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

Y
Y
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Y• 0.8
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General introduction
the cubic power transformation of von Bertalanffy 1, von Bertalanffy 2 is
an asymmetrical sigmoid like the Gompertz model.
1 2 3 4 5 6
Figure 10. Both von Bertalanffy 1 (curve in bold) and von Bertalanffy 2 (plain curve) models
with k = 1, Y∞ = 0.95 and t0 = 0. Both models describe asymptotic growth, but von
Bertalanffy 1 has no inflexion point, while von Bertalanffy 2 is sigmoidal.
e. The Richards model, a flexible curve that contains many
others
The general scheme for von Bertalanffy models is:
t
−k⋅( t−t0) ( )
m
Yt () = Y⋅
1− e
(12)
∞
Von Bertalanffy (1938, 1957) set m at either 1 or 3. Richards (1959) lets m
vary freely and thus his model has an additional parameter. This curve is
very flexible (Fig. 11) and one can demonstrate several other growth
models are just special cases with different m values. We have already
observed it reduces to von Bertalanffy 1 when m = 1, and to von
Bertalanffy 2 when m = 3. It also reduces to the logistic curve when m = -1
and one can demonstrate it reduces to the Gompertz model when |m| → ∞
(Tomassone et al, 1993; Ebert, 1999).
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