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The use of non-linear regression models in the analysis of biological data has led to advances in poultry nutrition. Spline or broken-line nonlinear regression models are commonly used to estimate nutritional requirements. One particular application of broken-line models is estimating the maximum safe level (MSL) of feed ingredients beyond which the ingredients become toxic, resulting in reduced performance. The objectives of this study were to evaluate the effectiveness of broken-line models (broken-line linear or BLL; and broken-line quadratic or BLQ) in estimating the MSL; to identify the most efficient design of feeding trials by finding the optimal number of ingredient levels and replications; and to re-estimate the MSL of various test ingredients reported in the nutrition literature for comparison purposes. The Maximum Ingredient level OptimizationWorkbook (MIOW) was developed to simulate a series of experiments and estimate the MSL and the corresponding descriptive statistics (SD, SE, CI, and R2). The results showed that the broken-line models provided good estimates of the MSL (small SE and high R2) with the BLL model producing higher MSL values as compared to the BLQ model. Increasing the number of experimental replications or ingredient levels (independently of each other) reduced the SE of the MSL with diminishing returns. The SE of the MSL was reduced with increasing the size (total pens) of the simulated experiments by increasing either the number of replications or levels or both. The evaluation of MSLs reported in the existing literature revealed that the multiple range procedure used to determine the MSL in several reports can both overestimate and underestimate the MSL compared to the results obtained by the broken-line models. The results suggest that the broken-line linear models can be used in lieu of the multiple range test to estimate the MSL of feed ingredients along with the corresponding descriptive statistics, such as the SE of the MSL. [ABSTRACT FROM AUTHOR]

Nutritional requirements and responses of all organisms are estimated using various models representing the response to different dietary levels of the nutrient in question. To help nutritionists design experiments for estimating responses and requirements, we developed a simulation workbook using Microsoft Excel. The objective of the present study was to demonstrate the influence of different numbers of nutrient levels, ranges of nutrient levels and replications per nutrient level on the estimates of requirements based on common nutritional response models. The user provides estimates of the shape of the response curve, requirements and other parameters and observation to observation variation. The Excel workbook then produces 1-1000 randomly simulated responses based on the given response curve and estimates the standard errors of the requirement (and other parameters) from different models as an indication of the expected power of the experiment. Interpretations are based on the assumption that the smaller the standard error of the requirement, the more powerful the experiment. The user can see the potential effects of using one or more subjects, different nutrient levels, etc., on the expected outcome of future experiments. From a theoretical perspective, each organism should have some enzyme-catalysed reaction whose rate is limited by the availability of some limiting nutrient. The response to the limiting nutrient should therefore be similar to enzyme kinetics. In conclusion, the workbook eliminates some of the guesswork involved in designing experiments and determining the minimum number of subjects needed to achieve desired outcomes.