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

i. The Preece-Baines 1 model for human growth
Y
1
Y• 0.8
0.6
0.4
0.2
General introduction
Preece and Baines (1978) described various growth models specific to
human growth. These models combine two different exponential growth
phases to represent the gradual growth of infants followed by a faster
growth of adolescents, but becoming rapidly asymptotic (Fig. 15). These
are indeed very flexible models. Among these curves, model 1 was used
for a sea urchin by Gage and Tyler (1985) and is:
2( ⋅ Y∞−d) Yt () = Y −
e + e
∞ k1⋅( t−t0) k2⋅( t−t0) 2 4 6 8 10 t
Figure 15. Example of a Preece-Baines 1 curve with k1 = 0.19, k2 = 2.5, Y∞ = 0.95, d = 0.8
and t0 = 6.
j. The Tanaka model for indeterminate growth
(16)
All the previous models are asymptotic, except the exponential one
(but it is only usable for the initial stages of a growth process). They
describe determinate growth that can never exceed horizontal asymptote at
Y(t) = Y∞. Knight (1968) questioned whether it is a biological fact or just a
mathematical artifact. In the later case, growth seems to be determinate
only because mathematical models used to represent it are asymptotical.
To overcome this constraint, Tanaka (1982, 1988) elaborated a new model
that allows for indeterminate growth:
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