MSttfcKX JBULL^IIJN: VUL. 84, INU. Z 



tions in sampling for estimating age composition of 

 rockfish landings based on recent widow rockfish 

 data from the California coast. Finally, we will 

 describe some of the measurement errors, which 

 would normally occur in simple random sample of 

 individual fish and which are taken care of in cluster 

 sampling adopted in our approach. 



The sampling plan arrived at may produce usable 

 results under the assumptions stated, though some 

 of the assumptions have been under attack during 

 recent years. 



DESIGN OF THE SURVEY 



Rockfish are being landed at 14 points on the 

 California coast. Of these, three cater only to com- 

 mercial fishing, four to sport fishing, and seven to 

 both sport and commercial fishing. The 10 commer- 

 cial ports are grouped into 6 port groups with a sam- 

 pler (six in all) assigned to each of the 6 ports— 

 Eureka, Fort Bragg, Bodega Bay, San Francisco, 

 Monterey, and Morro Bay. 



The commercial trawlers make trips varying in 

 length from 1 to 8 d. These vessels maintain log 

 books to keep records of area fished and appropriate 

 catch for each tow. Sampling by tow is generally not 

 feasible because it is not possible for the sampler 

 to be on board during haul time. For the same 

 reasons no estimates of fish being rejected and 

 returned to the sea are obtained because this would 

 involve collection of discarded fish from randomly 

 selected tows within sampled trips. 



Selection Procedure 



A two-stage stratified random sampling plan was 

 adopted with port-month group as a stratum and 

 boat trips within a stratum as first-stage sampling 

 units. Fish are sorted at sea into market categories. 

 The first stage sampling units are poststratified into 

 categories and at least one cluster of a given weight 

 is subsampled within each sort-type from a first- 

 stage sampling unit. Categories are based upon 

 species composition, size, and quality, but in other 

 contexts they could be strictly size or species 

 categories. Cluster (box) of 25 lb is taken when 

 sampling small fish, or any time small rockfish are 

 landed such that there would be more than 20 fish 

 in the 50-lb cluster. In all other cases 50-lb standard 

 cluster size is selected. A cluster is next separated 

 by number of each species and its weight, which are 

 recorded along with sex, total length, and otolith 

 of each member of a species in the cluster. 



The instructions are to "sample all market 



categories (sorts) from a boat, and from as many 

 boats as possible and select: 



"(i) 1 cluster per 20,000 lb of widow rockfish 

 landed by each boat, up to 4 clusters, 



"(ii) 1 cluster for all other species, if less than 

 5,000 lb landed, and 



"(iii) 2 clusters for all species if more than 5,000 

 lb are landed. 



"The second cluster should not be taken if this 

 precludes sampling another boat." 



Estimation with Poststratification of 

 Sample Trips by Categories 



Consider the problem of estimation of total catch 

 of a given species for a port-month stratum. Equa- 

 tions for estimation of other characteristics for 

 fisheries with mixed species are straightforward and 

 can be obtained by substituting the value of the 

 characteristic for the catch of the species. Totals 

 across strata are formed by simple additon. 



Notation 



For a given species, let 



N = total number of trips, 

 n = number of randomly sampled trips, 

 W = total weight of fish caught from all trips, 

 W { = weight of fish caught on trip i, 

 Wy = weight of fish for sort j caught in trip 



i, 



my = number of clusters sampled from sort j on 



trip i, 

 m i = number of clusters sampled on trip i, 

 m = number of clusters sampled over n trips, 



Wi = Z. Wy where L { is the number of sorts 



3 in trip i, 



y v - k = number of fish of the species in cluster k 



from sort j of trip i, 

 Yy- = total number of the species caught from 

 sort j of trip i, 



Y = total number of species caught from all 



trips, 



Y = mean catch per cluster for the species, 



y v - = 2. yyklrriy = unbiased estimate of Y v -, 

 w ijk = weight of the A;th cluster from the jt\\ sort 



of the ith trip, 



Wi 



Mi = -5=-^ where w,- = 2. 2. Wi^lZ. m^ = 

 w { j k l3k j y 



410 



