Powell et al.: Growth, mortality, and hatchdate distributions for Cynoscion nebulosus 



147 



and second (22-60 increments) measuring paths because 

 otolith increment width changed at a constant (age-inde- 

 pendent) rate for each path. We did not include fish with 

 >60 increments because the relationship past this number 

 was determined for only 10% of the fish and included obvi- 

 ous outliers. Letting Y be the otolith width measurement 

 for fish ; at age a , where y indexes time, the model for each 

 path was 



Y ,j = «o, + «i 



where a 0l and « 1; are the fish-specific intercept and slope 

 describing the relationship between increment width and 

 age for fish i, and e is a normally distributed error term; 

 thus, a h is the growth rate for fish i over the measuring 

 path. Temperature exhibited only negligible change for any 

 given fish over the measuring path; thus, temperature for 

 fish i was summarized as t r the average temperature over 

 the path for that fish. To determine an appropriate model 

 for the relationship between intercept and growth rate 

 and temperature, a preliminary analysis was performed in 

 which ordinary least squares estimates of « 0; and a h were 

 obtained separately for each fish i and plotted against tem- 

 perature. For the first measuring path (1-21 increments), 

 the appropriate model was 



«o, = A)0 + 0oi'i + b or «i, = Pw + Put, + P\4? + b ii> 



where b 0l and b h are normally distributed random effects, 

 allowing growth rates for fish at the same temperature to 

 vary across fish. For the second measuring path (22-60 

 increments), the appropriate model was, 



«o, = Poo + /V, + Po-i'r + V «ii = Pw + 0ii'i + Put? + b u- 



By substitution, these considerations yielded models 1 and 

 2 for the first and second paths, respectively; 



Y „ = { Poo + fVP + Cfto + 011*1 + 012*^ a „ + b o 



b lpii +e ii 



(•Pw + Pn l , + 012^ a a + b o, + b i, a „ + e ,j 



(1) 



(2) 



thus representing otolith increment width in each case 

 as having a straight line relationship with age, where the 

 slope (age-independent growth rate) depends on average 

 temperature according to a quadratic relationship. The 

 random effects allow observations on the same fish to 

 be correlated, whereas observations across fish are inde- 

 pendent. Models 1 and 2 were implemented in SAS Proc 

 Mixed (SAS/STAT software, version 6.12, SAS Institute, 

 Cary,NC). 



Daily temperature records were obtained from the Unit- 

 ed States Department of Interiors National Park Service, 

 Florida Bay monitoring stations and averaged over a 7-day 

 period. In 1995, temperature records were available only 

 for Johnson Key Basin ( JKB), Whipray Basin (WB), Little 

 Blackwater Sound (LBS), and Little Madeira Bay (LMB), 

 but spotted seatrout were also collected at other sites 



(Table 1). Daily temperatures were estimated for Sandy 

 Key (SK) and Roscoe Keys (RK) from values recorded dur- 

 ing sampling trips because both these stations are not in 

 close proximity to National Park Service monitoring sites. 

 Sandy Key values were regressed on JKB values (same 

 dates). Sandy Key temperatures were collected from Janu- 

 ary 1994 through August 1996. The regression model for 

 temperature was SK = 0.76 + 0.9536 JKB [r 2 =0.89; w=25], 

 Roscoe Key values were regressed on WB values (same 

 dates). Roscoe Key temperatures were collected from Janu- 

 ary 1994 through August 1996. The regression model for 

 temperature was RK = 5.60 + 0.7976 WB [r 2 =0.87; n=31). 

 Temperature values were available at Murray Key (MK) in 

 1997. To attain values for our 1995 analysis we regressed 

 MK on JKB (same dates). The temperature regression 

 model was MK = 0.77 + 0.9680 JKB [r 2 =0.99; re=342]. 



We reported measurements in standard length (SL). For 

 preflexion and flexion larvae, standard length was mea- 

 sured from the tip of the snout to the tip of the notochord. 

 For postflexion larvae and juveniles, standard length was 

 measured from the tip of the snout to the base of the hy- 

 pural plate. 



Results 



Overall growth of larvae and juveniles (<80 mm SL) was 

 best described by the equation log, standar-d length = 

 -1.31 + 1.2162 (log e age) [«=582; r 2 =0.97]. Growth in body 

 length of juveniles (12-80 mm SL) was best described by 

 the linear equation standard length = -7.50 + 0.8417 {age) 

 [n=486; /- 2 =0.84]; hence, juveniles between approximately 

 age 20-100 days grew on average 0.84 mni/d. There were 

 no significant differences in juvenile growth in body length 

 among three geographical subdivisions [F* 327 =0.756; 

 n=333] (Table 2), but there was a significant growth differ- 

 ence in length for one of six 1995 cohorts (Table 3, Fig. 5). 

 Growth in wet weight of juveniles ( 15-69 mm SL) was best 

 described by the equation log ( , wet weight = -AAA + 0.0748 

 (age) [n=347, r 2 =0.84]. There was a significant growth dif- 

 ference in wet weight for one cohort (Table 4, Fig. 6). 



Weekly 1995 hatchdate distributions, determined by us- 

 ing daily instantaneous mortality ( 0.0585. Fig. 7 ). indicated 

 juveniles in collections (i.e. survivors) were from spawning 

 that was cyclical and protracted (Fig. 8). The most intense 

 successful spawning occurred during 21-27 June (9.2% of 

 total). Using a 3-point moving average, we observed three 

 similar cycles (Fig. 8). From data on survivors, -25% of ju- 

 veniles were spawned by late May, 50% by early July, and 

 75% by late August and from data on cohorts, three cohorts 

 (cohorts C, D, and E; early June-late August) comprised 

 55% of the total estimated spawn of spotted seatrout. There 

 was no correlation between spawning and moon phase (pe- 

 riodic regression r 2 =0.019, P=0.754) (Fig. 8). 



The relative recruitment potential (G:M ratio) of the 1995 

 year class estimated from the wet-weight specific growth 

 coefficient (0.0748) and the instantaneous daily mortal- 

 ity rate (0.0585, Fig. 7) was 1.28. The G:M ratio for three 

 cohorts (B, May; D, July; and F, September) was greater 

 than the ratio for the total 1995 year class because mortal- 



