Non-ruminantsFull-length research article Multivariate analysis of sources of polyunsaturated fatty acids, selenium, and chromium on the productive performance of second-cycle laying hens ABSTRACT -An experiment was conducted to evaluate the effect of the intake of a mixture of fish and sacha inchi oils (iOM), organic selenium (iSe), and organic chromium (iCr) on egg pro duction (EP) and feed conversion ratio (FCR) of Isa Brown second-cycle laying hens (SCLH) for 16 weeks (91-106 weeks old). Egg production and FCR were evaluated using multivariate models that included conventional equations and artificial neural networks (ANN) to study multiple nutritional interactions as alternatives to univariate dose-response models. Based on the best models, iOM, iSe, and iCr levels were optimized, and a global sensitivity analysis was implemented to quantify their influence on EP and FCR. The modified logistic model was selected as the best strategy to represent EP. In the case of FCR, an ANN model with a feed-forward architecture and softmax transfer function was selected as the best alternative. One of the scenarios to simultaneously optimize EP (89.1%) and FCR (1.94 kg feed/kg egg) at 16 weeks of production was established with 3.3 g/hen•day of iOM, 0.132 mg/ hen•day of iSe, and 0.176 mg/hen•day of iCr. However, optimization considering only FCR results in much lower optimal iCr levels (between 0.083 and 0.105 mg/hen•day) with a slight decrease in EP (87.9%). The global sensitivity analysis showed that iSe is an essential factor associated with the increase in EP, and iCr is the most influential factor for the decrease in FCR. When both criteria were taken into account simultaneously from a desirability function, iSe was the most critical factor.