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

lividus. 10 to 15% of the largest individuals (the inhibitors) in the
populations grow at their maximal speed (i.e. the growth speed they would
have if they were alone in the same food and environmental conditions).
The growth of others depends upon their relative size in the population
(the smaller they are, the slower they grow). The cause of this inhibition is
not known yet, but it does not seem to be food-related: in the experiments,
all individuals had access to food ad libitum. Inhibition progressively fades
out when larger individuals reach their asymptotic size and are caught up
with smaller ones that are still growing.
According to these observations, a semantic formulation of the
problem becomes: "a young, small individual is potentially inhibited in its
growth, but gradually reaches its maximum size with age". It can also be
represented by two sets and one transition, but now the S set is the minimal
size with time (with maximum inhibition) and L set is the size at the age
where the growth speed is maximal (with no inhibition at all). The
transition is now the expression of a progressive release of the inhibition,
instead of a representation of the entire growth process. The difficulty
resides in the proper characterization of sets and membership functions
with age.
First of all, we use a time-scale t' with a well-defined origin that really
coincides with the initiation of the growth process. Until now, we used
(time-scale t) the age of sea urchins (since fertilization, thus including
larval life). However, growth of postmetamorphic sea urchins really starts
after metamorphosis. Knowing the age at metamorphosis (t0), t' is simply:
Part IV: A growth model with intraspecific competition
t' = t − t0
(23)
For the studied dataset, metamorphosis was artificially induced for all
echinoids in the batch at the same time at 30 days old. t' scale is thus
shifted to the left by t0 = 30 days.
Set S corresponds to the minimum possible growth, that is simply no
growth at all. Thus, in set S, size remains constant at its minimum initial
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