84 



Fishery Bulletin 94(1), 1996 



-0.5 



n < 



w"°"-w ./"*' 



-0.2 



Figure 2 



Nonlinear regression (Eq. 6 in the text) of mean log ( ,-trans- 

 formed smolt-adult survival, s, on smolt weight, W a (g), 

 and adult weight at return, W(gl, for five species of Pacific 

 salmon: pink (O. gorbuscha), chum (O. keta), coho (O. 

 kisutch ), steelhead (O. mykiss), and sockeye (O. nerka ). Val- 

 ues (±1 SD) of the regression parameters a and (5 are shown. 

 a is the ratio of the coefficient of instantaneous natural 

 mortality rate, c, to the coefficient of instantaneous growth 

 rate, a. p is the difference between the weight exponent of 

 growth rate, 6, and the weight exponent of natural mor- 

 tality rate, .v. Data from Table 1. 



There were no significant correlations between 

 residual mean log (s) and W , Wand latitude of nurs- 

 ery system. Residual mean log (s) did not vary sig- 

 nificantly among species (ANOVA: F 447 =1.995, 

 P=0.111), indicating that body weight was the most 

 important variable affecting mean smolt-adult sur- 

 vival. A sensitivity analysis showed that a changed 

 by 1% or less for a ±25% change in W, indicating that 

 its value was essentially independent of bias in esti- 

 mation of W (Table 2). J3 increased by 21% for a 25% 

 decrease in W and decreased by 15% for a 25% in- 

 crease in W. However, the maximum change in the 

 absolute numerical value of ft caused by ±25% 

 changes in W was only 0.008, indicating that the 

 near-zero value of /3 was essentially independent of 

 bias in estimation of W. 



Discussion 



Parameters a and /J 



The estimates of a and fi derived in this study are 

 consistent with the original hypotheses. The small, 

 near-zero value of fi estimated for sockeye salmon 

 alone and for five species of Oncorhynchus combined 



supports the hypothesis that the weight exponents 

 of growth and mortality for Oncorhynchus species 

 are virtually identical. There is no consensus on the 

 exact value of the weight exponent of growth rate of 

 Pacific salmon. However, the average of all reported 

 values of salmonid b is 0.37 ( Iwama and Tautz, 1981 ), 

 which is identical to the weight-exponent of natural 

 mortality for single species that was proposed by 

 Dickie et al. (1987). Thus, the cumulative evidence 

 supports the hypothesis that, on average, marine M 

 of Pacific salmon scales with W~° 37 . Although the 

 average value of x is close to 0.37, it may also vary 

 among populations and species, and among year 

 classes within populations and species. For example, 

 this study found that x varied from a low of 0.29 for 

 sockeye salmon to a high of 0.42 for the data from 

 five species. 



The second important feature of the regression 

 parameters is that a is significantly lower than 1.0 

 which supports the hypothesis that initial mortality 

 rate, c, is a fraction of initial growth rate a. The com- 

 bined regression indicates that c has a value equal to 

 52.8% of the value of a at any body weight. Therefore, 

 the best estimate of M for all species of Pacific salmon 

 combined can be predicted as: M - 0.528a W~°- 37 . Esti- 

 mates of M can be obtained if one has an indepen- 

 dent estimate of the parameter a, perhaps through 

 scale analysis. Alternatively, if one assumes that a = 

 G/W~° - 37 , then M = 0.528G. In other words, average 

 marine M for a short time period can be estimated if 

 one has an independent estimate of average G over 

 the same short period. 



Third, the absence of significant differences in re- 

 sidual mean log t ,(s) among species suggests that a 

 single survival-weight relationship may be applicable 

 to all five species of Oncorhynchus . This finding sup- 

 ports the basic assumption of this paper — that spe- 

 cies within the genus Oncorhynchus share similar 

 allometries of growth and mortality but differ in 

 smolt and adult body sizes. However, it is clearly in- 

 appropriate to assume that the survival-weight and 

 mortality-weight relationships developed in this 

 study can be applied without qualification to every 

 salmon population or to every brood year within each 

 population. Accurate brood-year-specific prediction 

 of salmonid survival will depend on information col- 

 lected from that brood year. 



Sources of error 



This paper presents preliminary numerical estimates 

 of a and ji for Pacific salmon. Improved estimates will 

 undoubtedly be calculated in the future as more infor- 

 mation on smolt-adult survival and smolt and adult 

 weights become available in the primary literature. 



