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

d. The von Bertalanffy curves
General introduction
The von Bertalanffy model, sometimes called Brody-Bertalanffy
(according to works of von Bertalanffy, 1938, 1957, and Brody, 1945) or
Pütter (in Ricker, 1979), is the first growth model specifically designed to
describe individuals. It is based on a simple bioenergetic analysis. An
individual is regarded as a simple dynamic chemical reactor where inputs
(anabolism) compete with outputs (catabolism). The result of these two
fluxes is growth. Anabolism is more or less proportional to respiration, and
respiration is surface-proportional for many animals (von Bertalanffy,
1957). Catabolism is always proportional to the volume or weight. These
mechanistic relationships are collected together in the following
differential equation when Y(t) measures a volume or a weight with time:
dY () t
2/3 1/3 2/3
= aYt ⋅ () −bYt ⋅ () = 3 k⋅⎡Y∞⋅Yt () −Yt
() ⎤
dt
⎣ ⎦ (9)
Solving this equation, we obtain the von Bertalanffy model in weight, also
called "von Bertalanffy 2" in the next part of this work:
−k⋅( t−t0) ( )
3
Yt () = Y ⋅ 1− e (10)
∞
The simplest form of this model occurs when one measures a linear
dimension for the body size, since a linear dimension is the cubic root of a
volume or a weight (not considering a possible allometry). The von
Bertalanffy for linear measurements, called von Bertalanffy 1 in the
present work, is simply:
−k⋅( t−t0) ( )
Yt () = Y⋅
1− e (11)
∞
A graph of both models is shown in Fig. 10. Von Bertalanffy 1 model
has no inflexion point. Growth is fastest at the outset, gradually
diminishes, and finally reaches zero. Growth is determinate and size
cannot exceed the horizontal asymptote of the curve at Y(t) = Y∞. Due to
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