BAILEY ET AL.: PRODUCTION OF FRY AND ADULTS AT AUKE CREEK 



from the creek. The daily numbers of marked fry 

 released from the hatchery and the creek were 

 roughly proportional to the respective migrations 

 of fry from these two sources. There was a slight 

 bias toward marking too few fry during the first 

 half of the migration, but the bias was in the same 

 direction and magnitude on both types of fry. 



Less than 1% of the creek fry died in the fyke net 

 and floating live-box, indicating slightly greater 

 physical abuse for marked creek fry than marked 

 hatchery fry. 



Recovery of Marked Adults 



Returning 1972 brood adults were counted at the 

 weir in Auke Creek in the summer of 1974; some 

 adult salmon were anesthetized and measured. 

 Mideye-to-tail-fork lengths were measured to the 

 nearest millimeter and weights to the nearest 

 0.01 kg. 



Analysis of Survival 



Survival probabilities from egg to fry and fry to 

 returning adult are estimated from estimates of 

 initial number of eggs, fry produced, and return- 

 ing adults. Ratios of these survival estimates are 

 used to compare survival of hatchery and creek 

 salmon. Variances of survival and estimates of 

 ratios of these survival estimates were approx- 

 imated by the delta method (Deming 1943; Paulik 

 and Robson 1969). Finite population correction 

 factors were ignored in variance calculations; 

 changes in variance estimates would have been 

 insignificant. 



Estimation of survival from marking requires 

 special argument. The expected total unmarked 

 returns from hatchery and creek fry combined is 



T = Us + U's' 



where U and U' are initial numbers of unmarked 

 fry from the creek and hatchery respectively, and s 

 and s' are the probabilities of survival of the two 

 unmarked groups at sea. Marking increases mor- 

 tality. If the probability of survival from marking 

 is T and identical for both groups, the probabilities 

 of survival from both causes are st and s't for creek 

 and hatchery fry respectively. The expected total 

 return of the unmarked fry had they been marked, 

 r, is 



r = UsT + U's't. 



The ratio of T to T is t. Therefore, we estimate 

 survival from marking from estimates of Tand T" 

 as 



f = f'/f. 



The expectation T is estimated by the total un- 

 marked recoveries to the weir. The expectation T 

 is estimated from appropriate combinations of 

 estimates of numbers of unmarked creek and 

 hatchery fry and estimates of marine survival of 

 marked fry of both groups. 



Total variation among incubators in estimated 

 survival from egg to fry is divided into three 

 sources: 1) Underlying variation due to hetero- 

 geneity of genetic composition of pink salmon and 

 environmental conditions among incubators, 2) 

 binomial variation within incubators, and 3) sam- 

 pling error in estimation of numbers of eggs and 

 fry. We imagine an unobserved universe of sur- 

 vival probabilities s with mean s has been sampled 

 randomly by our study; four members were drawn, 

 each applying to one of our incubators. Actual 

 survival within an incubator varies from its as- 

 sociated probability of survival due to binomial 

 variation; instead of a fraction s surviving, the 

 actual fraction is s. This actual rate was not 

 observed; rather, we estimated s by s, the ratio of 

 estimated fry to estimated eggs. 



Total variance of estimated survival among 

 incubators, a^, is defined by 



af=f(i-s)2 



where E denotes the expectation operation over 

 the three sources of variation. 

 This expression may be rewritten as 



o2 = Eli's -s) + (s-s) + is- s)f. 



After completing the square and evaluating the 

 expectations of the terms, we find 



of = a? + ai + a§ 



where al = E (s - sf, the variance of underlying 

 survival probabilities among incubators; <^2 = -^ 

 (s - sf, the average binomial variance; <J3=E 

 (s - sf, the average variance due to errors in es- 

 timates of fry and eggs ; £" denotes the expectation 

 operation over the first source of variation; and^ 

 denotes the expectaton operation over the first 

 two sources of variation. 



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