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

If a model does not fit correctly after fixing the origin, it means that it
is not adapted to describe growth in this case. The only good reason to
avoid constraint is when time (t0), size (D0) or both are unknown at the
origin of the growth process. It is unfortunately common with data
collected in the field (Ebert, 1973, 1980a), when it is not possible to
estimate age accurately (Ebert, 1998; Russell & Meredith, 2000). In this
case, only relative growth can be studied and the problem of origin is thus
eliminated de facto. However, the model must be reworked to fit relative
growth data.
In the present case, we have the information necessary to characterize
the whole size distribution at the origin because we worked in aquaria:
metamorphosis was artificially induced (same t0 for all individuals, see
Grosjean et al, 1998, see Part I), and we have measurements of initial sizes
just after it (Grosjean et al, 1996, see Part III). However, by using actual
distribution instead of approximating D0 by the mean value for all
quantiles, this parameter cannot be eliminated from eq. 31. The model is
still viable, and perhaps a little bit more accurate for small sizes (see
profile 1 in Fig. 34B). Yet, we preferred to keep the simplest model in the
present case.
At the other extreme of the growth process, a single parameter
characterizes its completion when growth is asymptotic in all models. It is
parameter a in models of Table 12 and ∆D∞ in eqs. 29, 31 and 35. Several
authors questioned whether asymptotic growth is a biological reality, or
just a mathematical artifact. Ricker (1979) wrote a section untitled
"asymptotic growth: is it real?" in a chapter of a book; Knight (1968)
devoted a whole article to demonstrate it is a biological non-sense. Some
models with infinite growth appeared (for instance, Tanaka 1982, 1988).
They were also tested on sea urchins (Ebert, 1998, 1999; Ebert & Russell,
1993). Some P. lividus were reared in our installations for 15 years. They
reached their maximum size at 4 to 5 years old. They thus kept exactly the
same size for more than 10 years, proving asymptotic growth is a fact for
Part IV: A growth model with intraspecific competition
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