Panfili and Tomas: Validation of age estimation and back-calculation of fish length in tilapias 
149 
tion may be result of back-calculation model being differ- 
ent or the marking-recapture interval being longer. Sec- 
ond, rather than fish growth rates alone, it appears that 
the coupling between fish growth and otolith growth plays 
a major role in explaining the observed overestimation 
of fish length. As shown in our study, underestimation 
of back-calculated fish length corresponds more to otolith 
growth rates compared with fish growth rates, and vice 
versa. These aspects must be discussed in light of the re- 
lationship between fish size and otolith size, the influence 
of fish growth on the overestimation of fish length, and the 
evidence of uncoupling between fish and otolith growth 
rates (Mosegaard, et ah, 1988; Reznick, et al., 1989; Secor 
and Dean, 1989). Figure 6 shows that the higher the fish 
growth rates, the higher the deviation of the back-calcu- 
lated fish length, implying that the faster a fish grows the 
further the fish is from the model. Secor and Dean (1989) 
considered that the ratio of otolith size to fish size increas- 
es in starved fish, as well as in fish with slow growth rates. 
Thomas (1983) considered this relationship to correct the 
underestimation resulting from using the Lee back-cal- 
culation model. Because fish growth rates have an influ- 
ence on the observed estimations, they raise the question 
of what was the influence of fish growth rates on otolith 
growth rates along the sulcus axis in our study? Geffen 
( 1992) proposed establishing the relationship between fish 
and otolith growth rates prior to back-calculation. Unfor- 
tunately this method is difficult to achieve in the field be- 
cause it would mean marking fish from any studied popu- 
lations, which unfortunately rarely happens. 
Finally, Bradford and Geen (1987) advised caution 
when back-calculating fish length because otolith growth 
seems to be more conservative than fish growth. In our 
study, this assumption takes force because tilapias used 
in the experiments were starved before the beginning 
of the rearing experiments and experienced high growth 
rates after placement in ponds. Otolith growth rates fol- 
lowed fish growth rates within a certain range. When fish 
growth decreased below a certain limit, the otolith contin- 
ued to grow. When fish growth increased, otolith growth 
also increased to a certain extent. This finding confirmed 
that the rate of growth in otoliths is conservative com- 
pared with the rate of somatic growth. Furthermore, the 
otolith represents an essential part of the equilibrium 
and sensory system of fish and thus cannot follow only 
fish growth rates. As a result, high growth rates in fish 
will imply a bigger dispersion of the data, or heterocedas- 
ticity around the relation of fish length to otolith length, 
which is observed here for larger individuals. The uncou- 
pling of fish and otolith growth thus explains the differ- 
ence between back-calculated and measured fish lengths 
at marking. Therefore caution should be taken when es- 
tablishing the relationship of fish length to otolith length 
by using a representative sample of the individuals in 
their natural environment. In conclusion, the model de- 
veloped by Whitney and Carlander represents a valid 
model for studies in the field because it considers individ- 
ual variability in the relationship of fish length to otolith 
length but further work is needed to validate the use of 
other back-calculation models. 
Acknowledgments 
We specially thank Saurin Hem (IRD, Montpellier, France) 
and Philippe Cecchi (IRD, Bouake, Cote d’Ivoire) for their 
valuable help in marking and rearing experiments. We ack- 
nowledge the CRO (Centre de Recherches Oceanologiques, 
Abidjan, Cote d’Ivoire) and the IDESSAGnstitut des Savanes, 
Bouake, Cote d’Ivoire) for their logistic support during the 
rearing experiments. Thanks are also due to Jacques Baron 
(Universite de Bretagne Occidentale, Brest, France) for his 
assistance and guidance in the statistical treatments. Marcus 
Belchier helped with the English text. We thank him espe- 
cially. We also appreciate the comments of one anonymous 
reviewer which improved the manuscript. 
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