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Fishery Bulletin 99(1 ) 
first day (intercept equal to 0). The difference between the 
number of microincrements and the number of days of 
growth was plotted against time. 
Validation of back-calculation for Oreochromis 
niloticus 
Using tagged individuals, we assessed the validity of back- 
calculating fish length at marking. Several back-calcula- 
tion models are described in the literature and each one 
assumes a different relationship between fish growth and 
otolith growth (Francis, 1990). Francis (1990) recommends 
Whitney and Carlander’s model where a constant propor- 
tionality between fish growth and otolith growth through- 
out the life of the fish is assumed. Moreover, Francis ( 1990) 
recommends the regression of fish length against otolith 
length. Two approaches were considered in this study. 
If the relationship between fish length and otolith length 
was linear, 
SL c = a + b x R c 
( 1 ) 
G SL (%/d) = 
log (SL c ) - log( SL m ) 
I) 
x 100 
G OL {% Id) 
log(fi„)-log(fl „) xl00 
(5) 
( 6 ) 
where SL c = standard length at capture; 
SL m - standard length observed at marking; 
R c = otolith radius at capture; 
R m = otolith radius at marking; and 
D ~ number of days of growth. 
The relationships between these specific growth rates 
and the differences between observed and back-calculated 
lengths at marking were established. 
Results 
Microincrement identification and tetracycline 
labeling 
with a body proportional hypothesis (BPH), then the back- 
calculation formula would be 
SL, 
i h 
a + bx R m 
a + bx R 
xSL. 
( 2 ) 
If the relationship between fish length and otolith length 
was nonlinear and for example multiplicative, 
Log(SL c ) = c + d x LogiR c ) (3) 
with a body proportional hypothesis (BPH), then the back- 
calculation formula would be 
Log ( SL mh ) - d x Log 
+ Log(SL c ), 
(4) 
where SL r = standard length at capture; 
SL inb = back-calculated standard length at marking; 
R c = otolith radius at capture; 
R m = otolith radius at marking (tetracycline 
mark); and 
a, b, c, d = constants. 
The validation of the back-calculation model was carried 
out on otoliths of adult O. niloticus labeled with tetracy- 
cline. For each individual, fish length measured at mark- 
ing iSL m , millimeters) was compared with the individual 
fish length back-calculated at marking from the otolith 
( SL inb , millimeters). The mean of the differences between 
measured and back-calculated fish lengths was compared 
by means of a Student test with a theoretical mean equal 
to 0. 
The specific growth rates of the fish length ( G SL in %/d ) 
or of the otolith radius length (G OL in %/d) were calculated 
following Ricker s formula (1975): 
Preparing tilapia otoliths for examination is time-consum- 
ing; it takes sixty to ninety minutes to prepare one otolith. 
A final polishing with 1 /3 pm alumina powder is an impor- 
tant improvement for microstructure reading when deal- 
ing with thin sections ranging between 10 and 40 pm of 
thickness. The central core of the otolith of both species 
seems to correspond to the fusion of several primordia (up 
to six) even though it remains a small structure easily 
recognizable during the grinding process. Two accessory 
growth centers are visible on any transverse section of 
juvenile otoliths between the 13th and the 28th microin- 
crements. They are located on both sides of the core on 
the dorsal and ventral halves of the otolith, where they 
appear to control the growth of the otolith on the dorso- 
ventral axis. Microstructures are more clearly identified 
along the sulcus or along the dorsoventral axis as typically 
alternated L-zones and D-zones. Cross-checking and nar- 
rower microstructures are more common on the dorsoven- 
tral axis than in the sulcus region. As a result, we chose 
to interpret the microincrements along the sulcus axis 
(Fig. 1). Microincrements were counted from the hatching 
check which was clearly identifiable in the core area. For 
at least the first 30 microincrements the otolith grows 
predominantly along the dorsoventral axis and towards 
the external face. To avoid underestimating the number 
of microstructures during this first growth stage, the first 
15 to 20 microincrements were counted along the core- 
ventral axis. Other microstructures along the ventral axis, 
interpreted as subdaily increments, rapidly increased in 
number and made the reading difficult. The shift to the 
sulcus axis was completed by following any conspicuous 
microincrement along the core-ventral axis to the sulcus 
region where the reading was finished (Fig. 1), provided 
accessory growth centers had not been encountered in this 
area. 
The tetracycline mark was present in all otoliths ex- 
amined, except one otolith of S. melanotheron sampled in 
April 1994. The mark was more intense on O. niloticus 
