SOMERTON AND KOBAYASHI: FISH LARVAE CATCHES IN PLANKTON NETS 



appeared to become clogged with algae despite 

 efforts to clean it between deployments. To de- 

 termine whether the test net was indeed clogged 

 and filtered less water than the standard net, we 

 assumed filtration volume was proportional to 

 the catch of nehu eggs and used a paired t-test to 

 compare egg catches between nets. The test net 

 caught significantly fewer eggs (P < 0.05); 

 therefore, the test net was assumed to have fil- 

 tered less water. To correct for the difference in 

 filtration volume, larval catches in the test net 

 were multiplied by the ratio of the egg catch of 

 the standard net to that of the test net in each 

 pair of deployments. 



Nehu larvae were subsequently measured to 

 the nearest 0.1 mm by using a video digitizing 

 system (Optical Pattern Recognition System 

 produced by Biosonics, Inc., Seattle, WA). For 

 preflexion and early flexion larvae, length was 

 measured from the snout to the end of the 

 notochord. For larvae with fully formed tails, 

 length was measured from the snout to the base 

 of the caudal fin rays. The length distributions 

 were not corrected for shrinkage due to preser- 

 vation, but since all samples were maintained in 

 preservative for about the same length of time, 

 it is unlikely that shrinkage varied among 

 samples. 



The entry and retention probabilities were 

 estimated by simultaneously fitting Equations 

 (5) and (6) to the length-frequency data by using 

 nonlinear regi'ession, but before this could be 

 done, three problems had to be solved. First, the 

 entry and retention probabihties could not be 

 estimated independently for each length inter- 

 val; therefore. Equations (5) and (6) had to be 

 modified so that the probabilities were ex- 

 pressed as functions of larval length. Retention 

 probabilities were chosen to vary with length as 

 logistic functions and thus have the form P = 

 1/(1 -I- ae "'''), where a and b are parameters 

 to be estimated and / is larval length (Ricker 

 1975). Entry probabilities, because they are de- 

 creasing functions of length, were chosen to have 

 the form P = 1 - (1/(1 + a e"*')). After the 

 logistic functions were substituted for the two 

 entry probabilities (P,., and P,,,.) and two reten- 

 tion probabilities (P,,, and P,^.) in Equations (5) 

 and (6), the resulting statistical model had eight 

 parameters. 



Second, variability in the catch ratio changed 

 with larval length, owing to the change in sample 

 size, and necessitated the use of weighting fac- 

 tors in the regi-essions (Draper and Smith 1981). 

 The weighting factors used were equal to 



l/variNos/No,), where var is the variance and Ngi 

 can be either N,,,- or Noe- Variance of the catch 

 ratio was approximated by using the delta 

 method (Seber 1973): 



var(A^„,/A^,„) = (1/^,,,)^ var(A^„,) 



+ (N,JNjf variN,.,) 



- 2 {N,JNJ) cov(A^„,,7V„,) , (9) 



where cov indicates covariance. The number of 

 larvae captured in each length class (A'^,,) was 

 assumed to vary as a multinomial random vari- 

 able. The variance of No was therefore ex- 

 pressed as N,P(l - P); where A^„ is either 

 Nos< Nor or Noe', N, [s the sum of A^„ over all 

 length intervals; and P = N„/N,. Although 

 the covariance between the catches of the stan- 

 dard and test nets could be estimated for the 

 retention experiment, it could not be estimated 

 for the entry experiment because samphng was 

 not conducted pairwise. However, the covari- 

 ance term for the retention experiment was, for 

 all size intervals, approximately 100 times less 

 than the sum of the two variance terms (Equa- 

 tion (9)). On this basis, we assumed that the 

 covariance term was generally small and could 

 be ignored in both the entry and retention 

 experiments. 



Third, since the catch ratios fluctuated widely 

 and often became infinite in the larger length 

 intervals where sample sizes were small, the 

 length distributions were truncated prior to fit- 

 ting the equations. For the entry experiment, 

 truncation occurred at the smallest length inter- 

 val with zero catch by the test net. For the 

 retention experiment, however, this rule re- 

 sulted in an extremely narrow length range be- 

 cause the catches obtained with the test net 

 were zero at relatively small lengths. To circum- 

 vent this problem, the inverse of Equation (5) 

 was fit to the data, and truncation occurred at 

 the smallest interval with zero catch by the stan- 

 dard net. Weights were calculated by using 

 Equation (9) after substituting A^,,., for A^,„ and 

 vice versa. 



Once Equations (5) and (6) had been fit to the 

 data, the values P,,„ P,e, Ps, and p,,. were esti- 

 mated by evaluating the logistic functions at 

 each 0.5 mm length interval using the parameter 

 estimates. P^ for the standard net was calculated 

 for each length interval as the product of the 

 estimates of Pp., and P,.,. Length-frequency data 

 from nehu larvae were then corrected for extru- 



449 



