precision of the seasonal cliinook catch for each 

 of tlie fisheries. Sucli estimates are not publislied 

 except in a few instances (e.g., California troll and 

 Oregon ocean sport fisheries). Lacking this in- 

 formation, we have assumed that the seasonal 

 cliinook catches in each fishery (excei)t for Alaska 

 troll and the ocean gill net and purse seine tish- 

 cries) are estimated within 15 percent of the true 

 value; i.e., the variance of the catch, V(C), is such 

 that one-half the width of the 95 percent confi- 

 dence interval, 2[V(C)]'''-, is 15 percent of the 

 estimated catch, C. We then have: 



V(C) = (0.5X0.15XC)- 



= 0.0056 C=. 



Where availal)le (e.g.. California troll), estimates 



of the pi-ecision of the catches are well within 



the assumed value. 



In the Alaska troll fishery and the ocean net 

 fisheries, catches are reported in numbers of fish. 

 The variance of the catch and, therefore, the 

 second term in equation (4) is zei'o for each of 

 these fisheries. 



Substituting these values of V(C) in equation 

 (4) and summing over the strata (i.e., fisheries 

 and years) gives 357,000; 26,000; 13,000; 1,100; 

 and 2,300 as appi-oximate variances for the esti- 

 mated numbers of Ad-im, Ad-LV-RM, LV-RM, 

 and RV-RM marks, respectively, in the total 

 catch. The resulting estimates of the 95 percent 

 confidence intervals for the numbers of marked 

 fisli in the catch are : Ad-RM 21,616±5.6 percent; 

 Ad-LV-RM 4,285 ±7.5 percent; Ad-RV-RM 

 2,141 ±10.6 percent: LV-RM 174 ±37.9 percent; 

 RV-RM 266 ±36.1 percent; where, for example, 

 the 5.6 percent refers to the estimated number of 

 Ad-RM marks (21,616) in the catch. Although 

 these confidence interval estimates are approxi- 

 mate, they illustrate the general level of precision 

 of the estimated total number of marks in the 

 catch. 



ESTIMATED CATCH OF 1961-BROOD 

 HATCHERY FISH 



In estimating the total number of marked hatch- 

 ery fish in the catch on the basis of an obsen^ed 

 number of mark recoveries and a sampling ratio, 

 as was done in the preceding section, we made 

 certain assumptions. These are assumptions 1, 2, 

 and 3, which dealt with the permanence of fin 

 marks, origin of observed fish marked with the 



hatchery marks, and accuracy of age assignments. 

 Data presented in tlie preceding section supitorted 

 these assumptions. 



Additional assumptions are inherent in the i)ro- 

 cedure for estimating the catch of unmarked and, 

 hence, total catch of luxtchery fish. These are as- 

 sumptions 4, 5, and 6, which were listed previously. 



From the distribution of nuirk reco\eries it 

 appears that cliinook salmon from Kalama and 

 Spring Creek Hatcheries had different ocean dis- 

 tributions. It is not likely, tlien, that the first part 

 of assumption 6 (same ocean distribution of fish 

 from each hatchery) is satisfietl. This poses no 

 problem, however, pro\ided the second jiart of 

 assumption 6 (same proportion of fish marked at 

 each hatchery) is satisfied. In tliis regard, it ap- 

 pears from api)endix table 1 that with the possible 

 exception of Klickitat Hatchery, proportions of 

 Ad-RM marked fish in the releases were much the 

 same at all of the hatcheries. Accordingly, we 

 consider that assumption 6 is reasonably satisfied. 



Information to test the assumption (assumption 

 5) concerning the distributions of marked and 

 unmarked hatchery fish is limited. The distribution 

 of marked fish is available from the present study ; 

 howe\er, concurrent data for unmarked fish are 

 lacking. The only information available on this 

 subject is from a review by Cleaver (1967) of past 

 tagging experiments in the ocean. Of 290 tagged 

 fish recovered in the Columbia River from these 

 experiments (during 1925-52 in coastal areas from 

 northern Oregon to Cape Fairweather, Alaska), 

 only 13 were recovered in hatcheries. Twelve of the 

 13 recoveries, however, had been tagged in areas 

 off the west coast of Vancouver Island, Canada — 

 an area of high concentration of marked hatchery 

 fish as shown by recoveries of the marked 1961 

 brood. Although this result is consistent with as- 

 sumption 5, it does not, of course, conclusively 

 support it. The assumption must, therefore, remain 

 an assumption. 



The validity of assumption 4 (equality of ma- 

 turity schedules and survival rates between 

 marked (Ad-RM) and unmarked hatchery fish) 

 can be examined by comparing the ratios of marked 

 to unmarked fish at times of release and return. 

 The marked to unmarked ratios by type of mark 

 and age of fish for the 1961-brood hatchery returns 

 are given in table 14. Ratios for Elokomin (LV- 

 RM) and Oxbow (RV-RM) liatcherias are not 



380 



U.S. FISH AXD WILDLIFE SERVICE 



