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

evaluated on basis of biological knowledge: determine the relation
between the dimension of growth and that of the measurement Y that
evaluates it.
But is there a privileged dimension when measuring growth? We have
already asked this question and must come back to it now, because two
concurrent observations suggest that the best dimension to describe growth
in the case of P. lividus is linear. First, using a linear measurement (the
diameter D), basic shape of growth curve, in absence of inhibition, is
exactly the von Bertalanffy 1 model, without inflexion point. With a
weight or a volume to evaluate size, growth of the largest (not inhibited)
fraction in the batch would have followed a more complex von Bertalanffy
2 sigmoidal model and it would have been difficult to distinguish the Sshape
due to dimension from the S-shape due to inhibition. With a linear
measurement, everything is clear: no S-shape means no inhibition and Sshape
means inhibition. Second, the diameters are normally distributed
before (at t' = 0) and after the growth process (when the asymptotic size is
reached that is, above 1600 days, see Fig. 28A). Normal distribution for
linear measurement means that size distribution of corresponding weight
or volume measures must be asymmetrical. In this circumstance, the
envelope model (eq. 35) would have been more difficult to fit because
eq. 34, normal distribution of ∆Y∞(t), is not correct any more. Hence, the
preferred dimension to describe growth of P. lividus seems linear. Using a
linear measurement of size, like the diameter D, we are in the right
dimension and parameter m in eq. 40 equals one, and thus, the model
reduces to eq. 29. If we had chosen to measure weight, we would have
been in a "wrong dimension" to describe growth and a transformation to
the right dimension would imply m ≈ 3 (or more precisely, the allometric
coefficient between weight and diameter).
Part IV: A growth model with intraspecific competition
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