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

dimension of the size measurement, and second it can only model mean
individuals.
If least-square regression is influenced by the dimension of the
dependent variable used to quantify size in time, what is a good
measurement of size? Is it a linear measurement (height, width, diameter,
etc…) or is it a volume, a weight, or any other tri-dimensional measure? It
could also be a two-dimensional measure such as, e.g., the surface covered
by a colony of sponges or corals. Is there a privileged dimension (1, 2 or
3D) to measure growth? Except for changes in the curve shape due to
distortion introduced by a power transformation –compare von
Bertalanffy's model in size and in weight (von Bertalanffy, 1957, his
Fig. 3, and Fig. 10 p 47)–, no criterion exists for choosing the best
dimension to describe growth. Accordingly, a length, a surface or a
volume/weight can each be acceptable, and the final choice will be
dictated by practical considerations: which measurement is the easiest to
obtain with the highest possible accuracy (see Grosjean et al, 1999, see
Part II, for a discussion of this problem in P. lividus). Thus if a regression
method is highly sensitive to power transformation, it will be less desirable
because results of the regression will vary according to the measure used.
By contrast, the median, as well as the quantiles, are insensitive to power
transformation. Hence, quantile regression is generally insensitive to any
transformation by a monotonous function (Koenker, 2001) and will not be
influenced by the dimension (1, 2 or 3D) of the dependent measurement.
Accordingly, a median individual in a regression of length against time
will remain the same median individual in a regression of a volume (as
length 3 , or any allometry coefficient) against time with a quantile
regression, while this is not true for a mean individual using a least-square
regression. Using median/quantiles instead of mean allows remaining the
independence of the dimension of size measurement in a context where the
dimension of the studied phenomenon (growth) is undetermined. As
suggested by von Bertalanffy (1938, 1957), growth could be a
multidimensional process, since it is a balance between anabolism (with
Part IV: A growth model with intraspecific competition
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