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

f. Conclusions
The new growth model with intraspecific competition is a very flexible
one. It can accommodate different situations and has meaningful
parameters that allow exploring and quantifying various aspects of growth.
Using a quantile regression method, modified for envelope modelling, and
constraining parameters ensures the meaning of the latter is saved into the
fitted model. It takes also individual variability into account. This is
particularly useful to model growth of P. lividus and probably of many
other sea urchins species and other animals or plants. It is original in many
aspects, including the way it was designed, by defuzzifying a fuzzy model
where most of the other growth models were built from their differential
equations. It is a general 'transitional' growth model. By distinguishing
'dimensional' and 'transitional' growth models, a duality in sigmoidal
growth curves comes to light. A preferred dimension for modelling growth
seems to exist. It is linear in the case of P. lividus but it should be most
interesting to check it for other species.
A generalized von Bertalanffy growth model, which is both
'dimensional' and 'transitional' and includes varying environmental effects
on growth, thanks to the use of metabolic time, was proposed (eq. 42). It
is, however, the visible tip of the iceberg. Fuzzy sets and transitions
(membership functions) can be combined in countless ways to create many
other similar models. In the present work, we studied models deriving
from von Bertalanffy 1 curve, because the latter seemed to be a good basis
for describing growth of P. lividus. Other models incorporating an
inhibition component or any other 'transitional' feature can be derived from
other growth models, including non-asymptotic ones, and would perhaps
be more adapted for other species. We propose to call this family of
functions 'fuzzy-remanent' models. From their fuzzy origin, they keep
nothing in appearance, but the biological meaning of their parameters is
still there. Recalling the fuzzy model they come from, one has a much
clearer idea of how various components –sets and membership functions–
interact to produce the final result. Fuzzy logic is closer to the way human
Part IV: A growth model with intraspecific competition
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