Lucena and O'Brien: Effects of gear selectivity and different calculation methods on growth parameters of Pomatomus saltatrix 
439 
Table 4 
Growth parameters and correlation between k and for different methods (1-4), and respective criteria (la, lb, Ha, lib) of back- 
calculation. Standard errors are given in parenthesis. “ — “ denotes that parameter estimates did not converge to a solution. 
Parameters 
Purse 
seine 
Gill net 
[1] 
Ia-IIa 
[2] 
Ia-IIb 
[3] 
Ib-IIa 
[4] 
Ib-IIb 
[1] 
Ia-IIa 
[2] 
Ia-IIb 
[3] [4| 
Ib-IIa Ib-IIb 
L x 
773 (32.6) 
743 (26.6) 
754(53.8) 
670(55.2) 
496(21.3) 
491 (17.1) 
589 (45.3) 
k 
0.25 (0.03) 
0.27 (0.03) 
0.26 (0.04) 
0.35 (0.07) 
0.65 (0.14) 
0.71 (0.13) 
0.39 (0.08) 
^0 
-0.21 (0.12) 
-0.27 (0.12) 
-0.15 (0.12) 
-0.09 (0.13) 
0.03 (0.20) 
0.09 (0.17) 
0.27 (0.2) 
r(k,LJ 
-0.97 
-0.97 
-0.98 
-0.98 
-0.89 
-0.87 
-0.98 
Discussion 
Back-calculation of length is widely used to obtain growth 
curves, to estimate length-at-age of individuals that are 
rarely observed, to compare growth differences among 
populations or sexes of the same species, and even to illus- 
trate gear selectivity (Francis, 1990). However, this tech- 
nique is poorly understood (Francis, 1990; Rijnsdorp et 
al., 1990) and some of the sources of bias in using the 
technique are 1) inaccurate counts of annuli and incor- 
rect estimation of time of formation of the growth mark; 
and 2) an erroneous choice of the mathematical function 
to describe the body-scale relationship. In respect to the 
first source of bias, our results corroborate the findings 
of Krug and Haimovici (1989). In respect to the body- 
scale relationship, the main concern of Francis ( 1990) was 
to decide whether the appropriate regression was TL on 
S (body proportional) or S on TL (scale proportional). 
The small difference between the back-calculation derived 
from the two approaches for the bluefish can be a mini- 
mum measure of precision of the back-calculation proce- 
dure (Francis, 1990). Campana (1990) and Wright et al. 
(1990) pointed out that slow-growing fish have larger bony 
structures (scales or otoliths) than fast-growing fish of 
the same size. For the bluefish body-scale relationship, 
we attribute this effect to gear selectivity. The fast-grow- 
ing fish (ages 1 and 2 from the gill-net catches) tend to 
occur above the purse-seine curve and the slow-growing 
fish (ages 4 and 5 from the gill-net catches) tend to occur 
below the purse-seine curve in a TL-S relationship. 
An additional source of bias may be introduced depend- 
ing on whether mean back-calculated lengths-at-ages or 
individual lengths-at-age are used to fit the von Berta- 
lanffy equation. The estimated growth parameters derived 
from the two methods may differ considerably (Hilborn 
and Walters, 1992). Use of mean values would ignore indi- 
vidual variability in length-at-age, giving the same weight 
for possibly uncertain ages because of low sample sizes. 
We suggest that back-calculated lengths-at-age derived 
from the last annulus only (criterion Ilahbe used rather 
than the back-calculated lengths-at-age derived from all 
annuli (criterion lib). Many investigators continue to use 
mean-weighted data (all annuli) (e.g. Krug and Haimov- 
ici, 1989; Barger, 1990) — a procedure in violation of the 
least-squares assumption of independence of sample ele- 
ments (Draper and Smith, 1966). This assumption is vio- 
lated when multiple measures from a single fish are used. 
Use of the last annulus only does not use all information 
available about growth of all cohorts and may result in an 
incorrect estimate of lengths-at-age for age classes absent 
or infrequently caught. However, if representative sam- 
ples are available for younger age groups, the use of back- 
calculated lengths-at-age derived from the last annulus 
only is to be preferred. 
Ricker (1969) noted that where differential mortality 
exists, the calculated average length of a particular age 
class calculated from the last annulus differs from the cal- 
culated average length of an age class calculated from pre- 
vious annuli — the latter representing the former size of 
the fish that has survived to the sampling age. The differ- 
ential mortality may be due to natural or fishing causes 
but under these circumstances, the average size of fish in 
the year class becomes different as time passes and the 
frequency distribution of the survivors would become pro- 
gressively skewed. Gutreuter (1987) suggested that back- 
calculation should be restricted to the most recent annu- 
lus to avoid bias from size-selective sampling. 
Gear selectivity can influence estimates of growth para- 
meters (Ricker, 1969; Potts et al., 1998), and we found that 
gear-related differences in parameters were significant. 
Gill nets, on the basis of their mesh size, are a selective 
gear. Trawls are selective for smaller fish that may not be 
able to avoid the nets because of slower swimming speed 
(Hilborn and Walters, 1992). Purse seines are probably 
a less selective gear (Cushing, 1968). Observed lengths- 
at-age reflect the differences in selectivity between gears. 
Gill nets catch the faster-growing fish at age 1 and 2 and 
the slower-growing fish at age 4 and 5, and trawls catch 
the smaller individuals for each age. 
The high selectivity of gill nets is visible in the body- 
scale relationship, the mean observed length-at-age, and 
in the back-calculated lengths-at-age which indicate the 
presence of Lee’s phenomenon (Lee, 1920). Size-selective 
mortality — caused by the differing catchabilities of fish at 
different sizes — is the probable reason for Lee’s phenom- 
enon in back-calculation of lengths from gill-net catches. 
