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

General introduction
model 1 for Echinus affinis Mortensen or by Dafni (1992) that proposed
the Johnson model to fit rapid growth with a very small initial lag phase of
the Toxopneustidae Tripneustes gratilla at Elat.
Based on this review (Table 1), it seems there is no ideal model to fit
growth data in sea urchins and, consequently, the use of one particular
model is more a question of personal preference. For instance, Ebert uses
the Richards model most of the time (Ebert, 1973, 1980a, 1982, 1999),
while Gage favors the Gompertz model (Gage & Tyler, 1985; Gage et al,
1986; Gage, 1987). This situation is problematic since parameters derived
from these models –and others– are not comparables. Using a single model
to fit all growth data would be preferable for comparison purposes (Turon
et al, 1995).
b. Fitting of growth models on real data for echinoids
In selecting a growth model, several conditions should be met when
fitting real data. First, animals sampled from a single homogeneous
population should be measured at various ages. Second, one particular
individual should be measured only once to ensure independence of the
errors (since authors consider individual variation as part of the error term:
they look for growth of a virtual "mean individual" among the population).
Third, as most regression methods assume no error on the dependent
variable –that is, time– (Sokal & Rohlf, 1981; Sen & Srivastava, 1990;
Draper & Smith, 1998; Zar, 1999), the age of each measured individual
should be known. Fourth, no interaction should exist between individuals
in the population. Such ideal conditions are so restrictive that they are
never met.
When the age of individuals can be determined precisely, such as for
sea urchins reared from the egg, it is common to measure the same
specimens several times (Bull, 1938; Michel, 1984; Cellario & Fenaux,
1990; Basuyaux & Blin, 1998; Lamare & Mladenov, 2000). Errors are
individual-dependent in such cases and this interaction is often ignored.
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