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

Constraining parameters as we did in eq. 30-34 leads to a double benefit.
First, it simplifies the model. In the present case, we started with a 5parameter
unconstrained classical model (eq. 29) and we ended with a 5parameter
constrained envelope model (eq. 35). Yet, the latter contains
much more information than the former. Second, if constraints are
formulated according to some knowledge about the underlying
phenomenon (value of the intercept corresponding to actual initial size) or
to some reasonable hypotheses (relation between l and τ, in regard with
information in the literature), parameters remain meaningful in the fitted
model. A correct formulation of both the initial unconstrained model and
of superimposed constraints is a bit of an art. It requires many trials and
errors, much patience and perseverance. But at the end, it pays off with a
model whose parameters are fully functionally interpretable, even on real
data.
Fitting and individual variations in growth
A good fitting is not a criterion for deciding if a model is adequate
(Fletcher, 1974). Choosing an inadequate model that fit the data very well
is not problematic if that model is just used for descriptive purposes. It
turns out to be a problem when parameters are functionally interpreted or
if it is used in population dynamic simulations. In this case, individual
variation should not be simply considered as an independent, normally
distributed "error" whenever it is not. Individual variation has often been
overlooked in the literature. The most aberrant calculations could result
from such mistakes. For instance, Basuyaux & Blin (1998) extrapolated
over 4 years a growth model for P. lividus where size distributions were
supposed to be normal and using measurements from 7 to 23 months only.
They calculated the fraction of the size distribution that would reach 40
mm (the minimal market size) with time on basis of this extrapolation.
Many techniques for population dynamic analyses are based on the
assertion that cohorts should distribute normally, including most recent
ones (Smith & Botsford, 1998; Morgan et al, 2000) and could be also
Part IV: A growth model with intraspecific competition
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