Lucena and O'Brien: Effects of gear selectivity and different calculation methods on growth parameters of Pomatomus saltatnx 
435 
la corresponded to mean values of back-calcu- 
lated lengths-at-age; and 
lb represented individual back-calculated lengths- 
at-age. 
Criterion II identified the type of data to be 
used: 
Ha corresponded to the back-calculated length- 
at-age derived from the last annulus only; 
and 
lib represented the back-calculated lengths-at- 
age derived from all the annuli up to the 
sampling age. 
We calculated growth parameters by using four 
methods for each gear: method 1 (where criteria 
la and Ha were used), method 2 (where criteria 
la and lib were used), method 3 (where criteria lb 
and Ha were used), and method 4 (where criteria 
lb and lib were used). 
The growth curves were estimated with the program AD 
Model Builder (Otter Research, 1996), which uses an au- 
tomatic differentiation algorithm to estimate the param- 
eters of a nonlinear function with an appropriate objective 
function. The software allows the calculation of confidence 
intervals for parameter estimates with asymptotic normal 
approximations. 
The objective function considered is the nonlinear least- 
squares regression criterion, R(.), either given by 
n=816 
n = 10 
n = 228 
n = 57 
Figure 2 
Relative proportion (%) of bluefish caught by various fisheries oper- 
ating off Brazil’s southern coast. 
l 
R{KXt 0 \O) = ^O t -L,? 
3 yr) and purse-seine fisheries caught fish of ages 1-7 
(mode=2-3 yr). Trawlers caught fish of ages 1-7. Individ- 
uals of ages 5 to 7 represented less than 2% of samples 
(individuals of 5 to 7 years old were underrepresented 
also in the back-calculation procedures). The deep-water 
(to 200 m) gill-net fishery targeting P. americanus caught 
individuals of age 5-10 and the only fish older than age 7. 
There was a considerable overlap in the range of observed 
lengths-at-age (Table 2), nevertheless significant differ- 
ences between gears were detected for some ages. Gill nets 
caught larger individuals of ages 1 and 2 and smaller 
individuals of ages 3-5 than purse seines. Trawls, on the 
other hand, appear to catch smaller individuals in all age 
classes. 
when mean values are considered, or given by 
T n, 
R(LM l°,) = £X (0 ' I - L ') 2 ’ 
t=l f=l 
when individual values are considered. 
Note that O t is the mean back-calculated length-at-age 
t, O ti is the ith individual back-calculated length-at-age t, 
T denotes the maximum number of distinct ages, and n t 
is the number of observations at age t. To compare growth 
curves between gears, Hotelling’s t-test (1979) was used. 
Results 
Age structure of the stock 
We examined a total of 1159 fish and 94% of samples were 
collected during the fishing season (June to September) — 
the remaining numbers represented bycatch during the 
off-peak season. Age determination (Fig. 2) indicated that 
the gill-net fisheries caught fish of ages 1-5 (mode= 
Weight-length relationship 
We found no statistically significant differences in length- 
weight relationships between gear types or between sexes 
(f-test, P>0.05). The relationship for both sexes and all 
gears combined is illustrated in Figure 3. 
Body-scale relationship 
Gear-specific regressions of TL on S (Fig. 4) showed that 
gill nets tended to catch the fast-growing fish of younger 
ages and the slow-growing individuals of older ages. These 
faster-growing younger fish (<360 mm TL, 1-2 years) have 
smaller scales than similar-size purse-seine-caught fish 
U-test; P<0.05). By contrast, the slower-growing fish (>410 
mm TL, 4—5 yr) had larger scales than fish of a similar 
length caught by the purse-seine fleet. For the length 
range that the gill nets target most efficiently (360-410 
mm TL, age 3), the TL-S relationship for both gill net and 
purse seine was similar. 
Periodicity of growth increments 
Our limited data showed marginal increment to be lowest 
in January-February, corresponding to ring deposition. 
