any particular stock. The base case includes an assumption of little inter- 

 action between hatchery and natural fish, small amounts of fry releases 

 (the bulk of hatchery releases are smolts), and no adult supplementation. 

 Almost all surplus hatchery fish are harvested. The logistic response func- 

 tion is used to describe juvenile production. 



Single Game The simulation of a single population over a 500-year period is shown 



in figure 6. The population's fluctuation over time is typical of the fluctua- 

 tions of state variables within the SLCM. Though we have not rigorously 

 compared the model output with empirical time series, the results appear 

 consistent with general observations of populations in nature. 



A second way of viewing simulation results is to look at the relationship 

 between the number of adults spawning naturally in a given year and their 

 offspring recovered in future years as adults. In figure 7, SPAWNERS and 

 associated RECRUITS for the 500-year period are plotted along with deter- 

 ministic representations of the underlying spawner-recruit relationship. 

 The curved line represents the density-dependent relationship between the 

 number of spawning adults and the expected number of recruits. The 

 straight line is the inverse of the relationship between a given number of 

 recruits and the number of spawners they would produce. In a determinis- 

 tic model, the population would move quickly to the equilibrium point de- 

 termined by the intersection of the two lines. 



In contrast, the SLCM suggests no single equilibrium point, but rather 

 a broad clustering of points located near the deterministic equilibrium 

 points. The first moment of the mass of point scattered within the spawner- 

 recruit plane is actually located below and to the left of the intersection 

 point. This suggests that while stochastic processes in the SLCM occasion- 

 ally lead to production levels much higher than average, average produc- 

 tion is less than predicted by deterministic models. 



11,000 

 10,000 

 9,000 

 | 8,000 

 I 7,000 



Q. 



S 6,000 

 tu 



c 5,000 



5 4,000 

 n 



w 3,000 

 2,000 

 1,000 

 



I ! il \ I Ml ' I 1 T I • 1 ( I ' ' 1 



*■■•*• •>•;'»»•,;,. 'Oj, '•;•.« v' - '.-- ~v , .*A*,,.' T>h!\x'P *U >; "•I.*.?** * ,. *,!> AVl'^T! «.V ''Wjf V;.- 1 



100 



200 300 

 Year 



400 



500 



Figure 6 — Subbasin escapement for a single simulation over time. Solid 

 line indicates natural fish, dashed line indicates hatchery fish. 



15 



