Panfili and Tomas: Validation of age estimation and back-calculation of fish length in tilapias 
145 
Table 5 
Linear regressions between the number of microincrements (N inc ) and the number of days between marking or birth and capture 
(D),Z) = a + b x N inc and Student tests for slope (6=1) and intercept (a=0) for Oreochromis niloticus. F = result of model ANOVA; ns = 
no significant difference (P>0.05); r 2 = coefficient of determination; s = significant difference (P<0.05). 
Intercept Slope 
Group 
n 
F 
r 2 (%) 
a 
t 
a = 0 
6 
t 
6 = 1 
Juveniles 
43 
1122.6 
96.5 
0.293 
0.21 
ns 
0.975 
-0.85 
ns 
Adults 
52 
1264.9 
97.0 
-4.522 
-3.47 
s 
0.989 
-0.45 
ns 
Juveniles and adults 
95 
1696.5 
94.8 
-1.347 
-1.12 
ns 
0.963 
-1.59 
ns 
ber of days of growth explains the num- 
ber of microincrements counted. Never- 
theless, the intercept differed from 0 for 
adults (P<0.05). It therefore seems that 
the deposition of new increments did not 
start on the first day after marking and 
that this difference (5 d) remained con- 
stant for one to two months of growth 
(Tables 4 and 5), suggesting that the in- 
crement technique is accurate for esti- 
mating the age of O. niloticus in days. 
Residual dispersal was similar for 
adults and juveniles and seems constant 
through time (coefficient of variation in 
Table 4 and Fig. 3). Age was especially 
overestimated in juvenile fish (Fig. 3). 
As for S. melanotheron, a difference be- 
tween the number of increments and the 
number of growth days equal to zero was 
very rare with O. niloticus otoliths. The 
trend in the deviation of the age estima- 
tion was the same over time for a given 
pond (Fig. 3). 
Validation of back-calculation of 
length in Oreochromis niloticus 
14 -- 
12 -- 
10 -- 
8 -- 
6 -- 
Q 
0 
-2 -- 
-4 -- 
-6 -- 
-8 -- 
— I- 
10 
20 
O 
□ 
□ □ 
□ □ 
, □ 
— h- 
40 
□ 
o 
o 
□ o 
o 
□ 
o 
□ o 
□ o 
o 
□ □ o 
□ o 
□ □ 
□ 
□ o 
□ □ 
-I ¥— B 1 
□ o 
50 D 70 
□ □ 
□ 
o 
D(d) 
Figure 3 
Individual differences between the number of days of growth (D) and the 
number of microincrements counted on transverse otolith section (IV ) for 
adults (O) and juveniles (□) Oreochromis niloticus. 
The relation between fish length and oto- 
lith length was determined by establishing the regression 
of fish standard length at capture on the otolith radius 
at capture (Table 6). Both the linear and the multiplica- 
tive models were tested by an ANOVA ( F calculated. Table 
6) and had highly significant relationships (P<0.001). A 
comparison of the variances suggested that the coefficient 
of determination in the multiplicative model was signifi- 
cantly higher than that in the linear model (P<0.05). As a 
result, the regression used for the back-calculation of fish 
length was the multiplicative form. The observed disper- 
sion of residuals reinforced this choice. 
The observed low value of r 2 for the linear regression 
was due to the importance of the dispersion of points 
around the model for adults (Fig. 4). Nevertheless, this 
dispersion was also observed in the relation between fish 
length and otolith diameter at capture (Fig. 4), prior to 
any otolith preparation. In this case the linear regression 
had a higher coefficient of determination (Table 6). The 
dispersion can be explained by the natural growth varia- 
tion which appears with age, and which is strong for this 
species. 
The back-calculated formula used to compare the ob- 
served length at marking and the back-calculated length 
with otolith transverse sections was therefore 
Log(SL mh ) = 0.899278 x Log 
' R n 
+ Log(SL i ). 
(7) 
Back-calculated lengths at marking were overestimated 
in the whole sample and this tendency did not depend on 
fish size at marking (Fig. 5). The mean of the differences 
