50,000 



1,000 2,000 3,000 4,000 5,000 6,000 



Natural Spawners 



Figure 7 — Simulated data showing the number of adult recruits 

 produced by a given number of spawning adult salmon. 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. 



Multiple Games Since the stochastic nature of the SLCM produces a different outcome 



for every game or simulation, the outcome from a single game is of little 

 value. It is more informative to run multiple games and examine the out- 

 put collectively. In this manner, one can evaluate possible future states 

 probabilistically. For example, we ran 500 games covering 50 years each 

 using the SLCM. When combined, the output from these games creates a 

 probability distribution for each year, such as the distribution of spawners 

 in year 50 (fig. 8). The distribution shown in figure 8 is characteristic of 

 the positively skewed distributions of state variables common to SLCM 

 results. 



Portraying the distribution of a state variable through time is problem- 

 atic. In figure 9, contour lines show the shape of the distribution of spawn- 

 ers through the simulation period. The contour lines depict the minimum, 

 10th percentile, median, mean, 90th percentile, and maximum from the 

 500 games. For this example, the bulk of the distribution is fairly stable, 

 with the most variation occurring in the upper tail of the distribution. 



16 



