. It does not seem to have 

 affected the night catches. This may be evidence 

 that schools tend to disperse at night. 



Each night station was paired with a day sta- 

 tion. These latter were taken late In the after- 

 noon at the same geographical point, but of ne- 

 cessity, several hours before the night station. 

 Examination of the data shows that this degree 

 of control was inadequate to allow meaningful 

 comparisons, at least on the basis of only 10 sets 

 of data. 



A DODGING MODEL 



In this section an attempt is made to ration- 

 alize the difference between the day plankton 

 net catches and the day purse seine catches on 

 the basis of the geometry of the towed net sit- 

 uation, the swimming speed of the larvae, and 

 the alarm distance, i.e., the distance in front of 

 the net that a larva would have to begin evasive 

 action in order to avoid capture. 



The algebra of the model is an extension of the 

 results of Barkley (1964). We start with his 

 equation (7) (our 1) which defines the escape 

 velocity, i.e., swimming speed, necessary to 

 escape a net assuming the larva is mathematic- 

 ally inclined and rational and, therefore, selects 



the shortest possible escape path, 

 Barkley's notation. 



We follow 



Ue = U 

 where: Ue 



1 + 





{R-r^y- 



_1 



(1) 



escape velocity (swimming speed) 

 (cm/sec) 

 U = towing speed of net (cm/sec) 

 Xa = reaction distance of the larva (cm) 

 7'o = initial offset of larva (from dead 



center of the net) (cm) 

 R — radius of net (cm). 



Equation (1) can be rearranged to provide 

 the minimum ?o from which escape is possible 

 given a swimming speed Ue yielding: 



To 



R — IXoUe iU^ — Ue'-)-']. 



(2) 



Of course, escape is possible from all larger ?'o's. 

 Now the proportion that escapes (P) is from 

 elementary principles: 



P = (tt R'~ — -rrn^) (tt R'-) 



-1 



(3) 



Substituting the right hand side of (2) into (3) 

 and rearranging yields the desired equation, i.e., 

 an expression relating the proportion escaping 

 to swimming speed and alarm distance as fol- 

 lows: 



P = 



= [r — ( ^0^^ ^1' 



R 



(4) 



From (4) we can define the proportion caught 

 (P') as simply 1 — P. Assuming that the purse 

 seine catches all larvae up to 10.5 mm by day, 

 the proportion caught (or escaping) can be esti- 

 mated as a function of size. The towing speed 

 of the net was about 1.5 knots (76 cm sec~^). 

 This leaves two unknowns, alarm distance {xo) 

 and swimming speed {Ue) . Our approach in 

 testing the model is to estimate swimming speed 

 as a function of size based on values in the lit- 

 erature, and solve for alarm distance — also as a 

 function of size. As will be seen, the derived 

 alarm distances seem intuitively reasonable and, 

 anticipating a later section, may explain the rel- 

 atively small increase in sampling power of 

 larger towed nets. 



Appropriate measurements on the swimming 

 speed of larval anchovies are not available. What 



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