Growth model of the reared sea urchin Paracentrotus ... - SciViews

General conclusions
GENERAL CONCLUSIONS
By focusing on variability and interactions in individual growth of the
reared sea urchin Paracentrotus lividus, we raised questions on the
adequacy of existing models and methods. To resolve these problems we
developed a new growth model with incorporating interspecific
competition by defuzzifying a fuzzy model and a quantile regression
method was adapted to account for individual variability (envelope
modelling). The model appears to be an appropriate functional description
of the process, as it is in agreement with all experimental results. It allows
quantifying the degree of growth inhibition in the P. lividus echinoids in
cultivation.
Similarly, one should question the validity of growth models, of fitting
methods and of calculation of size at age (growth ring analysis, sizefrequency
data analysis, mark and recapture) in all studies on either reared
or wild echinoids. Yet, if there is some interaction between individuals or
if individual variability is large (as both can be suspected in most if not all
cases), all these methods could lead to biased estimations of growth and,
consequently, to erroneous inferences about population dynamics.
Adequate tools remain to be developed for field data where age is not
measurable without error. A modification of the new model for relative
growth rate data would be a logical starting point.
The new model clearly has application both in sea urchin aquaculture
and in fisheries management. Indeed, the experiment with mixed Ff and Fg
batches (see Part III, p. 130) indicated a great growth potential of smaller,
inhibited individuals in a heterogeneous population. Yield per surface unit
should improve in cultivation when using mixed batches because they are
almost as productive as small plus large batches reared separately and thus,
on the double of the surface. If the mechanism of inhibition/catch up
growth also occurs in the field, a bimodal size distribution could be the
most efficient configuration to maintain a wild population of sea urchins.
When the largest fraction of the population is harvested, some mid-sized
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