Kellison and Eggleston: Modeling release scenarios for Paralichthys dentatus 



79 



Table 1 



Range of numbers of summer flounder (Paralichthys dentatus) released (and resulting postrelease densities), sizes-at-release, and 

 dates of release simulated in the model. 



Number released 



Postrelease density 



Size-at-release 



Dates of release 



100-400,000 



0.001-4.0 



30-80 mm 



1 April-15 July 



that incorporates size of fish released, date-of-release, and 

 number offish released to calculate 1) predicted numbers of 

 survivors and 2 ) economic costs associated with varying re- 

 lease scenarios under density-independent mortality. We in- 

 vestigated the sensitivity of model predictions to violations 

 of the assumption of density-independent mortality because 

 there is abundant evidence that mortality rates, or processes 

 underlying mortality rates (e.g. growth), are affected by den- 

 sity-dependent relationships in the wild ( see, for recent ex- 

 amples. Bucket et al., 1999; Bystroem and Garcia-Berthou. 

 1999; Jenkins et al, 1999; Kimmerer et al., 2000). We did 

 so by repeating model simulations under varying density- 

 mortality relationships (depensatory in nature at elevated 

 densities ), using experimental evidence from our own field 

 studies and published observations for similar species to 

 parameterize density-mortality relationships. Additionally, 

 we used a scenario in which the density-mortality relation- 

 ship changed over time to make inferences about the effect of 

 more complex density-mortality relationships on postrelease 

 mortality of juvenile summer flounder. Finally, we generated 

 predicted temporal patterns of field densities under vary- 

 ing density-mortality relationships and compared them with 

 observed (in the field) patterns to determine whether model 

 output under the considered density-mortality relationships 

 matched actual patterns in the field. The model provides 

 an example of a relatively easy-to-develop predictive tool 

 with which to make inferences about the ecological and 

 economic potential of stock enhancement with summer 

 flounder and provides a template for model creation for 

 additional species that are subjects of stock enhancement 

 interest, but for which limited empirical data exist. 



Materials and methods 



Background 



In North Carolina, wild summer flounder recruit to shal- 

 low-water estuarine nursery habitats from February to 

 May, after which small juvenile (20-35 mm total length 

 [TL] ) densities range from -0.1 to 1.0 fish/m 2 (Burke et al., 

 1991; Kellison and Taylor 2 ). Juveniles subsequently make 

 an ontogenetic habitat shift to deeper waters ( Powell and 

 Schwartz, 1977), apparently after reaching a total length 



2 Kellison, G. T., and J. C. Taylor. 2000. Unpubl. data. De- 

 partment of Marine, Earth, and Atmospheric Sciences, North 

 Carolina State University, Raleigh, NC 27695-8208. 



of -80 mm (Kellison and Taylor 2 ). By mid-July, densities 

 of juvenile summer flounder in the shallow water nursery 

 habitats are near zero (Kellison and Taylor 2 ). 



Model pathway 



Our compartmental model simulated the daily mortality 

 and growth of different-size hatchery-reared (HR) fish 

 released in the field over a 105-day period ( 1 April to 15 

 July, based on observed field abundances) in a hypotheti- 

 cal release habitat of 10 hectares. The model predicted the 

 percentage of released fish surviving and economic cost- 

 per-survivor under 2730 release scenarios for a specified 

 number offish released (see below). To begin the model, a 

 value of number offish released (NFR) ranging from 100 to 

 400,000 (Table 1) was chosen (Fig. 1), resulting in postre- 

 lease densities (assuming even postrelease distribution) of 

 0.001-4.0 fish/m 2 . These values included a range of densi- 

 ties of juvenile summer flounder observed in wild nursery 

 habitats ( -0-1 fish/m 2 ; mean -0.05 fish/m 2 ; Kellison and 

 Taylor 2 ), but also included unusually high densities (>1 

 fish/m 2 ) in order to examine how such release strategies 

 would affect model output (we did not examine densities 

 >4 fish/m 2 because of a lack of data on fish response to 

 resource limitation likely to occur as densities increased 

 past values for which we had empirical growth data). Each 

 group of NFR was initially assigned a "size-(TL) at-release" 

 of 30 mm (the smallest size-at-release simulated in the 

 model), after which a size-dependent economic cost associ- 

 ated with the release of the 30-mm-TL fish was calculated 

 (see below). The release group was then assigned a mini- 

 mum Julian "day of release" of 92 (corresponding to 1 April, 

 the earliest release date simulated in the model). A range 

 of Julian days of release was included in the model because 

 field-estimated growth rates were dependent on Julian day 

 (Kellison, 2000), and growth rates are potentially impor- 

 tant to the determination of mortality rates (Rice et al. 

 1993). With this model, we then calculated daily mortality 

 and growth (described below) in the hypothetical release 

 habitat over the number of days at large (DAL), where 



DAL = 197 (the Julian day corresponding to 15 July) - 92 

 (Julian release day), 



and output a number of survivors and a calculated cost- 

 per-survivor (CPS), where 



CPS = cost associated with release -f 

 predicted number of survivors, 



