Juvenile passage is expressed in the SLCM as a binomial-beta process. 

 The number of smolts surviving downstream migration is a binomial ran- 

 dom variate, where the survival probability (p) is drawn from a beta distri- 

 bution. The expectation and variance of p can be estimated using auxiliary 

 passage models that address this stage of the life cycle in more detail. In 

 our analyses of Columbia Basin stocks, we used CRiSP, a passage model 

 developed at the University of Washington, to estimate survival from 

 tributary rearing areas to the Columbia River Estuary. (Information on 

 CRiSP can be obtained from James Anderson, Center for Quantitative Sci- 

 ences, University of Washington, Seattle, WA.) The parameters of the beta 

 distribution were estimated from a set of survival estimates based on ran- 

 domly generated flow conditions. In earlier analyses, we used a fourth- 

 order autoregressive model with a random normal error term that was fit 

 to CRiSP output. Results from both approaches were similar. Other pas- 

 sage models can easily be substituted for CRiSP. 



Ocean and The advent of the coded wire tag (CWT) has permitted large-scale mark 



In-river Allocation anc * recapture experiments on Pacific salmon from the Columbia River Ba- 

 f Adults s * n ' ^ ^ e m illi° ns °f tagged fish released each year, however, only a 



small fraction of the tags are recovered. These recoveries provide a large 

 bank of information on the age-specific relative distribution of recaptured 

 adults among the several recapture sites, including ocean fisheries, in-river 

 fisheries, and hatchery racks or other in-basin recovery sites. Unfortu- 

 nately, the tag recovery data will never be sufficient to establish the abso- 

 lute, age-specific probabilities of dying in the ocean, returning to the river, 

 being harvested in the ocean or river, or dying in the river — parameters 

 often included in management models. These population parameters can 

 never be known precisely because there are more unknown parameters 

 than recovery sites. Fish that die of natural causes are never seen. Thus, 

 one cannot be sure if they died early or late in life. The best that CWT 

 data can suggest is the magnitude of the total mortality loss — that propor- 

 tion of the population that is never recovered or otherwise accounted for. 



Rather than modeling age-specific mortality rates and maturity sched- 

 ules, the SLCM is set up to correspond to the empirical model suggested by 

 CWT recovery data. The total number of adults recovered is simulated us- 

 ing a binomial-beta distribution. Again, the beta distribution is used to in- 

 troduce added stochasticity. A multinomial process is used to allocate the 

 total number of fish recovered by age class among ocean harvest, in-river 

 harvest, and return to the subbasin. Appendix B shows how the model cal- 

 culates adult recovery parameters from CWT data. 



Other models that simulate ocean and in-river harvest, such as a model 

 developed by the Oregon Department of Fish and Wildlife (1991), can be 

 used to estimate ocean and in-river recovery probabilities. In such cases, 

 the simulated harvest and escapement data are used instead of CWT data. 

 Harvest patterns that change with time are accommodated by using a spe- 

 cial subroutine that calculates cohort-specific recovery probabilities using 

 simulation results from the harvest model. Since the total fraction recov- 

 ered depends on harvest and mortality rates, adtrecv is adjusted for each 

 cohort to reflect changing conditions. 



12 



