density-dependent juvenile survival, downstream passage, adult recruit- 

 ment, and harvest. The expected system response in each component can 

 be reduced to a linear combination of certain model parameters (or a single 

 parameter in some cases). Thus, users can select a small subset of param- 

 eters to serve as surrogates for all parameters when conducting a sensitiv- 

 ity analysis. 



In a preliminary sensitivity analysis, we examined the sensitivity of the 

 natural population to parameter changes by systematically varying logitscl 

 and adtrecv to reflect different levels of early juvenile and postsmolt sur- 

 vival, varying mpass to reflect changes in downstream migrant survival 

 (passage survival), and varying the fraction of recruits within a given age 

 class that escapes to the subbasin (as opposed to being harvested). These 

 four factors were varied in combinations to create two-dimensional matri- 

 ces of parameter sets (either 11 x 11 or 10 x 10, depending on the vari- 

 ables). Within each matrix, logitscl, mpass, and adtrecv varied by a factor 

 of three, while the proportion of nonharvested fish varied by a factor of ten 

 (0.1 to 1). Five hundred games were simulated for each parameter set. 

 Number of spawners in years 15 and 100 were compared across all param- 

 eter combinations. The number of spawners in year 15 proved to be a good 

 indicator of short-term stock dynamics, while the 100-year results were 

 better indicators of long-term effects. 



Results of the 



Sensitivity 



Analysis 



Some comments on the sensitivity of the SLCM to changes in parameters 

 are appropriate, though we refrain from a detailed discussion. First, the 

 distribution in number of spawners is very sensitive to changes in param- 

 eter values of the magnitude that we examined. Most sensitive is the up- 

 per tail of the distribution, which changes rapidly following parameter 

 changes. 



Second, short-term model results are more sensitive to changes in adult 

 survival than to changes in juvenile survival. The mean number of spawn- 

 ers in year 15 was greater following increases in adult survival than after 

 equivalent increases in juvenile survival. This is understandable because 

 of the time lag required before changes in juvenile survival manifest them- 

 selves in changes in spawning escapement. Given a longer time period 

 (such as 100 years), equivalent changes in juvenile survival and adult sur- 

 vival produced equivalent effects. However, the management implications 

 of the apparent short-term effectiveness of increasing adult survival should 

 not be ignored. 



Among the variables that we examined, the model first appeared to be 

 most sensitive to changes in passage survival. On further inspection, the 

 apparent sensitivity to passage survival could be explained by the rela- 

 tively low variance used for passage survival compared to the variance 

 used for juvenile and postsmolt survival. The SLCM, like other stochastic 

 models of this type, is most sensitive to the survival factor with the lowest 

 variance. The interplay between survival and variance in survival can be 

 demonstrated by plotting the changes in the mean number of spawners as 

 the coefficient of variation (CV) in egg-to-adult survival increases (fig. 11). 

 While the decline in the mean number of spawners is significant, the in- 

 crease in the CV of state variables such as the number of spawners is more 

 dramatic. We observed that the relationship between the CV of spawners 

 and the CV of survival had a slope that is very close to (but slightly greater 

 than) one. 



19 



