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

∆D∞
D0 +∆D∞ − D0 +∆D∞
/ l
Dt (') = D0−
+ ⇔
−kt ⋅ '+ ln( l)
l 1+ e
Dt (') = D +
−kt ⋅ '
∆D∞⋅( −1−l⋅ e + 1 + l)
0 −kt ⋅ '
l⋅ (1+ l⋅e
)
which gives, after further simplification:
Dt (') = D +∆D
1−e 1+ l ⋅e
−kt ⋅ '
0 ∞ −kt ⋅ '
Part IV: A growth model with intraspecific competition
(38)
(39)
Eq. 39 is equivalent to eq. 29 where k1 = k2 = k. Thus the 4-parameter
logistic is another parameterization of the new growth model where both
growth speed constants k1 and k2 are equal. With this new
parameterization, reduction to a von Bertalanffy 1 model when l = 0 is
now obvious. The 4-parameter logistic model also represents a transition
between same sets S and L as our fuzzy model, but with k1 = k2. It is a
mathematical coincidence that the same model represents also, with
another parameterization, a transition between two constant states,… a
misleading coincidence as it hides its affinity with the von Bertalanffy 1
model!
Whether eq. 29 or eq. 39 is more appropriate to describe P. lividus
growth is hard to tell. From a biological point of view, we do not see any
reason why k1 should equal k2, but we perhaps miss it. Without
confidence intervals on parameters, it is not possible to show if k1 is
significantly different of k2 for the dataset studied (see Fig. 32B).
The distinction between 'dimensional' and 'transitional' models does not
help to explain why one model fits the data better than another. On the
contrary, both types fit data very well. Indeed, dimension change
('dimensional' models) and inhibition of growth ('transitional' models) both
have the same effect on the shape of the von Bertalanffy 1 function: they
transform a curve without inflexion point into a sigmoid. P. lividus growth
data are S-shaped for low τ values because of an inhibition caused by an
intraspecific competition (according to background knowledge on the
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