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

ecapture, McDonald & Pitcher, 1979; Baker et al, 1991; Francis, 1995;
Ebert 1999) to confirm it.
An interesting potential of this model, thanks to variations in the
relations between l and τ, is the possibility of predicting growth of the
remaining fraction after elimination of largest animals (fisheries or
harvesting of largest fraction in aquaculture). Virtual individuals just
below minimum harvesting size suddenly become the largest fraction and
will exhibit a very rapid catch up growth to reach the maximum growth
speed curve (as evidenced by Grosjean et al, 1996, see Part III). This goes
far beyond the scope of this paper.
Relations with other growth models
Several authors have formulated general growth models, of which
many other models are just particular instances. Richards' model
D = a·(1 – e -b·(t – c) ) d is an extension of a von Bertalanffy 1 to a von
Bertalanffy 2 model with a variable exponent as an additional parameter d
(Richards, 1959; Ebert, 1980a). Depending on the value of d, it reduces to
one of the two von Bertalanffy's models (d = 1 or d = 3), to a logistic (d = -
1), or to a Gompertz curve (|d| → ∞) (Ebert 1999). Schnute (1981), from a
formulation of the derivative of growth rate with time, developed a
sophisticate model that contains most other ones, and also some
unexplored functions. These studies are most useful to show relations
between models that are sometimes hidden by different parameterizations.
For instance, it is hard to tell which is the relation between the Gompertz
(1825) curve and other models in Table 12 just by looking at their
equations.
Starting from von Bertalanffy 1 as the simplest asymptotic growth
model with no inflexion point, one possible contrasting classification of
derived models is 'dimensional' versus 'transitional'. A typical
'dimensional' model is Richards'. Parameter d is an exponent that changes
the dimension of the value returned by the function. Hence, with d = 1, we
Part IV: A growth model with intraspecific competition
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