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

Another feature of this dataset is that the error terms are time- and
individual-dependents. Since the same (surviving) individuals are
measured at each sampling time, this constitutes a time-series thus having
autocorrelated errors. Moreover, even if artificial rearing conditions are
kept as constant as possible (Grosjean et al, 1998, see Part I), some
seasonal variations are possible, partly because animals are fed with
freshly field-collected kelp whose chemical composition is seasondependent
(Abe et al, 1983). To be rigorous, autocorrelation terms and
some seasonal variation should be introduced into the model. However, to
simplify the model as much as possible, and also because these effects are
very limited (see further), we decide to ignore them here and we will thus
fit growth curves without autocorrelation terms.
Table 12 and Fig. 28B illustrate quantile regressions on P. lividus
dataset with some usual growth models. 4-parameters models fit all 3
quantiles while 3-parameters models seem adequate for some quantiles
only. Logistic function yields unreliable results in all cases. Criteria to
decide which model best fits the data (deviance δ1 and visual impression
on a graph) are neither rigorous nor discriminant. Two to four models
among the six tested seem adequate in each situation with these criteria.
Indeed, the increasing lag-phase for quantiles 0.5 and 0.025 compared to
quantile 0.975 (more pronounced S-shape, see Fig. 28B) was
experimentally demonstrated to be an inhibition in growth (Grosjean et al,
1996, see Part III). None of these models, no more than many others like
Richards (1959), Preece & Baines (1978), Johnson (Ricker 1979), Schnute
(1981), Tanaka (1982), Jolicoeur (1985)… contain explicit parameters that
quantify such an inhibition and thus none of them are really adequate in
this case. Good fitting of data does not imply that the model is correct.
Part IV: A growth model with intraspecific competition
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