results are alb = 1.35, c = 3.74 (standard error = 

 0.79), R^ = 0.88, ln(6-i) = 46.98. 



Hence Equation (1) becomes 



Y = 6X3^4/(1 + 1.356X3^") . ft ^ g -46.98 



Inasmuch as Y ranges between zero and bla, it 

 seems unlikely that Y, or a corresponding statistical 

 error term for Equation (1) would be approximated 

 by a normal distribution. On the other hand, so long 

 as Y does not rise above b/a (to which Equation (1) 

 constrains it), the left side of Equation (2) lies 

 between - «> and + <», and the error term is more 

 likely approximated by a normal distribution. Con- 

 sequently, we cautiously used the standard error 

 associated with c, to test whether c > 1.0; that is, 

 whether the functional response curve is sigmoid 

 (Type III). In fact, c lies more than 3.5 standard 

 errors above 1 (Type II response) and more than 2.2 

 standard errors above 2 (Type III response). Al- 

 though the power of a test involving only 5 data 

 points is weak, we feel that a tentative conclusion 

 of depensatory predation by juvenile coho salmon 

 is justified. 



Discussion 



Many adult salmon as they attempt to get to the 

 spawning grounds, and as they spawn, are killed by 

 Kodiak brown bears. Card (1971) reviewed the 

 available literature concerning predation of salmon 

 by bears at Karluk and, in years when fish were not 

 abundant, noted that bears had been observed to 



leave the salmon spawning areas to feed on berries 

 in the local area, indicating that their predation also 

 may be depensatory. We used data from Card's 

 summary to approximate the relation between the 

 number of adult sockeye salmon in a nm (X) and 

 the number of unspawned adults (Y) estimated to 

 have been killed by bears (Fig. 4). Although R^ was 

 only 0.424, a depensatory relation was indicated as 

 Y = X2io6/(3io2.85 + 0.00435X2106). c, from 

 Equation (1), was 2.106, with a standard error of 

 1.098. Because predation of sockeye salmon by 

 bears, as well as predation by coho salmon, appeared 

 to be depensatory, it is unlikely that predation by 

 coho salmon alone was the sole cause of the com- 

 plex stock-recruitment curve for sockeye salmon. 

 Prudent management of these salmon, and of 

 salmon in systems similar to Karluk, may require 

 regulation of harvest to prevent collapse of popula- 

 tions into relatively low equilibrium regions. Harvest 

 levels that would have prevented collapse of the 

 Karluk population can be estimated from the stock- 

 recruitment curve (Fig. 2). An exploitation rate 

 between 30 and 35% of the recruits should have 

 maintained stock sizes associated with the upper 

 equilibrium region. Exploitation at a constant rate 

 of 0.40 increases the slope of the replacement line 

 to the point that collapse of the population into the 

 lower equilibrium region becomes inevitable (see 

 Peterman 1977 for a description of the relation 

 between the size of stability regions and exploita- 

 tion rate). When depensatory mortality is potentially 

 high for economically important populations, it may 

 be necessary to limit exploitation to less than 35% 

 of the recruits to prevent collapse. 



X) 

 V 



V 



E 



Z3 



0.2 0.4 0.6 



Millions of Adult Salmon 



Figure 4.— Functional response curve for predation of sockeye salmon by 

 bears. Number killed is thousands of unspawned salmon. 



615 



