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

tend to form aggregates where a pH gradient is measurable from outside to
inside. Smaller animals are more likely found inside and larger sea urchins
outside. This was described as a protective behavior against predators in
the field (Tegner & Dayton, 1977; Tegner & Levin, 1983; Levitan &
Genovese, 1989; Ebert, 1998). But then, parallel gradients in both pH and
size distribution could be the explanation of the size-based inhibition of
growth: a lower pH possibly lowers the speed of skeletogenesis and,
consequently, the growth rate (the soma of sea urchins is made of ca. 90%
of mineralized tissues). No matter what the cause of the inhibition may be,
in such simple experimental conditions, the relationship between l and τ
appears amazingly simple. A precise measure of the pH gradient among
aggregates and the quantification of skeletogenesis speed with pH drop
should bring some more insight into these relations and causalities.
Lacking such information (the only experiment on sea urchins growth
related to pH was performed on larvae, Bouxin, 1926), eq. 32 is currently
the only way to quantify the degree of inhibition.
Even in the present example, eq. 32 seems to be a very simplified
relationship between l and τ. The 10% smallest animals do not follow it.
Profile 2 of Fig. 34B at 600 days shows that the model overestimates the
smallest fraction (and thus underestimates the peak of mid-sized animals)
at this age. Adaptation of l, or even k2, is perhaps necessary to better fit the
smallest fraction. Again, the simplest possible model was presented but
many variations can be conceived.
Relation between l and τ could be even more complex in other
circumstances: different rearing methods, large and small animals of
different ages and/or genetic origins maintained together, periodic size
sorting in culture, etc. Profiles of l in function of τ must be studied in each
particular case. It is also probably very different in the field, or for other
species. The model still needs to be reformulated and tested before being
used with field-collected data (mainly cohort separation, or mark-
Part IV: A growth model with intraspecific competition
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