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

General conclusions
In this classification, all models derive from simplest forms described
by the general differential equation y' = ay m - by n , that is, a damped
exponential growth with the first term being the limiting factor and the
second one representing the exponential growth (Fletcher, 1974; Mueller-
Feuga, 1990). The various forms of basic growth models are obtained from
different particular values for m and n. With m = 1 and n = 1, we obtain the
exponential growth, which is a simple indeterminate growth model. If
m = 0 and n = 1, we get the von Bertalanffy 1 model (von Bertal. 1),
which seems to be the simplest determinate growth model for individuals.
If m = 1 and n = 2, we obtain the logistic curve, which is probably the
simplest determinate growth model for populations (Verhulst, 1838). It is
not clear if other solutions of the differential equation could be considered
as useful roots in the classification. Some solutions correspond to more
complex models that are best placed in a stem instead of as a root in this
classification. For instance, using m = 2/3 and n = 1, we obtain the von
Bertalanffy 2 model that we prefer to position inside the "von Bertalanffy
1 family" (see Fig. 35). Some authors have generalized this differential
equation (Fletcher, 1974; Schnute, 1981) to a point that it describes almost
all existing models. Our concern here is just to derive the simplest models
as roots of our classification tree and consider a di- or a polychotomous
system to position more complex models in the tree as generalizations of
the simplest root models. One should consider each of the simplest models
as the root of a distinct tree. However, in our presentation (Fig. 35), we
mixed all existing models in a single tree for conciseness (because, except
for the "von Bertalanffy 1 family", the trees would not been much
populated).
Starting from those simplest models, one could consider a first
dichotomous separation: monophasic versus polyphasic models. While
the group of monophasic models is more populated (because they probably
represent more common growth processes), the second group contains two
items:
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