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Fishery Bulletin 94(1). 1996 



to the rule of combining smolt ages were those popu- 

 lations of coho and sockeye salmon for which the 

 number of returning adults could be assigned an age 

 at smolting based on scale patterns. In those cases, 

 each age class of smolts was treated as a separate 

 "brood year" and separate smolt-adult survivals cal- 

 culated for each smolt age class. 



Smolt-adult survival is log normally distributed 

 (Peterman, 1981), so the best estimate of the central 

 tendency of smolt-adult survival for a system is the 

 geometric mean survival or the arithmetic mean of 

 the log -transformed survivals for each brood year 

 for a particular system. Only log,(s) was used to esti- 

 mate the parameters of Equation 6 because only in a 

 few cases was each brood year's survival accompa- 

 nied by a mean smolt weight or a mean adult weight, 

 or both. In almost all cases, all that was available 

 from the literature was a mean smolt weight and a 

 mean adult weight for each system. The exceptions 

 were those systems for which mean smolt weights 

 and mean smolt-adult survivals were available for 

 each of several age classes of smolts (i.e. sockeye 

 salmon from rivers entering Bristol Bay Alaska; Yuen 

 et al., 1981; Woolington et al., 1991). 



Weight In the absence of direct reports, mean smolt 

 weights of pink and chum salmon were assumed to 

 be the midpoints of the ranges of emergent fry 

 weights reported by Beachum and Murray ( 1990 ) for 

 eggs incubated at a constant 8°C (0.25 g for pink and 

 0.35 g for chum). For studies that did not report mean 

 smolt weight for coho and sockeye salmon, and for 

 which there were no accompanying reports that in- 

 cluded smolt weights, mean smolt weight was esti- 

 mated from mean smolt length by using weight- 

 length equations reported by Chapman (1965) and 

 Koenings and Burkett ( 1987). 



Mean adult weight of coho salmon from Carnation 

 Creek was calculated from mean length of returning 

 adults by using the weight-length relationship re- 

 ported by Holtby and Healey (1986). Mean adult 

 weight of steelhead trout from the Keogh River was 

 calculated from mean length of returning spawners 

 with the weight-length regression reported by Hooton 

 et al. (1987). Mean adult weights for other systems 

 were taken from records of commercial fisheries be- 

 cause there was no published information on their 

 mean size at re-entry to freshwater (Gunsolus, 1978; 

 Ricker, 1981; Yuen et al., 1981; Kyle 1 ). I converted 

 mean lengths (L, mm) of Bristol Bay sockeye to mean 

 weights (W, g) using a functional regression of log* W) 



1 Kyle. G. 1994. Alaska Dep. of Fish and Game. 34828 

 Kaliforsky Beach Road, Soldatna, AK 99669-3150. Personal 

 commun. 



on log t ,(L) calculated from mean weights and lengths 

 for separate age groups of Bristol Bay sockeye for 

 the years 1963-77: W = 1.713 x 10' 5 L 300 (n=61, 

 r 2 =0.94, P<0.001 ). Mean adult weight for each nurs- 

 ery system was the mean weight for the ocean sta- 

 tistical area adjacent to the stream for which smolt- 

 adult survivals were available. This procedure as- 

 sumes that the majority of the catch from a popula- 

 tion is taken by marine salmon fisheries near the 

 mouth of the population's natal stream. 



In most systems in British Columbia, mean adult 

 weight was calculated from the years for which 

 smolt-adult survivals were reported. This is impor- 

 tant because mean weight of pink, chum, coho, and 

 sockeye salmon in British Columbia has decreased 

 over the last 30 years (Ricker, 1981). However, this 

 was not possible for all systems, particularly those 

 with smolt-adult survivals reported after 1981. In 

 those cases, mean adult weight was taken from the 

 latest catch data available. Thus, the accuracy and 

 reliability of mean adult weights is variable, being 

 relatively high for most systems in British Colum- 

 bia but lower for most systems in Alaska. The excep- 

 tions are the sockeye rivers of Bristol Bay where a 

 20-yr time series of adult sockeye weights was re- 

 ported by Yuen et al. ( 1981). 



Mean adult weight for nursery systems with more 

 than one age group of smolts was assumed to be the 

 same for all smolt ages. This assumption was neces- 

 sary because adult weights were rarely reported for 

 separate smolt ages. 



Fitting the model 



Equation 6 was fitted with nonlinear regression 

 (NLR)by using the Levenberg-Marquardt algorithm 

 contained in the NLR procedure of the computer pro- 

 gram SPSS (SPSS Inc., 1993). The mean log e (s) for 

 each system was first regressed on mean W and W () 

 for sockeye salmon and then for all species combined. 

 Mean log p (s) was weighted by sample size under the 

 assumption that the accuracy of mean log ( ,(s) is di- 

 rectly proportional to the number of brood years used 

 to calculate it. The coefficients of determination (r 2 ) 

 of the regression models were adjusted for the num- 

 ber of degrees of freedom in the model. Standard er- 

 rors of regression parameters were based on asymp- 

 totic or large-sample approximations. It was not pos- 

 sible to test the statistical significance of a nonlin- 

 ear regression using the usual F-test applied to lin- 

 ear regressions, because the residual mean square 

 of a nonlinear regression is not an unbiased estimate 

 of the error variance (SPSS Inc., 1993). The signifi- 

 cance level, P, for linear correlations was set at 5%, 

 i.e. P = 0.05. 



