McGurk: Allometry of marine mortality of Pacific salmon 



83 



Estimation ofx and c from/3 and a 



An estimate of x was obtained by subtracting an es- 

 timate of fi from the weight exponent of growth rate, 

 b, i.e. x = b - p. Estimates of ji were obtained by fit- 

 ting regression Equation 6 to survival and weight 

 data. The appropriate value of 6 was obtained from 

 a review of the scientific literature on salmonid 

 growth experiments (see introductory section). Esti- 

 mates of c could not be obtained directly. Instead, c 

 was expressed as a fraction of the initial growth rate, 

 i.e. c = aa. Estimates of a were obtained from re- 

 gression Equation 6. 



Results 



I found 20 studies that reported 52 mean smolt— adult 

 survivals for five species of Pacific salmon (Table 1). 

 The means were calculated from 432 brood years 

 released from 38 nursery systems ranging over more 

 than 15° of latitude from the Oregon coast (44.0"N) 

 to southcentral Alaska (61.5"N). Over 60% of the 

 mean survivals were reported for sockeye salmon. 



Sockeye salmon 



The regression of log,(s) on W and W Q for sockeye 

 salmon explained 33% of the variance in mean log^s), 

 with parameter values (±1SD) of a = 0.226 ±1.171 

 and P = 0.120 ±0.990 (Fig. 1 ). The estimate of a indi- 

 cated that c had a value that was only 22.6% of the 

 value of a. The estimate of P indicated that x has a 

 value of 0.29, if 6 for sockeye salmon is assumed to 

 be is closer to 0.4 1 than to 0.37 ( Brett and Shelboume, 

 1975). 



There were no significant correlations between 

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

 ery system, or the predominant smolt age, indicat- 

 ing that body weight was the single most important 

 variable affecting smolt-adult survival. The sensi- 

 tivity of a and p to possible underestimation or over- 

 estimation of adult sockeye weight was examined by 

 fitting Equation 6 after altering W by -25 to +25% 

 at 5% intervals: a decreased by 8% for a 25% de- 

 crease in W and increased by 6% for a 25% increase 

 in W, indicating that a was relatively insensitive to 

 bias in estimation of W (Table 2); p increased 26% 

 for a 25% decrease in W and decreased 17% for a 

 25% increase in W, indicating that p was about three 

 times more sensitive to bias in estimation of W than 

 was a. The adult weights of sockeye salmon shown 

 in Table 1 are more likely to be underestimates of 

 the true weight at return than overestimates because 

 they were calculated from mean weights of commer- 



1.0 



W ' -w 



1.2 14 



0.120 



Figure 1 



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

 transformed smolt-adult survival, s, on smolt weight, 

 W Q ig), and adult weight at return, W (g), for sockeye 

 salmon iOncorhynehus nerka). Values (±1 SD) of the 

 regression parameters a and p are shown, a is the ra- 

 tio of the coefficient of instantaneous natural mortal- 

 ity rate, c, to the coefficient of instantaneous growth 

 rate, a. /3 is the difference between the weight expo- 

 nent of growth rate, b, and the weight exponent of natu- 

 ral mortality rate, x. Data from Table 1. 



cial catches rather than mean weights of spawners 

 in their natal stream. The last few months of growth 

 may not be included in adult weights from commer- 

 cial catches. Because underestimation of W tends to 

 inflate p, the true value of P for sockeye salmon is 

 lower than 0.120 and, therefore, the true value ofx 

 for sockeye salmon is greater than 0.29. 



Combined species 



A regression of mean log (s) on W and W Q for the five 

 species of salmon combined explained 68% of the 

 variance in mean log ( ,(s) with parameter values 

 (±1SD) of a = 0.528 ±6.490 and p = -0.053 ±0.221 

 (Fig. 2). The estimate of a indicated that c had a 

 value that was 52.8% of the average value of a. The 

 estimate of p indicated that x had a value of 0.38 to 

 0.42 for an average b of 0.33 or 0.37, respectively. The 

 doubling of the r 1 statistic over that measured for the 

 sockeye regression was accompanied by s substantial 

 decrease in the variance of a and p. The coefficient of 

 variance of a, CV^ (=SD a -100/a), decreased from 518% 

 for the sockeye regression to 93% for the combined re- 

 gression. CV\j decreased from 825% for the sockeye re- 

 gression to 417% for the combined regression. 



