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Fishery Bulletin 102(1) 



For example, a strong positive (compensatory) density- 

 mortality relationship driven by predators might become 

 weaker in years when predator abundance was lower than 

 average. We included the temporally shifting functional 

 response scenarios to determine the extent to which tem- 

 poral variation in the form of the functional response would 

 affect model predictions. Temporal variation in the form of 

 the functional response might occur because of temporal 

 changes in the predator community, or because of changing 

 predator-prey size dynamics (e.g. Stoner, 1980; Black and 

 Hairston, 1988). For example, as the nursery season for 

 summer flounder progresses, proportionately greater num- 

 bers of juveniles grow to sizes at which they are capable 

 of preying on smaller juveniles (Kellison, personal obs. ). If 

 cannibalistic summer flounder exhibit a different predatory 

 functional response from that of the predator guild commu- 

 nity predominating earlier in the season, then the density- 

 mortality relationship may change seasonally. 



We replicated all model simulations over each of the six 

 density-mortality relationships (weak and strong types 2 

 and 3, and shifting patterns [type 2 to 3 and type 3 to 2] ) 

 to determine optimal release scenarios (maximum num- 

 ber of survivors, minimum cost-per-survivor) under each 

 relationship. We then compared results to those obtained 

 under density-independent mortality to make inferences 

 about the importance of density-mortality relationships to 

 model results. 



Correspondence between predicted and 

 observed temporal abundance patterns 



Different density-mortality relationships may result in 

 distinct temporal patterns of abundance (e.g. rapid versus 

 more gradual declines in abundance) depending on initial 

 densities. We generated predicted patterns of temporal 

 field abundance of juvenile summer flounder under den- 

 sity-independent mortality and four additional density- 

 mortality relationships (governed by weak and strong type 

 2 and 3 functional responses) and under varying initial 

 densities (0.1, 0.3, and 0.5 fish/m 2 ) to examine whether the 

 different density-mortality relationships would result in 

 distinct temporal patterns of abundance. We used 1998-99 

 field data and logarithmic or polynomial regression models 

 to generate curves that best fitted (based on r 2 values) 

 observed (from natural nursery sites) temporal declines in 

 abundance under varying initial densities. We compared 

 the best-fit curves to those predicted by the model under 

 density-independent and four additional density-mortal- 

 ity relationships. These comparisons allowed us to make 

 qualitative inferences about which density-mortality 

 relationship* s) resulted in the best match between pre- 

 dicted and observed temporal patterns of abundance. 



Model assumptions 



The assumptions of the model are the following: 



1 Daily mortality is independent of size. Although there 

 is strong evidence that mortality of fishes in the wild is 

 size-dependent (Lorenzen, 2000 ), particularly in regard 



to the importance of size to susceptibility to predation 

 (see, for example, Elis and Gibson, 1995; Furuta, 1999; 

 Manderson et al., 1999), we found no evidence (from 

 recaptures of released hatchery-reared fish ) of size- 

 selective daily mortality for juvenile summer flounder 

 ranging in size from -30-80 mm TL in shallow-water 

 nursery areas (Kellison et al., 2003a). Implications for 

 violations of this assumption are addressed in the "Dis- 

 cussion" section. 



2 Daily growth is independent of fish density. We based 

 this assumption on field experiments that indicated 

 no growth limitation at densities roughly equal to the 

 maximum densities explored in the model (Kellison 

 et al., 2003b). Similar findings (i.e. no food-limitation 

 or density-dependent growth) have been reported for 

 similar-size plaice in shallow-water nursery habitats 

 (van der Veer and Witte, 1993). 



3 Economic cost per fish (C PF ) is independent of the 

 number of fish acquired for release (i.e. within the 

 range of numbers offish released in model simulations, 

 there is no decrease in cost per fish as the number of 

 fish acquired from the production hatchery for release 

 increases). This assumption is likely to be valid over 

 changes in numbers of fish released common to stock 

 enhancement programs (Sproul and Tominaga, 1992) 

 but may not be valid as numbers released change 

 over orders of magnitude because of economy of scale 

 (Adams and Pomeroy 1991; Garcia et al., 1999). 



4 There is no emigration from the release habitat until 

 fish exhibit an ontogenetic shift in habitat at 80 mm TL. 

 Although pre-ontogenetic habitat shift emigration may 

 not truly be zero, we feel that it is also unlikely that pre- 

 ontogenetic habitat-shift emigration accounts for more 

 than a minimal amount of loss of released fish from 

 the habitat of release, as supported by several points. 

 First, rates of pre-ontogenetic shift emigration in wild 

 juveniles are apparently low (Kellison and Taylor 2 ), 

 suggesting that large-scale spatial migrations may not 

 be part of the behavioral repertoire of early juvenile 

 summer flounder. Second, irregular temporally repli- 

 cated sampling outside of experimental release sites 

 resulted in zero captures of emigrating hatchery-reared 

 fish (Kellison et al., 2003b). Third, emigration rates of 

 closely related HR Japanese flounder {Paralichthys 

 olivaceus) are reported to be very low (Tominaga and 

 Watanabe, 1998). In combination, these points suggest 

 that our zero emigration assumption is appropriate. 



5 Fish that do not grow to 80 mm TL during the model 

 period (i.e. by 15 July) do not survive. Although this 

 assumption cannot be examined with our field data, 

 data do show that juvenile summer flounder are 

 absent from shallow-water nursery habitats by mid 

 to late July (Kellison et al. 3 ). Thus, all fish have either 

 perished or made ontogenetic habitat shifts to deeper 

 habitats by this time. Our field observations suggest 

 that the deeper habitats to which larger flounder 



:t Kellison, G. T., J. C. Taylor, and J. S. Burke. 2000. Unpubl. 

 data. Department of Marine, Earth, and Atmospheric Sciences, 

 North Carolina State Univ., Raleigh, NC 27695-8208. 



