FISHERY BULLETIN: VOL. 84, NO. 2 



is variation among categories. This is true for 

 all fish. 



7. With few categories (species-size-qualities) the 

 chance of missing a category is reduced. Equa- 

 tions (9) and (13) should be used for clusters of 

 equal size and Equations (21) and (22) for un- 

 equal size clusters. This result is, of course, ap- 

 plicable to all commercial fish. 



8. As far as practicable, selection of a cluster for 

 a market category should be done before any 

 presorting is done at the port either from bins, 

 strap boxes, or off conveyor belts. 



9. Variation (within categories) in length and age 

 for a species was considerably higher among 

 boat trips than among clusters within boat trips. 

 Also, variation among clusters was not signifi- 

 cant, compared with variation within clusters 

 (Table 5). Hence, for precise estimation of 

 species number, length, and age composition for 

 a category at a port during a season data should 

 be collected from a large number of landings 

 and from few clusters from a category within 

 a sample landing. This result should hold for all 

 commercial fish. 



10. For the cost function C = c x n + c 2 nm where 

 Cj is the average cost (in minutes) per boat trip 

 due to transport, contact, and delay in making 

 a contact, c 2 the average cost of data collection 

 (identification of species, sex, length, otoliths, 

 etc.) per cluster per boat trip and C is the total 

 cost involved in visiting the primary sampling 

 units (boat trips) and collecting data, the opti- 

 mum number of clusters per sampled trip for 

 a fixed cost for a category is two (Table 4). This 

 should provide valid estimates of error as re- 

 quired in Equations (13) and (22). 



11. The principal contribution of the paper is that 

 a minimum of four sample landings be sub- 

 sampled for each category from a port-month 

 stratum, i.e., about 1 per week and two clusters 

 of 50 lb (25 lb for small fish) each should be 

 sampled to provide port-year estimates with a 

 reasonable degree of accuracy. 



If a category is infrequently landed, sampling 

 should be directed towards the infrequent 

 category, as long as the number of landings for 

 the category is less than four per month. 



12. The efficiency of the ratio estimator (Equation 

 (28)) based on poststratification by categories 

 at port-year level and using constant cluster 

 weight within a category was compared with 

 two other estimators, including the ratio esti- 

 mator based on jackknife. Empirical evidence 

 indicated that the ratio estimator using constant 



cluster weight within a category proved most 

 efficient for estimation of species catch. 



13. Age-length keys can yield most inefficient 

 estimates of the numbers at age for extremely 

 small and large fish. It is suggested that cluster 

 sampling for length be based on a number of 

 clusters separated in space and time; also, sam- 

 pling for age should be intensified for small and 

 large fish. This approach is applicable to all 

 fish. 



14. Double-sampling was adopted for estimating 

 proportion of widow rockfish in 11-yr age group. 

 A sample of fish was divided into 3 strata and 

 optimum allocation for age was adopted within 

 strata. The estimated proportion was 27% more 

 efficient than if single sampling were adopted. 



The best length-age did not change significantly 

 if age determination is made on every other fish 

 selected in ascending order of length. 



The method is general and is applicable to all fish. 



ACKNOWLEDGMENTS 



Thanks are due to William Lenarz of Tiburon 

 Laboratory for providing information on problems 

 related to widow rockfish landings on the Califor- 

 nian coast, to Candis Cooperider and Mark Allen for 

 the computations done on data collected, to the field 

 staff of the California Department of Fish and Game 

 responsible for collection of relevant data, and to 

 Norman Abramson, Director, Tiburon Laboratory 

 for all the assistance rendered to me during my work 

 in the Laboratory. My thanks are also due to Pat 

 Dalgetty, Department of Mathematics and 

 Statistics, University of Calgary, for assistance in 

 typing the paper and finally to the referees for 

 helpful comments. 



LITERATURE CITED 



Bartoo, N. W., and K. R. Parker. 



1983. Stochastic age-frequency estimation using the von Ber- 

 talanffy growth equation. Fish. Bull, U.S. 81:91-96. 

 Clark, W. G. 



1981. Restricted least-squares estimates of age composition 

 from length composition. Can. J. Fish. Aquat. Sci. 38: 

 297-307. 

 Cochran, W. G. 



1977. Sampling techniques. 3d ed. Wiley and Sons, N.Y., 

 428 p. 

 Fridriksson, A. 



1934. On the calculation of age-distribution within a stock of 

 cod by means of relatively few age-determinations as a key 

 to measurements on a large scale. Rapp. P. -v. R6un. Cons. 

 Perm. int. Explor. Mer 86:1-14. 



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