Kellison and Eggleston: Modeling release scenarios for Paraltchthys dentatus 



81 



NFR x S D DAL = NOS, 



where NFR = number released; 

 S D = daily survival; 

 DAL - days at large (from release date 



until Julian day 197); and 

 NOS = estimated number of survivors. 



Daily mortality (M D ) was then calculated from 

 the equation 



M r 



1-Sr 



At the end of each simulated day, all fish that 

 were alive increased in growth according to the 

 equation 



G D = -0.0061 x Julian day + 1.2487, 



which was derived from mark-recapture data 

 (Kellison, 2000), and in which G D is daily growth 

 in millimeters. Fish reaching 80 mm TL during the model 

 (i.e. by 15 July) were considered to make an ontogenetic hab- 

 itat shift to deeper waters. These fish were then subjected 

 to one half year of natural mortality to simulate mortality- 

 related losses from deeper-water habitats (M=0.28; Froese 

 and Pauley, 2001). Remaining fish, now having survived 

 -one year of natural mortality, were considered to be sur- 

 vivors (available to the commercial fishery), which is a con- 

 servative assumption because 1-yr-old summer flounder are 

 only partially recruited to the commercial fishery. All fish not 

 reaching a total length of 80 mm were assumed to perish. 



To determine size-dependent economic costs offish pro- 

 duction, we used the following regression equation derived 

 for Japanese flounder (Paralichthys olivaceus) by Sproul 

 and Tominaga ( 1992 ) because equivalent economic data for 

 summer flounder were unavailable: 



C PF = 14.24 + 1.234 x TL, 



where C PF = the cost per fish in Japanese yen (¥); and 

 TL = the total length of the HR fish. 



Costs were then converted into US$ by using an exchange 

 rate of 106. 7¥ per 1 US$ (universal currency converter). 

 We feel use of this cost-of-fish-production equation is appro- 

 priate because the Japanese flounder is closely related 

 and similar in life history traits to the summer flounder 

 (Tanakaet al., 1989; Burke etal., 1991 ), resulting in similar 

 optimal rearing practices for hatchery-reared Japanese and 

 summer flounder (Burke et al., 1999), and thus likely simi- 

 lar rearing costs. Additionally, the scale of Japanese floun- 

 der hatchery production is similar to, or greater than, other 

 government subsidized hatchery production programs (e.g. 

 red drum in Texas, cod in Norway [Svasand, 1998] ). 



Density-mortality relationships 



We tested the sensitivity of the model results (optimal 

 predicted number of survivors and cost-per-survivor esti- 

 mates under varying NFRs) to violations of the assumption 



of density-independent mortality by incorporating varying 

 types and strengths of density-dependent mortality (depen- 

 satory in nature at elevated densities; see below) into the 

 model. As a basis for these sensitivity analyses, we assumed 

 that predation was the driving mechanism underlying the 

 postrelease mortality of HR summer flounder under the 

 densities examined (Kellison et al., 2000; Kellison et al., 

 2003b). Thus, we made daily mortality rates correspond 

 to either a type-2 or type-3 predator functional response 

 (Holling, 1959; see Lindholm et al., 2001 for example), in 

 which proportional mortality due to predation decreases 

 with increasing density (type-2 response) or increases ini- 

 tially with increasing density, reaches a zenith, and then 

 decreases with increasing density (type-3 response) (Fig. 

 2). Both type-2 and type-3 responses result in decreasing 

 (depensatory) mortality at elevated prey densities due to 

 predator satiation. We did not include scenarios in which 

 mortality increased at elevated densities (as would be 

 expected when densities reached those likely to result in 

 resource limitation ) because we did not include in the model 

 elevated release densities likely to result in resource limita- 

 tion. We parameterized the daily mortality curves so that 

 each response (type 2 or 3) incorporated the daily mortality 

 rate of 0.02153. These mortality curves contain mortality 

 values that are within ranges reported in the literature for 

 other species of juvenile marine fishes (Bax, 1983; Houde, 

 1987; Nash, 1998; Rose et al, 1999). To make further infer- 

 ences about the importance of density-dependent mortal- 

 ity to model results, we included a 1) weak and 2) strong 

 form of each functional response (types 2 and 3) (Fig. 2), as 

 well as scenarios in which the response shifted temporally 

 from 3) type 2 to 3, and 4) type 3 to 2 at the midpoint of 

 the nursery season (Julian day 145). We included both the 

 weak and strong forms of the type-2 and type-3 functional 

 responses to determine the extent to which variation in the 

 strength of the functional response would affect model pre- 

 dictions. The strength of the functional response could vary 

 because of annual variation in the presence or abundance 

 of prey or because predators could affect the density-mor- 

 tality relationship (see, for example, Hansen et al., 1998). 



