Using nonlinear model to predict the egg weight increase on laying hens

The revenue of egg production system is obtained according to the egg weight and egg production. The artifices to increase the egg weight becomes desirable on production system. The aim of this study was estimate the weight increase in the laying hens' egg based on diet protein intake, using two models and compare both. It was used the Gompertz function and sigmoidal function y=p+q/(1+e^((r+(s*x)))) where y=egg weight; p=bottom asymptote; p+q=upper asymptote; r=constant; s=constant; x=poultry body weight, to estimate body weight and egg weight respectively. Two models were adjusted to describe the increase in egg weight on the basis of diet protein intake. The first, used the saturation kinetics equation and the second, used a quadratic polynomial equation, IEW=a-(b(*(c-CP))^2), where IEW=increase in egg weight; a=constant; b=intercept on ordinate axis; c=diet protein intake value which is maximum increase and CP=crude protein(%). These models were adjusted and evaluated using database from studies conducted in the Poultry Science Laboratory. The statistical criteria used MSE (Mean square error), ED (Error due to deviation from regression slope) and R² (Coefficient of determination) to evaluate the fit of curves using NLINMIXED and REG procedures of SAS. The models fitted to estimate body weight, egg weight and increase in egg weight are: Pt=1,5608*exp*{-exp*[-ln(0,0414/1,5608)-0,1677*Age)]}, y=44,8554+19,0642/(1+e^((38,2741+(-26,2461)))), IEW=(((3,1723*9,7966^1,9697)+(23,2256*CP^1,9697))/((9,7966^1,9697)+(CP^1,9697))) and IEW=3,5375-(0,1316*(12,6249-CP))^2) respectively. The evaluation of models that they estimate the egg weight increase in function of the diet protein intake had for saturation kinetics model, 2,94, 0,30 and 0,91 for MSE, ED and R²
whereas for the quadratic polynomial model, the values were 16,85, 1,01 and -0,07. According to statistic made, the model based on the saturation kinetics(non-linear) equation had lower values of MSE and ED then higher R² that explain a better fit than the other model(linear). These results shown that is possible to estimate the increase in egg weight using the proposed non-linear model, however other parameters will be adding to improve the accuracy of estimation.