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Fishery Bulletin 105(1) 



with constant mean and variance, when none of the 

 components of the sample autocorrelation and partial 

 autocorrelation functions differed significantly (P=0.01) 

 from zero (Wei, 1990). 



Multivariate time series models in the form of linear 

 transfer function (LTF) models (Liu and Hudak, 1992) 

 were developed to describe the relationship between 

 MSWl^ ^, I and our index of survival rate for each fresh- 

 water age group and river system. All the univariate 

 time series of survival rate indices contained signifi- 

 cant positive first-order autoregressive parameters (see 

 Table 2). Therefore, we included the first order autore- 

 gressive parameter in the LTF models. The models were 

 defined as 



f,.a.,='-,..+^,.aMSWl,,,+ 



(l-0i.,.oB) 



-N. 



(2) 



where t, i, a are described in Equation 1; 



MSWl = the early marine growth index for sockeye 

 salmon during their first year at sea; 

 the autoregressive lag 1 parameter; 

 the symbol for the backshift operator (i.e.. 



B 



c, g and A, ^ = parameters within the model; and 



N^^i = a sequence of random errors that are 

 independently and identically distributed 

 with a normal distribution. 



Parameters within the univariate and LTF models were 

 deemed significant when their lvalue was greater than 

 2.0(P<0.05). 



Autocorrelation analysis was used to examine wheth- 

 er the model residuals were white noise. Univariate and 

 LTF models were compared by using Schwartz's Bayes- 

 ian criterion (SBC; Wei, 1990) to determine if the inclu- 

 sion of MSWl in Equation 2 improved the model fit. 



Analyses of data from juveniles collected by trawling 



Next, we developed an index of relative survival rate 

 of adult Bristol Bay sockeye salmon for 2000-02, and 

 indices of abundance and marine-stage survival rate 

 of juvenile sockeye salmon collected during 2000-02 to 

 compare with mean lengths of juvenile sockeye salmon 

 collected during those years. Relative survival was 

 defined as the number of returning adult sockeye salmon 

 from brood-year escapements that contributed to the 



