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

considered factor on the curve's shape). For instance, current models
hardly cope with a superimposed effect of intraspecific competition on
growth, though the latter was evidenced in sea urchins (Ebert, 1977;
Himmelman, 1986; Levitan, 1988; Grosjean et al, 1996) as in many other
species (Branch, 1974, for the limpet Patella cochlear Born; Timmons &
Shelton, 1980, for the largemouth bass Micropterus salmoides (Lacepede);
Kautsky, 1982, for the mussel Mytilus edulis L.).
One method to model growth in a functional way is by building
equations that directly represent underlying processes, i.e., by elaborating a
dynamic model that balances inputs (food, oxygen intake…) and outputs
(carbon dioxide, feces…) from which it is possible to calculate variation of
size with time, thus yielding an estimation of growth. This is the
bioenergetic and/or ecophysiologic approach, using the scope for growth
concept, which has proved very successful for filter feeders (Willows,
1992). Such an approach requires a lot of measurements and equations. It
is most often used in the simplest cases, where environmental conditions
are constant, or vary in a very predictable way, like in a protected reef
lagoon for cultivated pearl oysters (Pouvreau et al, 2000). Indeed, similar
studies on European oyster cultures in the intertidal zone –a very changing
and unpredictable environment– lead to a much more complex model
(Bacher et al, 1991). As far as we know, no such model has been
completely successful when applied to sea urchins because a large part of
the carbon or energy absorbed is lost as dissolved organic matter that is
hard to quantify and to enter in equations (Miller & Mann, 1973; Lawrence
& Lane, 1982).
Being a basic feature of life, growth has been widely explored but it
still remains unsatisfactorily modelled in a functional way, possibly
because of the approach used. Most growth models were elaborated from
their differential equations. Functions obtained by solving these equations
were then systematically used to determine growth of a "mean individual"
(by least-square regression) and no parameter of the model was
constrained using particular knowledge (such as size at birth or at
Part IV: A growth model with intraspecific competition
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