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

e. Discussion
Fig. 34B shows three sections across the surfaces of Fig. 33 at three
given times t' = 300, 600 and 1800 days. Overall size spreading and
asymmetries in the original dataset are quite well respected by the model.
The higher peak in the first section of the model at 300 days is partly a
consequence of considering D0 as strictly equivalent for all individuals
while, in reality, it is normally distributed. With the simple relation
between l and τ, as established in eq. 32, multiples modes are just
approximated by a unimodal, skewed distribution. This is most visible in
the second section, at 600 days. A more complex model would be required
to fit multimodal distributions.
Fitting methods
We have argued in favor of quantile regression instead of least-square
regression in modelling growth. Distribution of the "error", that is, mainly
individual variation in the present case, can be either asymmetrical or
multimodal and this is a violation of basic assumptions of the least-square
model. In the same circumstance, a mean effect obtained by least-square is
less representative of the tendency. Quantile regression fits any part of the
distribution, including extremes, and accommodates any kind of size
distribution. It is also robust against any power transformation and it is a
guarantee that the regression remains independent from the dimension of
measurements for size (linear versus surface versus volume/weight). Leastsquare
regression is very sensitive to any power transformation, and thus
to the dimension of the variables.
For purely descriptive fittings, we introduced the triple
τ = 0.975 / 0.5 / 0.025 quantile regression representation as an informative
summary of the data. 5% is a commonly used critical level in statistics.
The curves for τ = 0.975 and t = 0.025 materialize a kind of two-tailed 5%
nonparametric conditional confidence interval of the dataset: 95% of data
Part IV: A growth model with intraspecific competition
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