The Euclidian Pathway to more Instructive Broiler Bioassays: Nutritional Geometry

Hi Swamy, thank you for your question and sorry for this late response. Most commercial programs can design and analysis response surface design. I am using R because it is free of charge and relatively more flexible to use than other packages. It is hard for beginners but it is such a valuable skill as both R and Python are booming in data science.

Excel can be used to define equation parameters from response surface results and can also generate the data table needed to generate graphs. Excel can also do an excellent job of generating these 3D graphs as well. While not as powerful as R, JMP or SAS, in statistical analysis, it can play a role in helping to visualize response surface results.

" Would broiler bioassays be more instructive using nutritional geometry ? " If I have to answer this question, my reply is "maybe". From many studies initially using single factor experiments, we realize that there are interactions among single factors . Designs for factorial experiments were made to address this interaction problems. Thereon, we know about inverse relations, augmentative and synergistic relations among factors. Complications arise when we want to put so may eggs in one basket, that is, to study more that 4 factors in a factorial experiment. Principal component analysis (PCA) or Response Surface Analysis (RSA) can assist us to visualize the complex interactions among studied factors, but not necessarily the underlying mechanisms involved. The introduction of " Nutritional Geometry" will certainly be as useful as PCA or RSA but it cannot replace basic studies to understand the mechanisms of interactions which are still badly needed thru carefully planned factorial experiments using 2-4 factors at a time. Such inputs will definitely shed lights on what we visualize from findings with new approach

Hi Dr Vinh, thnak you for your comment. Full factorial design is definitely an important tool along with other statistical method we can use. if we read a classic Response Surface Methodology book, it often suggests that the first step to test an hypothesis is factorial design. this helps us to answer yes or no question. to identify the influential factors for a dependent response. Then, RSM can be used in the next step for optimization. the adoption of design really depends on the purpose of the experiment and the outcomes of previous literature. However, I do not agree RSM cannot explain the underlying mechanism. One example to address this point is, Solon-Biet, et al, 2014. The Ratio of Macronutrients, Not Caloric Intake, Dictates Cardiometabolic Health, Aging, and Longevity in Ad Libitum-Fed Mice. Cell Metabolism 19, 418-430. This work has been sited 75 time according to web of science in just two years.

Hi Dr. Liu, I appreciate very much for your prompt response. What I mean is that we already figure out the underlying mechanism(s) thru smaller factorial experiments ( whether we use RSA or not in these experiment). Later on, when we design larger experiments, such prior information becomes handy, e.g. setting the spaces/levels and the ranges for individual factors,assisting us in interpreting results of RSA , finding saddle points, explaining the contours of surface. If we did not use orthogonal comparisons, regression analysis in smaller factorial experiments and go directly to RSA , then You and I have no disagreement on the issue about RSA can or cannot use to study underlying mechanisms among factors involved. Congratulation for your good work.