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

some two-dimensional processes like respiration or digestion, i.e.,
exchanges across surfaces) and catabolism (proportional to the volume of
the animal, and thus a process quantified in 3D).
The second argument against the least-square regression method is its
limitation to model a "mean individual" in the presence of individual
variations in the dataset. Yet, the concept of mean individual lacks
meaning when the distribution of the error is not symmetrical and even,
sometimes, multimodal. Considering a bimodal distribution with two
similar, but well-separated modes, the mean value is located just in the
middle of the two groups, where there are no individuals! In this example,
the median is located at the same place and will also be a poor
representation of the dataset. Quantiles, however, can be used more
efficiently (1 st and 3 rd quartiles will be located around each of the two
modes). Clearly, a regression that can fit a curve on another part of the
distribution than a symmetrical position can be useful in situations where
the distribution is asymmetrical or multimodal. For instance when sizebased
intraspecific competition occurs, the largest animals are inhibitors,
while the smallest ones represent the most inhibited fraction. Growth
curves fitted on large and small individuals thus contain information about
the impact of the interspecific competition (by comparison). This
information is not available using a least-square regression, but it is when
two quantile regressions are used, based on large and small quantiles
respectively.
Quantile regression, as defined by Koenker & Bassett (1978) is an
extension of the least-absolute deviation regression that fits a function for a
median individual. In quantile regression, the objective function (called
here deviance δ1) to be minimized is:
with:
Part IV: A growth model with intraspecific competition
n
δ 1= ∑ ρτ( Di−ξ1) (21)
i=
1
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