A functional growth model with intraspecific competition applied to a sea urchin, Paracentrotus lividus

A new growth model is fitted on data from reared sea urchins, Paracentrotus lividus. Quantile regressions are used instead of least-square regressions, because they are insensitive to the dimension of the measurement and accommodate more than just symmetrical distributions. Quantile regressions allow comparison of fittings on various parts of the size distributions, including large competitors versus small, inhibited animals, in the presence of a size-based intraspecific competition. The model has functionally interpretable parameters and allows quantifying of the intensity of growth inhibition. An extension of this model, called envelope model, fits the whole data set at once, including size distributions. Its parameters are constrained using information about underlying biological processes involved, namely asymptotic growth with inhibition in early ages as the result of intraspecific competition, the intensity of which depends on the relative size of the individual in the cohort. The new model appears most adequate to describe growth of P. lividus and probably many other sea urchins species as well as other animals or plants.