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

involved processes). It is thus appropriately described by a 'transitional'
model. However, by fitting data, only the shape that is matched or not by
the model is considered. Consequently, 'dimensional' models fit equally
well, although their mathematical formulation does not match biological
observation.
Considering this distinction, we can now formulate a model that is both
'dimensional' and 'transitional':
⎛ −k1⋅t' 1−e m
⎞
0 ∞ −k2⋅t' Yt (') = Y+∆Y⎜ ⎟
⎝1+ l ⋅e
⎠
Part IV: A growth model with intraspecific competition
(40)
Y being any kind of measurement of size and m (corresponding to d in the
Richards model) indicating the power transformation required to be in the
best 'dimension of growth'. To further generalize eq. 40, we could also
replace k1·t' (the chronological time modulated by a constant kinetic
parameter) with tM, the metabolic –or physiologic– time (Brody, 1937),
using:
t = f( t, x , x ,..., x )
(41)
M 1 2 n
where x1-n are environmental variables that modulate growth, e.g., season
(Cloern & Nichols, 1978) or temperature (Muller-Feuga, 1990). This
gives:
−t
m
M ⎛ 1−e ⎞
= 0 +∆ ∞ ⎜ −kt ⋅ ⎟ M
Yt (') Y Y
⎝1+ l ⋅e
⎠
(42)
where k = k2/k1. This is a general functional model for an asymptotic
growth that derives from the von Bertalanffy 1 curve. Therefore, we call it
a generalized von Bertalanffy model. This model is impossible to fit
without some precautions because the two effects, 'dimension' (m) and
'transition' (l and k), are impossible to separate with solely a shape
criterion. From a fitting point of view, this model is overparameterized
(Draper & Smith, 1998). The dimension parameter m must first be
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