Kellison and Eggleston: Modeling release scenarios for Parahchthys dentatus 



89 



OS- 



04- 



0.3 



0.2 



01 



00 



E 



Strong type 2 



Strong type 3 



150 



Dl 



B 



Weak type 2 



05 

 0.4 



3 

 02 



110 130 150 170 190 210 



D 



Weak type 3 



Julian day 



Figure 10 



Predicted temporal trends in summer flounder abundance under initial densities of 0.5, 0.3, and 0.1 fish/m 2 

 under the assumption of a functional response that is a (A) strong type 2. IB) weak type 2, (C) strong type 

 3. i D i weak type 3. and under the assumption of (E) density-independent iDIl mortality. The curves in iFi 

 are best fitted (highest r 2 value) to data collected in Duke Beach 1999 (curve a, r 2 =0.82). Haystacks Marsh 

 1999 (curve b, r 2 =0.73), Prytherch Marsh 1999 (curve c. ;- 2 =0.82), Towne Beach 1999 (curve d, r 2 =0.91). 

 Radio Beach 1999 (curve e, r 2 = 0.27), Duke Beach 1998 (curve f, r 2 =0.31), and Prytherch 1998 (curve g, 

 r 2 =0.16) (see Fig. 11 for data). 



gradually decrease regardless of initial density if mortal- 

 ity is density independent. From examinations of tempo- 

 ral abundance patterns from several nursery sites (see 

 Kellison et al., 2003b, for site descriptions), it is evident 

 that observed declines at relatively low initial densities 

 are similar to predicted declines under both density-inde- 

 pendent mortality and a weak type-3 functional response; 

 whereas observed declines at relatively high initial densi- 

 ties are somewhat less gradual than predicted under den- 

 sity-independent mortality, but somewhat more gradual 

 than predicted under the weak type-3 functional response. 

 These results suggest that model predictions made under 

 the assumption of a weak type-3 response may give rea- 

 sonably accurate but conservative predictions of juvenile 

 summer flounder mortality and economic costs associated 

 with stock enhancement for comparison with alternative 

 management methods. As a caveat, although we found no 

 evidence of size-dependent daily mortality over the range 

 of fish sizes examined in this study, it is very likely that 



such a relationship exists to some extent (Sogard, 1997; 

 Lorenzen, 2000). Incorporating size-dependent mortality 

 into the model would decrease the slopes of the predicted 

 temporal abundance curves but should not change the 

 conclusion that the observed data lie somewhere between 

 values predicted under density-independent mortality 

 and those governed by a weak type-3 functional response, 

 respectively. Additionally, because the portions of the 

 curves used to delineate between temporal abundances 

 expected under density-independent versus varying den- 

 sity-mortality relationships are from early in the growth 

 season (later parts of the curve converge on very low den- 

 sities) and because nearly all fish in these portions of the 

 curves are at sizes well below that at which ontogenetic 

 emigration occurs, the exclusion of emigration from these 

 simulations should not affect the general conclusions 

 reached. These issues could be clarified with further field 

 trials to investigate the dependence of daily mortality 

 rates on fish size. 



