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

General conclusions
component validates it as the basic process for the whole cohort and shows
how intraspecific competition delays actual growth.
Growth is the result of many complex mechanisms that interact:
feeding, digestion, respiration, building up of new somatic tissues,
maintenance, reproduction, etc. A general consensus is that growth is too
complicated and could only be reliably described by complex models.
Indeed, it is surprising that a simple 2-parameter model like von
Bertalanffy 1 (D(t) = D∞·[1 – e -k·t ]) could represent individual growth of
many organisms. It is also surprising that, considering interactions and
individual variability in addition to the basic processes, a quite simple 5parameter
model (our envelope curve, eq. 35 p 160) represents growth of a
whole cohort of reared sea urchins.
Most of the simple models of the first half of the twentieth century,
attempt to interpret, in a functional way, either individual growth (von
Bertalanffy, 1938, 1957; Brody, 1945) or size/shape at age (Huxley, 1932;
Teissier, 1934, 1948; d'Arcy Thompson, 1961). In the last half of the
century, these models have been replaced by more complex, but purely
descriptive and/or speculative ones (Richards, 1959; Schnute, 1981;
Tanaka, 1982, 1988; Jolicoeur, 1985). Clearly, it is worth revisiting old
concepts using new tools, e.g., fuzzy logic or quantile regression. Such
revisitation was accomplished for instance by van Osselaer & Grosjean
(2000) in their study of the suture of coiled shells reflecting the ontogeny
of molluscs. Despite the conclusion of Tursh (1998) that the shape of the
suture is too complex to be modelled with a simple equation, they
demonstrated that a simple 4-parameter helicospiral model was the best
descriptor for most coiled shells and that some methodological errors
prevailed when using much more complex 8- to 16-parameter models (for
a review, see Stone, 1996). This example demonstrates another case where
growth is less complex in reality than in theory. The discipline (call it
"ontogenology") of describing individual growth or ontogeny with models
that are both reasonably simple and functional may reveal one day how
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