Modelagem do crescimento de truta arco-íris na fase de engorda

Abstract

The mathematical modelling through the use of nonlinear equations is an important tool to represent animal growth. In the present study, four nonlinear models (Gompertz, Von Bertalanffy, Logistic and Brody) were used to model the growth in weight and length of rainbow trout (Oncorhynchus mykiss) during 98 days of culture on the fattening phase. These models have 03 parameters: A (weight "g" or length "cm" in the first maturation of the fish), B (precocity index), T (age "days" where the growth rate is maximum, in Logistic and Gompertz equation), K (integration parameter without biological interpretation, in the Brody and Bertalanffy equation). Nine hundred trouts of average initial weight and length and post hatch age of 122.11 ± 15.6g, 22.42 ± 0.71cm and 273 days, respectively, were maintained in nine similar tanks (100 fish by tank). Each three tanks were fed with 03 different commercial rations. The adjustment was based on the Least Squares theory using the Marquardt iterative method. The computational procedures were performed by PROC NLIN of SAS. Three levels of weight and length analyzes were performed to test the robustness of fit of the models used: i) individual analysis of data growth for each tank), ii) analyzes of data growth from three tanks submitted to the same feed, and iii) analysis involving data growth from all the tanks. Adjustment criteria was: convergence capacity, coefficient of determination (R2 ), mean square of residue (QMR), Akaike criterion (AIC), mean absolute residue deviation (DMA), mean percentage error (EPM), congruence and usefulness of the information generated by the adjusted model regarding the biological growth of the trout, and the examination and distribution of the residues and studentized residues. Only the Logistico, Gompertz and Bertalanffy models converged to weight data for all the levels analyzes. Parameters A (≤580,10 – 714,10≥), B (≤0,0196 – 0,0346≥) and T (≤311,80 – 341,40≥) obtained by the Logistic model reached the best values of the fitters (R2 ≤0,9460 – 0,8051≥ QMR ≤2889,60 –1223,80≥; AIC ≤14062,06 – 1391,37≥; DMA ≤35,92 – 24,59≥). For length data, there were cases of non-convergence in all models at level analyses i and ii. However, the parameters A (≤39,63 - 387,30≥), B (≤0,0041 – 0,0144≥) and T (≤255,20 – 959,80≥) obtained by the Logistic model reached the best values of the fitters (R2≤0,9984 – 0,9970≥; QMR ≤2,20 –1,18≥; AIC ≤1395,20 – 37,48≥; DMA ≤1,08 – 0,82≥) and their calculated growth values were congruent with biological features growth of rainbow trout. Notwithstanding, this model tends to overestimate growth (EPM ≤-1.00 – -3.78≥) and presents discrepant values.We concluded, weight data growth of rainbow trout on fattening phase was more able to fit to the Logistic model. Finally, length data growth have presented more complex distribution pattern and, therefore, difficulties in adjusting by all the models. Then, these models are not recommended for length growth modelling of rainbow trout on fattening phas.