February 15-18, 2009 Washington State Convention Center Seattle ...

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MIXTURE DESIGNS FOR FEED FORMULATION AND FISH NUTRITION STUDIES
Kari Ruohonen* and Juhani Kettunen
EWOS Innovation
N-4335 Dirdal
Norway
kari.ruohonen@ewos.com
Mixture designs are natural choices for problems on fish feed formulation or fish nutrition. Usually the factors affecting responses,
i.e. the formulations, have constraints that, if not accounted for, will confound the effect estimates. The main constraint
always present for a formulationfollows from the fact that the total amount of ingredients of the mixture must sum up to one
hundred percent. More constraints normally exist. Existing knowledge of fish nutrition introduces minimum/maximum constraints
for main nutritive substances. Furthermore, also production technology and prices of raw materials set up constraints
for technical and economical feasibility of the feed mixtures. In the paper, we will demonstrate the use of mixture models by
summarizing our experience from case studies. We will show how a typical mixture problem is designed and analyzed. Principally,
the problem solving is a process of consecutive, systematic change of scales connected with linear models. The scaling
process is necessary for at least the following four reasons. First, it is used to take into consideration the constraints of the problem.
Second, the scaling is needed to give an optimal statistical weighing of the ingredients in the mixture. Third, the scaling
greatly improves the estimation accuracy. Fourth, the scaling saves money and effort, because it constraints the experimental
effort into a feasible region and abolishes idle levels of ingredients. The mixture designs and models are a great improvement
to the present status of feed formulation and nutrition studies. However, we demonstrate also some challenges in their use. One
issue in applying mixture designs is whether the component axes should be based on raw ingredients or nutrient composition.