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

Growth models
General introduction
The previous section on the biology of P. lividus was brief because we
do not need much information to model growth. Indeed, when modelling
growth, the animal is mainly regarded as a black box. We care about its
global change through time, but we do not have to detail all the complex
biochemical and physiological processes (feeding, digestion, assimilation,
respiration, excretion, etc…) or anatomical modifications that lead to such
changes. On the other hand, a good understanding of the various growth
curves and their respective shapes and properties is required. This section
is thus dedicated to a "portrait gallery" of all growth models that have been
used for sea urchins.
There are two types of growth models in biology: population and
individual. Population models describe the change in the number of
individuals through time. A typical population growth model is the logistic
curve (Verhulst, 1838). Another model often used to describe decreasing
number of individuals, i.e., mortality, is the Weibull function (Weibull,
1951).
Individual growth models represent changes in the size of a single
individual with time. A typical individual growth model is the von
Bertalanffy curve (von Bertalanffy, 1938, 1957). Although we will deal
exclusively with individual growth in this work, population growth models
are also often used to model individuals, particularly Gompertz or logistic
curves (for examples that used them for sea urchins, see Gage et al, 1986;
Gage, 1987; Ebert, 1999) and we will do so as well.
a. The exponential curve, a simple Malthusian growth model
In 1798, Thomas Malthus described a mathematical model for growth
of human populations. According to Murray (1993), this model was
previously suggested by Euler. Today this model is not used much,
however its historical significance should not be overlooked. It is the first
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