22 



Likelihood of Extinction 



The probability that Snake River fall chlnook aalmon would become 

 extinct was estimated to be 10.8% by Waples et al. (1991) uaing an 

 exponential diffusion model (Dennis et al. 1991). This estimate was 

 made using natural escapements from 1980 to 1990 above Lower Granite Dam 

 and employed a five-year averaging routine. Since that report, no one 

 has been able to duplicate those results (see Cramer and Neeley 1993); 

 and, many of the assumptions behind the analysis and the analytical 

 technique itself may be suspect. In addition, there are four additional 

 years of recent escapements which should help better aBsese the trend in 

 escapements and project future stoc)( abundances. 



We developed a more robust method of evaluating trends in eecapements 

 and estimating the probability of extinction of Snake River fall chinook 

 within 100 years (by 2089). This method (termed the bootstrap method) 

 employs a bootstrapping technique which randomly selects a ratio of 

 observed escapement by age that has resulted from a given escapement 3, 

 4, and 5 years before. This method makes no assumption on underlying 

 statistical models, incorporates the age structure of the population 

 into the analysis, and uses a nonparametric error structure. Four time 

 series of data were compared using the bootstrap method: 



(1) escapements from 1980-1990; 



(2) escapements from 1975-1990; 



(3) eecapements from 1980-1994; and, 



(4) escapements from 197S-1994. 



The two time series ending in 1990 represent the information available 

 at the time Snake River fall chinook were first listed. The two time 

 series ending in 1994 represent the information available today and 

 differences in the likelihood of extinction between these ending dates 

 reflect the changes in extinction probability or the change in risk that 

 the listed stock faces. The two time series starting in 1980 reflect 

 the time period when the stock was affected by all Snake River dams 

 during their life cycle; whereas, the time series starting in 1975 

 reflect a changing period in terms of affects of dams on the listed 

 stock. 



A fifth evaluation was conducted using the bootstrap method. The fifth 

 comparison weighted the ratios from parent escapements to 1991-1994 age 

 specific escapements so that these ratios were twice as likely to be 

 randomly chosen as other earlier ratios. This took into account that 

 changes initiated to protect Snake River fall chinook salmon after 1990 

 would continue and thus ratios calculated using escapements in these 

 years would be more likely to occur than ratios in previous years. 



For each simulation in the bootstrap method, the age composition of 

 1975-1982 and 1994 escapements were randomly selected from the estimated 

 age compositions of the 1983-1993 escapements. The ratios of: (1) 

 escapement in year i to the age 3 escapement in year i*3 for the years 

 1975-1991; (2) escapement in year i to the age 4 escapement in year 1*4 

 for the years 1975-1990; and, (3) escapement in year i to the age 5 

 escapement in year l-*-5 for the years 1975-1989 were calculated to 

 provide the set of ratios to randomly choose from to produce age 

 specific escapements from the parent escapements. Thus production, by 

 age, from a give escapement was randomly selected from historical 

 production ratios. 



The escapements use^ in the bootstrap method are presented in Table 7 

 and are taken from "Dygert (1994) and Matylewich (personal communication) 

 The age compositions of the escapements were taken from Roler (1994). 

 The bootstrap method, used 1,000 simulations. Probabilities of achieving 

 specific escapements were estimated as the proportion of times that the 

 1,000 simulations reached these escapements in the year 2089. 



The bootstrap selection process can best be described by illustrating 

 the process with an example (Tables 8 and 9). Table 8 demonstrates how 



