Ballagh et al.: Methods for determining length-at-age for two large scombrids 
95 
adjusted methods for both sexes and the observed and 
category-adjusted methods for female S. semifasciatus. 
Significant differences in the estimates of K and t 0 were 
observed between the observed and category-adjusted 
methods, and no significant difference was observed be- 
tween any of the VBGF parameters for the two adjusted 
methods for male S. semifasciatus. 
Selectivity effects 
Comparison of length-at-age between the two back- 
calculation methods using ANOVA revealed significant 
differences in mean length-at-age existed for female S. 
commerson only (F 17 =2.13, P=0.039). Multiple t-tests 
revealed differences in mean back-calculated length for 
age-1 female (t 245 = 3.94, P<0.001), and age-1 (t 184 = 2.68, 
P=0.008), and age-2 G 129 = 2.38, P<0.019) male S. com- 
merson. 
Substitution of data 
Comparison of length-at-age between the back- 
calculation to all annuli and observed methods with 
ANOVA revealed significant differences in mean 
length-at-age for both species and sexes (S. commerson 
females: F x 9 =32.3, P<0.001, males: F x g =37.8, PcO.OOl; 
S. semifasciatus females: F 18 = 52.5, PcO.OOl, males: 
F x 9 =53.9, PcO.OOl). For S. commerson, t-tests revealed 
differences in mean length between back-calculated and 
observed methods for the first four consecutive ages for 
both sexes (females age 1: t 332 =20.39, PcO.OOl, age 2: 
t 2 i8=5.44, PcO.OOl, age 3: t 132 =2.14, P=0.034, age 4: 
t i 4 o = 3.54, PcO.OOl; males age 1: t 242 =17.72, PcO.OOl, 
age 2: £ 172 =8.61, PcO.OOl, age 3: t 104 =3.64, PcO.OOl, 
age 4: t 10S = 3.94, PcO.OOl), as well as age 6 for males 
(t 47 = 2.68, P=0.01). For S. semifasciatus, differences in 
mean length between back-calculated and observed 
methods were observed for the first three consecutive 
ages for females (age 1: t 353 = 16.61, PcO.OOl, age 2: 
t 329 = 6.00, PcO.OOl, age 3: f 250 =3.37, PcO.OOl), and the 
first two consecutive ages for males (age 1: t 332 =16.5, 
PcO.OOl, age 2: t 332 =5.43, PcO.OOl). Consequently, sub- 
stitution of observed and adjusted length-at-age with 
back-calculated length-at-age was done for the first four 
ages for male and female S. commerson, the first three 
ages for female S. semifasciatus, and the first two ages 
for male S. semifasciatus. Von Bertalanffy growth func- 
tions were then fitted to the combined data sets (Table 
4, Fig. 2). 
Growth estimates from substitution displayed a gen- 
eral pattern of higher estimates of K and lower esti- 
mates of L ^ than the respective observed or adjusted 
methods alone, and higher estimates of than the 
respective back-calculated methods alone (Table 4). 
All observed length-at-age data beyond age 8 for S. 
semifasciatus, and male S. commerson, and age 9 for 
female S. commerson, had a greater length than the 
back-calculated and substituted VBGF estimates (Fig. 
2). Comparison of the different combinations of sub- 
stituted methods revealed no significant differences 
for S. semifasciatus (Table 5). However, there were 
significant differences between some combinations for 
S. commerson, mostly for females (Table 5). Notably, all 
the significant differences occurred between combina- 
tions with BC-last and BC-all substituted data, with 
the combination of BC-last and observed data differ- 
ing to all combinations with BC-all data for female S. 
commerson. 
Discussion 
Alternative methods for estimating length-at-age from 
otoliths resulted in significant differences in estimates 
of growth. A clear pattern emerged that revealed 
large differences between the back-calculation (BC- 
all, BC-last) methods and the observed and adjusted 
methods (Obsv, Adj-cat, Adj-frm) for both species of 
mackerel. However, the pattern was more pronounced 
for S. commerson than for S. semifasciatus, most likely 
because of the more pronounced effects of selectivity 
on S. commerson length-at-age data. The method of 
substituting length-at-age data obtained from observed 
or adjusted methods with back-calculated length-at-age 
produced different estimates of growth to the individual 
methods. This technique proved valuable for providing 
estimates of population growth, which are likely to be 
more accurate than those provided with the individual 
methods alone, particularly in the presence of selec- 
tivity biases; the technique also improved estimates 
of length for younger ages over observed or adjusted 
methods and provided more realistic estimates of mean 
maximum length than estimates from back-calculation 
methods alone. 
A significant difference in growth between back- 
calculated length-at-age to all annuli and the last 
annulus was observed for S. commerson if the result 
of the overall likelihood ratio test is taken in isola- 
tion of the multiple comparisons with other methods 
(i.e., P<0.05), indicating that selectivity bias was in- 
herent in S. commerson samples. Comparison of the 
two back-calculation methods for S. commerson indi- 
cated that fish are fully recruited to the fishery at 
approximately 900 mm fork length, above which no 
difference in length-at-age was observed between the 
back-calculation methods. No significant difference was 
observed between the two back-calculation methods for 
S. semifasciatus and therefore indicated that selectivity 
was not biasing length-at-age data. 
In choosing which method! s) to use in determining 
length-at-age for growth estimation, careful con- 
sideration should be given to the growth characteristics 
of a species. We examined relatively fast growing 
species with similar growth characteristics in this 
study, and thus some of our conclusions may not be 
applicable or practical when applied to other species 
with different growth characteristics. Each method for 
determining length-at-age has its pros and cons, which 
differ depending on the growth characteristics of the 
species in consideration. 
