NOTE Roemer and Oliveira: Validation of back-calculation equations for luvenile Pomatomus saltatnx 



307 



calculated as the slope of fork length (v) plotted against 

 otolith radius (x). In linear form the BPH is expressed 

 as follows: 



c + dR, 

 c + dK 



(4) 



The otolith radii and fork lengths were fitted to lin- 

 ear, quadratic, and cubic regression models. The data 

 fitted all the models similarly: r- for the linear and 

 quadratic functions were 0.86 and the cubic function 

 had an r- of 0.85. A visual comparison of residuals 

 between linear and nonlinear models showed the data 

 to be homoscedastic and therefore the linear model was 

 chosen because of its parsimony. Using these formulae, 

 we estimated the lengths of individual bluefish at the 

 start of the experiment and then compared our esti- 

 mates to the actual measured lengths. The best model 

 for estimating growth was determined by using paired 

 ^tests. All statistical analyses were made with SPSS. 

 vers. 13.0 (SPSS, Inc., Chicago, IL). For all comparisons 

 P<0.05 was considered significant. 



Results 



Seventy-seven fish were injected with tetracycline and 

 13 produced readable otoliths that could be used for age 

 and growth analyses. Mortality was high in the first 

 day of the experiment when 26 fish died. Five fish that 

 appeared to be diseased were also removed from the 

 experiment. An additional 21 fish that survived did not 

 show the tetracycline mark and 12 fish had unreadable 

 otoliths. Growth increments were distinguishable and 

 the number of observed rings after the tetracycline injec- 

 tion was within 5% of the number of days in captivity for 

 all tetracycline-injected fish. All replicate counts were 

 within two days of the number of days in captivity. 



Some fish died before the 32-day intended experimen- 

 tal time period, and two distinct groups of fish that 

 died were evident. Group 1 included the seven fish that 

 survived at least three weeks (23-32 days) and group 2 

 included the six fish which lived one week or less (3-7 

 days). Group 2 did not survive the entire study period 

 but did have the same growth patterns as group-1 fish. 

 For this reason, the data were analyzed as 1) pooled 

 data (all 13 fish), and 2) data from group 1 (7 fish). 



Measured growth estimates from all fish varied be- 

 tween 0.4 and 3.0 mm FL/day (Table 1). There was no 

 significant difference (P=0.13) in otolith growth rates 

 and body growth rates for the wild fish used to develop 

 the BCFs and the experimental fish, indicating that 

 uncoupling of the relationship did not occur under ex- 

 perimental conditions. 



The closest estimate of the measured L^ came from 

 the Dahl-Lea equation, showing no significant differ- 

 ence (P=0.48) between the estimates and the initial 

 lengths of the bluefish. The estimates from the Fraser- 

 Lee equation, BPH, and SPH were all significantly dif- 

 ferent from the measured initial length (P<0.01). The 



Dahl-Lea equation estimated the L, by a mean absolute 

 difference of 2.0% ±0.6 standard error (SE) and had 

 a tendency to over-estimate the initial lengths. The 

 Fraser-Lee equation and the BPH were similar in their 

 estimations, tending to under-estimate length by 2.9% 

 ±0.9 SE and 3.0% ±0.9, respectively. The SPH under- 

 estimated lengths by a mean of 5.3% ±1.4 SE. 



Our analysis of the same data without group-2 fish 

 produced results similar to the results with the pooled 

 data. The Dahl-Lea equation estimations were not sig- 

 nificantly different from the L, (P=0.41), whereas the 

 other three equations were significantly different from 

 the measured length (s0.02). Percent differences for 

 all the equations were slightly higher for group-1 fish 

 alone than for the pooled fish. Dahl-Lea estimates dif- 

 fered from the measured lengths by 3.1% ±0.9 SE, the 

 Fraser-Lee and BPH estimates both differed by 4.7% 

 ±1.3 SE, and the SPH differed by 8.6% ±1.7 SE. 



Discussion 



The agreement between the number of daily rings and 

 the days after injection indicates that the observed ring 



