A Method for Correcting Catches of Fish Larvae 

 For the Size Selection of Plankton Nets 



David A. Somerton and Donald R. Kobayashi 



ABSTRACT: Length distributions of fish larvae 

 obtained with plankton nets are usually biased be- 

 cause large lar\'ae avoid the net and small larvae 

 are extruded through the meshes. Such bias is often 

 corrected by determining the ratio between a stan- 

 dard net and a test net with either zero extrusion or 

 zero avoidance. However, when avoidance of the test 

 net with zero extrusion or when extrusion through 

 test net w ith zero avoidance differs from the stan- 

 dard net, then the usual method of correcting for 

 size selection results in biased estimates. For such 

 situations, we propose a method that explicitly con- 

 siders both differential extrusion and differential 

 avoidance and that provides estimates of variance 

 for the corrected length-frequency distributions. 

 The method was applied to length-frequency data 

 for the Hawaiian anchovy or nehu, Encrasicholina 

 purpurea. It was shown that a 1 m plankton net 

 with 0.335 mm mesh dropped vertically through the 

 water column during the day effectively samples 

 nehu larvae only between 2.25 and 6.75 mm, 

 roughly one-third of the total length range. 



originally in the path of the net (AO: 

 No = Pc N, 



(1) 



where the proportionality constant (Pc) varies 

 with larval length. P^ can be considered as the 

 probability of capturing a larva, and this, in 

 turn, can be considered as a product of an entry 

 probability (Pp) and a retention probability (Pr): 



P P  



(2) 



where P^ is equal to 1 minus the probability of a 

 larva avoiding the net and P^ is equal to 1 minus 

 the probability of a larva being extruded through 

 the meshes, given that it has entered the net. 



Since an estimator for A^ can be obtained by 

 combining and rearranging the above equations, 



A^ 



N, 



P.Pr 



(3) 



For many aspects of larval fish ecology, accurate 

 estimates of length distribution are imperative, 

 yet the length distribution of larvae obtained 

 with a plankton net is nearly always biased be- 

 cause large larvae avoid the net and small larvae 

 are extruded through the meshes. Previous 

 research on methods to correct larval catches for 

 such size selection has focused on either extru- 

 sion (Lenarz 1972) or avoidance (Barkley 1972; 

 Murphy and Clutter 1972), implicitly assuming 

 that the two aspects of size selection are inde- 

 pendent. Although this assumption seems 

 reasonable, situations arise in which the prob- 

 lems of estimating extrusion and avoidance are 

 unavoidably linked. 



Nearly all empirical or analytical studies of 

 avoidance and extrusion are based on the prem- 

 ise that the number of larvae captured by a 

 plankton net (A'^,,) is proportional to the number 



David A. Somerton and Donald R. Kobayashi: Southwest 

 Fisheries Center Honolulu Laboratory, National Marine 

 Fishery Service, NOAA, Honolulu, HI 96822-2396. 



the problem of correcting for size selectivity is 

 one of estimating P^ and Py for each length inter- 

 val. 



To estimate Pp or Pr, catches of a standard net 

 are usually compared with those obtained by 

 some test net used to sample the same popula- 

 tion of larvae. In this paper, we will refer to 

 these comparisons as either entry or retention 

 experiments. Assuming catches are standard- 

 ized to reflect equal filtration volumes, the gen- 

 eral form of a net comparison is 



A^„ 



N, 



P P 



P P 



= N, 



(4) 



where the second subscript refers to the stan- 

 dard net (s) and to the test net used in either an 

 entry experiment (/ = e) or a retention experi- 

 ment (i = r). Expressed in words, Equation (4) 

 states that the corrected catches from the stan- 

 dard and test nets are both unbiased estimates of 

 the true abundance of larvae and are therefore 

 equal. 



Manuscript Accepted April 1989 

 Fisheries Bulletin, U.S. 87: 447-455. 



447 



