FISHERY BULLETIN: VOL. 87, NO. 3 1989 



For an entry experiment, an appropriate test 

 net is one that has no larval avoidance (i.e., Pee = 

 1.0) over the size range of interest. After sub- 

 stituting this value for the entry probability and 

 rearranging terms. Equation (4) can be ex- 

 pressed as 



No 



(5) 



Likewise, for a retention experiment, an appro- 

 priate test net is one that has no larval extrusion 

 (i.e., P„. = 1.0). After substituting this value for 

 the retention probability and rearranging terms. 

 Equation (4) can be expressed as 



N^ 



(6) 



To simplify Equations (5) and (6) further, pre- 

 vious studies have assumed that either the larval 

 retention of the test net used in an entry experi- 

 ment was identical to that of the standard net 

 (i.e., P,., = P,.e\ Barkley 1972; Murphy and Clut- 

 ter 1972) or that the larval entry into the test net 

 used in a retention experiment was identical to 

 that of the standard net (i.e., P^,, = Pp,.; Lenarz 

 1972; Colton et al. 1980; Leak and Houde 1987). 

 With these assumptions, Equations (5) and (6) 

 become 



and 



No., 



N„e 



N„ 



p 



* es 1 



(7) 



(8) 



In other words, entry and retention probabilities 

 of the standard net were estimated as the ratio 

 of the catches of the standard and test nets 

 within each length interval. 



When neither assumption can be made, the 

 estimation procedure is complicated in two ways: 

 First, Pes and P,.,, cannot be estimated as simple 

 ratios of the catches of the standard and test nets 

 because they additionally depend on other un- 

 known entry and retention probabilities. This 

 means that Pp., and Prs cannot be estimated inde- 

 pendently for each length interval and must in- 

 stead be expressed as functional relationships of 



larval length and estimated simultaneously for 

 all size intervals. Second, the equations for the 

 entry experiment. Equation (5), and the reten- 

 tion experiment. Equation (6), contain both Pes 

 and P,s; therefore, the two probabilities are con- 

 founded and must be estimated jointly. 



In this paper, a method is described for esti- 

 mating the entry and retention probabilities for 

 this more difficult situation, and this method is 

 then applied to correct the length-frequency dis- 

 tribution of larval Hawaiian anchovy or nehu, 

 Encrasicholina purpurea, obtained with plank- 

 ton nets. 



MATERIALS AND METHODS 



The standard plankton net that we used to 

 sample eggs and larvae of nehu was constructed 

 of 0.335 mm Nitex' and measured 1 m in 

 diameter and 5 m long. The net was not towed 

 but deployed instead by our allowing it to drop 

 vertically through the water column until it hit 

 the bottom, then retrieved with a line attached 

 to a choke collar surrounding the mesh approxi- 

 mately 15 cm from the mouth of the net. 



Retention and entry experiments were con- 

 ducted on 28 March 1988 within Pearl Harbor, 

 HI. The retention experiment consisted of 10 

 paired net drops, in which the standard net and a 

 test net were deployed simultaneously at one 

 location during daylight hours when the stan- 

 dard net was normally used. The test net was 

 identical to the standard net in all dimensions, 

 but it had a smaller mesh size (0.183 mm). The 

 entry experiment was conducted at each of three 

 nearby (<0.5 km distance) locations and con- 

 sisted of five deployments of the standard net 

 during the day and five deployments of the same 

 net the following night at each location. Since 

 sampling could not be paired in this experiment, 

 we were concerned that patchiness and hori- 

 zontal movement of fish by tidal currents might 

 alter the length distribution between day and 

 night sampling. To reduce this, the sampling 

 locations chosen had weak tidal currents, and in 

 addition, sampling was partitioned between 

 three locations rather than concentrated at one. 

 Water depth at all sampling locations was ap- 

 proximately 12 m. The sample obtained from 

 each deployment of each net was stored sepa- 

 rately in 10% buffered formalin. 



During the retention experiment, the test net 



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