genotypic and phenotypic heterogeneity, or (3) uncertainty about the 

 proper value of p resulting from experimental error. Press (1989) describes 

 how the beta distribution arises as a model of uncertainty surrounding p in 

 a binomial process, given limited information. 



In the binomial-beta distribution, a beta distribution defines the prob- 

 ability distribution of p. Using the notation introduced above, the 

 binomial-beta distribution is defined by 



Prob{N(* + l) =X} = N( * )! P{[X+a],[N(*)-X+b]} 

 [N(*)-X]!X! |3{a,b} 



where a and b are parameters of the beta distribution, and (3 {a,b} is the 

 beta function. The moments of the binomial-beta are 



mean = N(t)a I [a+b] 



variance = N(*)ab[a+b+N(*)] / [(a+b)2(a+b+l)]. 



Boswell and others (1979) provide a fuller discussion of the derivation of 

 the binomial-beta and its use in ecology. 



While natural stochasticity and measurement error can be expressed in 

 identical terms mathematically, they might have different implications 

 when the results are interpreted. Thus, it may be useful to keep the two 

 forms of uncertainty separate in an analysis. The SLCM has the capability 

 to accommodate many such instances (see the operational notes below). 



OVERVIEW OF MODEL 



The SLCM can be thought of as a series of compartments corresponding 

 to stages within the life cycle of anadromous salmonids. The total popula- 

 tion is divided into two stocks, hatchery and natural. The natural stock in- 

 cludes all fish spawned in the wild and hatchery-produced juveniles that 

 are released as fry, regardless of the origin of their parents (fig. 1). Simi- 

 larly, the hatchery fish include all fish spawned in the hatchery and re- 

 leased as smolts (fig. 2). For much of their lives, hatchery-produced fish 

 and naturally produced fish share a common life cycle. Transitions from 

 one compartment to the next determine the model dynamics. At each tran- 

 sition, random draws from the appropriate probability distribution deter- 

 mine the values of the state variables (table 1). The model runs on an an- 

 nual time step, but multiple transitions can occur within a single step. 

 Each transition is described in more detail in the following sections. State 

 variable names are given in capital letters and parameters in italics. 



The model uses a set of production, passage, and harvest parameters 

 (table 2) gleaned from the various input files (described below). A set of 

 control parameters determines the number of replicates (games) within 

 each simulation, and the number of years per game. The user must specify 

 initial numbers for each life stage. As the model runs, it creates a data 

 set containing identification variables and updates state variables at the 

 end of each year. For simulation purposes, a "y ear " begins with natural 

 spawning. 



Currently, two versions of the base model are available, incorporating 

 two different approaches to modeling production of juvenile migrants 

 (smolts). Version 1 is more descriptive, as it tracks egg production and 

 egg-to-smolt survival in a more conventional form. The user can choose 

 among three different functional forms to describe density-dependence in 

 early juvenile survival. Interactions between hatchery-released fry and 



4 



