Applied Ecophysiology: An Integrative Form to Know How Culture Environment Modulates the Performance of Aquatic Species from an Energetic Point of View - Aquaculture and the Environment: A Shared Destiny - page 185

and (ii) it made the cyclic residual pattern disappear. The estimated range parameter
associated with this correlation structure was 74.3 (Table 5), representing the interval (in
days) necessary to avoid correlation between two consecutive weight measurements of the
same animal. Heterogeneity of variances was identified based on an increase in weight
variation with age and was accounted for by including a variance structure of the type:

ε i ~ N(0, σ 2 • |age i | 2δ )
Including this term significantly improved the model (L-ratio = 70.00; p < 0.001; AIC =
251.4). Finally, visual inspection of residuals revealed uniform dispersion and no evident
patterns, and σ (a constant representing the increase in residual weight variation with age)
was estimated to be 0.20 (Table 5).

Parameter Value Significance test

α -2.182 ± 0.22 a t = -100.92 b

β 0.030 ± 0.001 t = 48.60 b

σ 0.209

δ 0.204 L.ratio = 70.00 b

Range 74.3 L.ratio = 114.20 b

AIC 251.4

Table 5. Parameters of the exponential growth model: α = intercept; β = slope; σ = residual
standard error; δ = variance structure parameter; range: correlation structure parameter
defined by the variogram. Significance values of statistics used are also shown; a log-
transformed values; b p < 0.001.

5.00

W = 0.013 e 0.03 (age)

4.50

4.00

3.50

3.00

2.50

2.00

1.50

1.00

0.50

0.00

0 15 30 45 60 75 90 105

Age (d)

Fig. 9. Exponential relationship of weight and age (to age 105 d) in individually housed
juvenile Octopus maya kept at 27 ± 1°C. Data points and continuous line are observed and
predicted values, respectively.