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Fishery Bulletin 105(2) 



Figure 1 



Transverse section of a tetracycline-marked otolith from a juvenile bluefish 

 iPnmatomus saltatrix) 32 days from marking viewed with reflected UV light. 

 The white line indicates the axis of fastest growth and indicates the total 

 radius iR^). The arrow indicates the tetracycline mark. The line segment 

 from the origin (O) to the arrow is the radius of the otolith at the beginning 

 of the experiment (i?,). 



with age, a straight line measurement from nucleus 

 to edge would not reflect the true radius and therefore 

 would bias the estimation of growth increments associ- 

 ated with the curvatures. In order to account for this 

 curvature, radial measurements were made along the 

 axis of fastest growth, which was the sum of several 

 straight line measurements from the nucleus to the 

 edge. The second measurement, i?,, was defined as the 

 distance from the primordium to the inner edge of the 

 tetracycline mark deposited on the otolith, along the 

 axis of fastest growth, and represents the radius of the 

 otolith at the time of injection. 



The frequency of ring deposition was also determined. 

 The sectioned otoliths were observed at 400x magnifi- 

 cation under reflected UV light. When necessary, com- 

 puter images were enhanced by alternating changes in 

 contrast, and further digital magnification was used 

 to observe rings. The tetracycline mark was located 

 and then the UV light was turned off and the number 

 of rings between the tetracycline-marked ring to the 

 edge of the otolith were counted in normal transmitted 

 light. Two replicates were made for otolith daily ring 

 counts. 



Back-calculation formulae 



Growth rates from bluefish were estimated by using four 

 back-calculation growth models as described in Francis 

 (1990). In these equations, L, is the initial fork length 

 of the fish and L^ is the fork length of the fish at the end 

 of the experiment. 



The Dahl-Lea equation (based on the study of Lea [1910]) 

 is a simple linear ratio of scale growth to body growth, 

 with the assumption that the two are in exact proportion. 



L,=L, 





(1) 



The Fraser-Lee equation (based on the approach de- 

 scribed by Fraser [1916]) is similar to the Dahl-Lea 

 equation but with the Fraser-Lee equation there is 

 the assumption that each back-calculation line passes 

 through the point c, resulting in Equation 2. The value 

 c was calculated as the intercept of the regression of 

 otolith radius and body length (Fig. 2). 



L=c + (.L, 



-c) 



(2) 



With the SPH (Whitney and Carlander, 1956) there 

 is the assumption of a constant proportional deviation 

 from the mean in scale size such that if the scale is ten 

 percent larger than average for a fish of that length, 

 then it will be ten percent larger throughout the life of 

 the fish. The a and b values for the SPH were calcu- 

 lated as the intercept and the slope of the regression of 

 otolith radius (y) against fork length (x) (Fig. 2). In its 

 linear form, the SPH is expressed as follows: 



'Af} 



+ L + 



R^ 



(3) 



The BPH (Whitney and Carlander, 1956) is similar in 

 principal to the SPH but carries that assumption that if 

 a fish is ten percent smaller than an average fish with 

 that size scale, it will be ten percent smaller throughout 

 its life. For the BPH, c is as in Equation 2 and d was 



