FISHERY BULLETIN: VOL. 82, NO. 3 



mm 3.5 macro lens which projected an image of 

 the section on to a monitor screen at 20 x magni- 

 fication. Illumination was by transmitted light. 

 Translucent (light) bands on the cross sections 

 were counted and the distances (in millimeters) 

 from the center of the spine to the distal edge of 

 each band was measured. The spine radius (R) 

 was defined as the maximum distance (in milli- 

 meters) from the center of the section (appears as 

 a small hole) to the posterior distal edge (Fig. 1). 



Additionally, before the spines were sectioned, 

 the anterior-posterior thickness (T) of 200 dorsal 

 spines was measured to the nearest 0.01 mm at 

 the sectioning site. 



The type of growth (opaque = dark, translucent 

 = light) of the margin of each section was noted. 

 The sections were read three times. 



The relationships of R, T, and body weight to 

 FL and the relationships between TL, SL, and FL 

 were determined by least squares methods fol- 

 lowing the suggestions of Ricker (1975). A com- 

 puter program by Abramson (1971) was used to fit 

 weighted back-calculated mean length at age to 

 von Bertalanffy growth curves. The growth equa- 

 tion (von Bertalanffy 1938, 1957) and values were 

 as follows: 



lt= I (1 - e 



-K(t-t ) 



) 



where It = length at age t, 



I = asymptotic length, 

 K = growth coefficient, 

 ^o = time when length would theoretically 

 be zero. 



Estimates of annual mortality (a), annual sur- 

 vival (s), and instantaneous mortality (i) were 

 developed for the total collection (2,808 fish) 

 (Ricker 1975). Length-frequency data were con- 

 verted to age-frequency distribution (N y = num- 

 ber of fish caught in age class y ) by applying age- 



FIGURE 1. — Sections of gray triggerfish first dorsal spines from 

 fish collected off Panama City, Fla. (A) Spine section from a 

 1-yr-old male (263 mm FL) collected 4 September 1980 with 

 spine radius R labeled. (B) Spine section from a 2-yr-old 

 female (336 mm FL) collected 11 September 1980. (C) A 3-yr- 

 old female (315 mm FL) collected 8 August 1980. (D) A 4-yr- 

 old male (350 mm FL) collected 13 August 1980. (E) A 5-yr-old 

 female (331 mm FL) collected 24 September 1980. (F) A 6-yr- 

 old male (477 mm FL) (seventh mark forming on margin) 

 collected 25 June 1980. 



length keys. Ages III through IX of the resultant 

 catch curves were analyzed by the methods of 

 Heincke (1913), Jackson (1939), Robson and Chap- 

 man (1961) and by finding the slope (m) of a 

 regression line fitted to l n (N y ) and y and substi- 

 tuting the equation a = 1 — e m . 



RESULTS 



A positive relationship was found between the 

 growth of the first dorsal spine and FL. The 

 relation between FL and R was as follows: FL = 

 4.58 i? 0951 with a correlation coefficient (r) of 

 0.84. The relation between FL and T was as 

 follows: FL = 24.87 T 1422 with r = 0.89. The 

 variation in the two relationships probably re- 

 sulted from the slight tapering of the spine in the 

 area from which the sections were taken and the 

 effect of sectioning. The Fh-R relationship was 

 used for back-calculation of sizes at previous 

 ages. The spine sections possessed distinct dark- 

 light banding patterns (Fig. 1) and the agreement 

 between readings as to the numbers of bands was 

 98% [Beamish and Fournier's (1981) index of 

 average error was 0.0072]. The translucent 

 (light) band formation occurred during spring 

 and summer (April to October with a peak during 

 June-July), and the mean marginal opaque in- 

 crement was least during this period of time 

 (Table 1). We thus considered the translucent 

 bands on the first dorsal spines to be annular 



TABLE 1. — Percent frequency of dorsal spines with translucent (light) margins and mean marginal 

 measurements of opaque (dark) margins in millimeters for gray triggerfish from northeast Gulf 

 of Mexico, 1979-82. 



486 



