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recenc levels will significantly reduce the probability of 

 extinction and will provide an adequate short-term buffer against 

 inbreeding and loss of genetic variability due to low population 

 size. 



Comparative Values for Evaluating Benefit Ratios 



As was indicated earlier, the life cycle models will be used to 

 provide measures of relative change rather than absolute 

 abundance. The relative change will be expressed in terms of a 

 benefit ratio calculated using average escapements from model 

 runs depicting proposed and base period conditions . In order to 

 evaluate the benefit ratios, it is necessary to develop 

 independent estimates of the relative change in population 

 parameters that can be used as comparative values. This was done 

 using projections from the Dennis model. The analysis is 

 described here in general and in more detail in a memorandum 

 dated December 23, 1992 (Wainwright 1992). 



NMFS has used the Dennis model in conjunction with other 

 information in previous analyses to evaluate the degree of risk 

 faced by a population. The Dennis model is a simple exponential 

 population model that incorporates measures of random variation. 

 The model uses observations of abundance from past years (the 

 calibration period) to project population abundance into the 

 future. The future projection of the current trend line 

 represents the base period condition assuming that there will be 

 no change in actions that affect the populations. 



The stability criterion defines a target for the future abundance 

 of the chinook salmon populations, i.e., average abundance in 

 2004-2008 should be equal to or greater than that ooserved in 

 1986-1990. Given the base period trend as defined by the Dennis 

 model and the future target for the populations, it is possible 

 to estimate the changes in model parameters necessary to meet the 

 target population levels. The model therefore provides an 

 alternative trajectory for the populations comparable to the 

 proposed action scenarios considered in the life cycle model 

 analysis. Because the Dennis model incorporates measures of 

 variability observed during the calibration period, it is also 

 possible to estimate the degree of confidence with respect to 

 meeting the specified objective. Greater confidence is obviously 

 associated with higher benefit ratios. 



One of the features of the Dennis model analysis is the 

 assumption that the population would continue to decline for a 

 few years, before increasing to pre- 1990 levels because of the 

 time lag between the implementation of actions and the full 

 accrual of benefits to returning adults (Figure 1). Results of 

 the analysis can be summarized in terms of three parameters 

 including 1) the benefit ratio that shows the relative change in 



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