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

this species. For other species, where no plateau is observed, lifetime could
be simply too short to reach it. Yet, it is then impossible to tell if growth is
determinate or indeterminate. Anyway, if maximum size is not actually
reached, it is very difficult to estimate the corresponding parameter in the
model.
We constrained ∆D∞ to be normally distributed in the envelope model
(eq. 35). It is in agreement with the analysis of size distributions for fullgrown
animals (Grosjean et al, 1996, see Part III; current dataset). It is also
a consequence of the genetic homogeneity of the batch as all individuals
are issued from a single artificial fertilization, i.e., from one male and one
female. In case where D0 is also considered as normally distributed, the
model relates individuals with largest D0 with individuals with largest
∆D∞. But remember these are virtual individuals. This could be the case
for real echinoids or not. We cannot verify it without tagging individuals to
track them through time in the cohort.
As a consequence of fixing k1 (eq. 33), ∆D∞ is the only parameter to
contain information on relative growth potential of the individuals among
the cohort in eq. 35. The kinetic parameter k1 could be viewed as
environment-dependent (temperature, food, water quality, etc…). Since
these are the same for all animals because they are in the same aquarium,
they are fed ad libitum and have access to the food the same way, it
appears logical to fix k1. Fixing k2 is motivated by a similar reason: we
want it to express one global aspect of the inhibition. When homogeneous
batches of animals of same age and same genetic origin are reared
together, speed at which inhibition is released is supposed to be about the
same for all individuals. This way, only l quantifies changes between
virtual individuals (inhibitors versus inhibited). Of course, many other
variants are possible, but at the cost of an increasing complexity of the
model.
Indeed, as discussed by Grosjean et al (1996, see Part III), water
quality is not exactly the same for all echinoids in culture because they
Part IV: A growth model with intraspecific competition
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