518 



Fishery Bulletin 90|3). 1992 



was calculated from the Saila et al. (1988) statistical 

 package (FISHPARM program using Marquadt's non- 

 linear least-squares method) and fitted to mean back- 

 calculated lengths-at-age. The VBGF is 



Lt = L^ (1 - 



-K(t- 



'"'), 



where 



Lt 



Loc 



K 



t 



to 



= length at age t 



= asymptote of the growth-in-length 

 curve 



= Brody growth coefficient 



= age of the fish 



= the theoretical origin of the growth 

 curve, i.e., age at which fish would have 

 zero length if it had always grown in a 

 manner described by the equation. 



To establish chronological age at the time of first 

 opaque zone formation, data on the early growth of 

 juvenile red hind were assembled from field collections 

 and observations taken over 9-month periods follow- 

 ing spawning in January of 1985 and 1987 (Sadovy, 

 unpubl. data). Since spawning occurs over a limited 

 period, during, at most, 2 months each year (Erdman 

 1976, Beets and Friedlander 1992, Shapiro et al. In 

 press), and settlement may be assumed to occur be- 

 tween 3 weeks to 2 months after spawning (Colin et 

 al. 1987), growth rates of individuals in the months 

 following settlement could be estimated. 



160 zoo 240 280 320 360 400 440 480 520 



FORK LENGTH lmm| 



Figure I 



Size-frequency distributions of all Epinephelus guttatus col- 

 lected (stippled) from Puerto Rico and St. Thomas, and sub- 

 samples from which otoliths were analyzed (solid). 



Results 



Samples 



Of 1684 Epinephelus guttatus collected from Puerto 

 Rico, otoliths were sectioned from 1098. Opaque and 

 translucent zones were detectable in almost all otolith 

 sections. When zones lacked sufficient definition for 

 focus-to-ring measurements, the otoliths were dis- 

 carded as unsuitable for use in calculating growth 

 parameters, although some were used to assign ages 

 to sexed fish by counts of opaque zones. A total of 624 

 (63%) otoliths were used to count growth zones and for 

 focus-to-ring measurements. Of these, a subsample of 

 73 otoliths was read by an independent researcher; only 

 one was rejected because of a discrepancy of more than 

 one zone compared with our readings. Of the 501 St. 

 Thomas samples, otoliths were sectioned from 490, and 

 162 (33%) were judged to be sufficiently clear for 

 analysis; it is not known why otolith legibility was so 

 low for St. Thomas samples. 



Size-frequency distributions of all fish collected in 

 Puerto Rico and in St. Thomas, and the subsamples us- 

 ed for analysis of otoliths from each location, are shown 



in Figure 1. For Puerto Rico, size-frequency distribu- 

 tions of individuals and subsamples used for age deter- 

 mination did not differ significantly (Kolmogorov- 

 Smirnov: D = 0.043, NS). This confirmed our impres- 

 sion that illegible otoliths occurred at all fish sizes and 

 ages, and affirmed that their elimination introduced no 

 bias to the calculation of growth parameters. For St. 

 Thomas, however, the distributions differed signifi- 

 cantly (D = 0.150, p<0.05). Therefore, growth param- 

 eters derived for St. Thomas should be treated with 

 caution. 



Frequency distributions of the distance from the 

 focus to each opaque zone in Puerto Rico collections 

 are shown in Figure 2. Relationships of SL:FL and 

 W:FL were established for each location. 



Puerto Rico: 



FL = 3.86-H 1.2044 SL (r2 0.99; Af 227) 



LogW =-5.21-^3.1422 Log FL (r^ 0.97; A^ 1619) 



St. Thomas: 



FL = 24.49-H 1.1101 SL (r2 0.98; Af 494) 



LogW =-4.68-1-2.9402 Log FL (r2 0.92; iV 493) 



