The number of fish in the catch, the number 

 sampled and the number of marks recovered from 

 zones 1-5 and zone 6, were combined. 



CALCULATIONS 



Because the marks used to distinguish the 

 groups of hatchery fish have a negative effect on 

 survival, two different steps were employed to cal- 

 culate the hatchery fish contribution. The deter- 

 mination of the level of contribution required an 

 estimation of the number of hatchery fish in the 

 catch for each year sampled. This was calculated 

 from the estimated number of marked fish plus the 

 estimated number of hatchery unmarked after a 

 correction for differential mark mortality. Poten- 

 tial catch is that which would be expected if mark- 

 ing did not cause postrelease mortalities. 



Differential Mark Mortality 

 (Survival Factor) 



We suspected that there would be adverse ef- 

 fects on the survival of the fish because of the 

 excised fin and maxillary bone. Foerster (1968) 

 reported that marked sockeye salmon at Cultus 

 Lake had an estimated return of only 38'/f of the 

 unmarked return. 



To obtain a mark survival factor, a modification 

 was made to the procedure for marking the 1961- 

 brood fish. In addition to the group that received 

 an Ad-LM, a second gi-oup received only a chemi- 

 cal (tetracycline) mark, while a third had both 

 marks. In sampling returning adults, a compari- 

 son of the three groups showed that only 40^ of 

 Ad-LM fish expected, returned (Weber and Wahle 

 1969). Because we believe that tetracycline had no 

 effect on survival, we considered that the differ- 

 ence between returns was caused by mortality due 

 to marking by excision. 



Marks in Catch 



To calculate the number of marks in the catch 

 for a certain year, the number of ri marks in the 

 sample was divided by the sampling ratio: 



n marks (catch) 



n marks (sample) 



I) fish (sample)//! fish Icatch) 



This assumed a random sample of the catch. The 

 mark survival factor was not considered in this 

 equation. 



236 



FISHERY BULLETIN: VOL, 77. NO. 1 



Hatcher)' Contribution to the Fishery 



To determine the percent of sockeye caught in a 

 specific year that originated at Leavenworth 

 Hatchery, the number of (n) unmarked hatchery 

 fish in the catch was estimated by using the 

 number of(n) marked fish in the catch and divid- 

 ing by the sampling ratio and the marked 

 unmarked ratio at release, corrected by the mark 

 survival factor. The correction was necessary be- 

 cause this ratio changes from the time of release to 

 time of catch due to the effects of marking: 



n unmarked hatchery catch = 



ft marks icatch) 

 n fish (sample) n marked release 

 „ fish (catch. "" Tiinrmarked releas^ "" «""'^^' f^'^'"'- 



Summing the marked and unmarked hatchery 

 fish for a catch year and dividing by the total catch 

 gave the estimated percent produced by the 

 Leavenworth Hatchery. For 1964-67, contribu- 

 tions averaged 13.&/t of the total catch (Table 3). 

 The 21.6'7f figure for 1966 may not be representa- 

 tive as the sample size that year was small. 



T.^BLE 3. — Estimated numbers and percent of hatchery sockeye 

 in Columbia River commercial catch. 



'Not applicable as no 1964 brood hatchery frsh were marlted 



Potential Hatchery Catch 



A potential hatchery catch figure is a theoretical 

 number that represents what could have been 

 caught in a given fishery assuming the same effort 

 and no marking progi-am and was required to cal- 

 culate benefit/cost ratios. It allows for the large 

 number of fish failing to survive because of the 

 mark. Potential hatchery catch (Table 4) was cal- 

 culated by dividing the number of marks in the 

 catch by the mark survival factor and adding the 



