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

This way, one obtains a 4-parameter model with an origin constrained to
be D'(t' = 0) = 0, size increase being null just after metamorphosis for all
quantiles.
Fitting the modified growth model of eq. 31 with quantile regression
for various quantiles is shown in Table 14 and Fig. 31. The model is
flexible enough to accommodate any quantile. Adding a constraint on one
parameter leads to a slightly poorer fitting according to δ1 and visual
impression, which is not surprising.
Table 14. Results of quantile regressions for different values of τ, using the new growth model
constrained to the origin (eq. 31). Curves for quantiles τ = 0.025, 0.5 and 0.975 (in bold) are
also presented graphically in Fig. 31. Relations between some parameters of the model and τ
are shown in Fig. 32.
ττττ ∆D∞ k1 k2 l deviance δδδδ1
0.975 64.5 1.97·10 -3 1.89·10 -3 0.806 2251
0.95 68.2 1.25·10 -3 7.51·10 -3 1.60 4048
0.9 60.9 2.16·10 -3 2.80·10 -3 1.96 7105
0.85 59.8 2.39·10 -3 2.76·10 -3 2.65 9542
0.8 58.8 2.31·10 -3 2.82·10 -3 3.09 11448
0.75 58.3 2.39·10 -3 2.82·10 -3 3.77 12871
0.7 57.5 2.35·10 -3 2.84·10 -3 4.07 13898
0.65 57.9 1.88·10 -3 3.02·10 -3 3.99 14577
0.6 57.0 2.21·10 -3 2.89·10 -3 4.93 14968
0.55 57.2 1.70·10 -3 3.33·10 -3 5.04 15094
0.5 56.6 1.89·10 -3 3.11·10 -3 5.38 14943
0.45 55.9 1.93·10 -3 3.15·10 -3 6.16 14616
0.4 55.8 1.96·10 -3 3.17·10 -3 7.00 14049
0.35 55.6 1.73·10 -3 3.38·10 -3 7.28 13296
0.3 55.1 1.74·10 -3 3.43·10 -3 8.11 12338
0.25 55.6 1.44·10 -3 3.65·10 -3 8.25 11152
0.2 55.4 1.35·10 -3 3.84·10 -3 9.57 9702
0.15 55.4 1.25·10 -3 3.90·10 -3 9.80 7993
0.1 57.7 9.92·10 -4 4.58·10 -3 13.8 5948
0.05 54.0 1.03·10 -3 4.83·10 -3 19.4 3429
0.025 53.3 9.24·10 -4 5.84·10 -3 39.9 1943
Part IV: A growth model with intraspecific competition
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