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

It does not consider respiration associated with gonadal growth or
gametogenesis. There are two possibilities for mature individuals: either
gonadal growth competes with somatic growth (and the later should be
lower than predicted while β remains 0.67) or it just adds to it (and β
should be somewhat larger). Giese et al (1966) measured no difference in
the respiration of S. purpuratus in function of gonad index. This could
indicate a competition between somatic and gonadal growth in the
presence of a limiting factor. However, it should imply a different somatic
growth model for juveniles and adults. In the present case, a single model
fits both juvenile and adult stages for reared P. lividus. Measurements of
respiration and a more accurate comparison between both phases are
required to evidence a possible effect of maturity on the somatic growth
curve. In any case, β-values between 0.6 and 0.8 do not contradict von
Bertalanffy's law. Thus, the present study rehabilitates its theory that was
too often rejected after observation of a sigmoidal growth (and now we
know it could result from an inhibition).
Functional analysis of the constrained parameters
Constraining the model to the origin is very easy, in theory. Most
models in Table 12 and also eq. 29 have a free intercept. It could be
formally expressed: D0 in eq. 29, or it could be hidden in the
parameterization: a⋅(1 – e bc ) for von Bertalanffy 1, a - d for Weibull, for
models of Table 12. Unconstrained intercept means the parameter
representing size when the growth process initiates is estimated at the same
time as all others, and is thus influenced by their values (intercorrelation).
In real life, the initial size can influence following growth (for some
experimental studies on P. lividus, see Vaïtilingon et al, 2001). We believe
that a meaningful model should follow the same logic: initial size is fixed
first and parameters that characterize growth are estimated afterwards.
This is done in eqs. 30-31. Of course, "initial" size just after
metamorphosis is the result of another growth process during larval life but
the model describes postmetamorphic growth, not larval growth.
Part IV: A growth model with intraspecific competition
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