Fishery Bulletin 102(1) 



Is density important? Effects of varying density-mortality 

 relationships 



Our results suggest that the relationship between density 

 and mortality has the potential to significantly affect opti- 

 mal release scenarios associated with stock enhancement 

 efforts. Because the original simulations were performed 

 under density-independent mortality, the number of 

 survivors originally increased linearly with the number 



B 



1e+5 



released, resulting in a density-independent cost-per- 

 survivor. Thus, when mortality is independent of density 

 (over a given range of densities) for a target species for 

 stock enhancement, managers will maximize the number 

 of survivors produced by releasing the greatest number of 

 fish possible within that range for a given size class. When 

 mortality varied with density of released fish, the number 

 of survivors and cost-per-survivor depended on the den- 

 sity-mortality relationship. In some cases, optimal results 

 (maximum survival and minimum cost) differed 

 depending on whether the response variable was 

 number of survivors or cost-per-survivor. Under 

 the assumption of a strong type-3 functional 

 response and under relatively low postrelease 

 densities, survival was optimized (maximized) 

 by releasing the largest fish ( 80 mm TL) possible; 

 however, cost-per-survivor was optimized (mini- 

 mized) by releasing smaller fish (42-44 mm TL). 

 This result occurred because mortality at low 

 postrelease densities was sufficiently low that 

 the difference in total mortality attributed to the 

 longer "susceptibility" period of the smaller fish 

 was insufficient to override the economic advan- 

 tage of releasing smaller fish. Simulations under 

 shifting functional responses (type 2 to type 3 

 and type 3 to type 2) produced optimal results 

 similar to those obtained when nonshifting type- 

 2 or type-3 functional responses were employed 

 because densities were generally reduced to such 

 low numbers by the time the shift occurred that 

 the changing density-mortality relationship was 

 inconsequential. Importantly, when functional 

 responses shifted temporally, the predicted 

 number of survivors and economic cost per 

 survivor was at times very dependent on date of 

 release, suggesting that identifying or ruling out 

 shifting functional responses in the wild may be 

 critical to accurate prediction of response vari- 

 ables (survivors and economic costs) associated 

 with stock enhancement. Although we are not 

 aware of reports in the literature of shifting 

 functional responses in the wild, we are also 

 not aware of studies that have tested for such 

 a phenomenon, possibly because of the logisti- 

 cal difficulties inherent in identifying a shifting 

 functional response. 



Correspondence between predicted and 

 observed temporal abundance patterns 



Figure 9 



(A) Response surface of optimal number of summer flounder survivors 

 as a function of date of release and size at release at number released 

 (NR) = 100,000 (postrelease density=1.0 fish/m 2 1 under the assumption 

 of a temporally shifting functional responses from type 2 to type 3. 

 <B> Response surfaces of optimal number of survivors as a function of 

 date of release and size at release at number released (NR) = 100. 000 

 (postrelease density=1.0 fish/m 2 > under the assumption of a temporally 

 shifting functional responses from type 3 to type 2. 



Predictions of field abundance patterns of juve- 

 nile flounder density over time were noticeably 

 different under density-independent mortality 

 and density-dependent mortality governed by 

 type-2 and type-3 functional responses. For 

 example, our simulations predict that fish den- 

 sity should decrease rapidly under relatively 

 low initial densities if the functional response is 

 type 2, decrease rapidly at relatively high initial 

 densities if the functional response is type 3, and 



