In order to evaluate biological trial results for their economic relevance, their statistical interpretation needs to be discussed first. Studies designed to quantify the requirement for any essential nutrient including amino acids have to be set up carefully because 'the requirement' is not a single, accurately defined point and never describes totally what the animal needs (from a nutritional point of view). Moreover, it needs to be defined what criterion will be used and at which level we expect the animal to perform. Usually, this definition is related to criteria of economic significance, e.g. weight gain, gain/feed ratio or protein accretion. For example, Gahl et al. (1991) found in rats that the quantity of essential amino acids required for weight gain were on average 71% of those required for protein accretion. In dose-response studies with Met+Cys broiler chickens required a concentration for weight gain that was only 83% (Jeroch and Pack, 1995) and 92% (Huyghebaert and Pack, 1996) of that required for optimal gain/feed ratio. Hence, it may be more appropriate when discussing response curves to 'derive recommendations' rather than to quantify 'the requirement'. This is important for the general understanding of the present approach.
In requirement studies, fitting response curves to the experimental data has been suggested as the preferred way of evaluation. In order to do so, the number of dietary levels has to be sufficient and there has to be a sufficiently wide range in dietary supply; from highly deficient to a level definitely not promoting further increment (Baker, 1986). Any kind of a paired-comparison test of response data often leads to misinterpretation of the results because of the lack of sensitivity of the statistical model, which typically is not good enough to pick up small differences (Baker, 1986; Berndtson, 1991; Pack, 1997). However, with regard to the model chosen, fitting response curves has been handled quite differently and several non-linear models as well as the linear Broken Line approach have been suggested.
The paper by Robbins et al. (1979) has prompted the widespread use of the Broken Line approach. This model of a linear increase up to a presumed performance plateau represented by a horizontal line has been widely used to describe the response to variation in amino acid supply, although even Robbins et al. (1979) stated that 'the Broken Line, with its discontinuous first derivative, cannot be more than a rough approximation'. The popularity of the Broken Line approach may be the consequence of the fact that one single point can be objectively defined as 'the requirement'. This simplifies the interpretation of response curves; however, it assumes that the response of an animal to supplementation of a limiting nutrient is linear until the requirement is met and that no further response can be expected above this point. The model of choice fitted to response data should satisfy both mathematical and biological considerations (Mercer, 1992). The assumption of constant utilization of a limiting nutrient up to the level of requirement does not appear realistic from the biological context although sections of a response curve, indeed, can be nearly linear (Robbins et al., 1979). It therefore needs a basic decision, which model is most appropriate to describe the response from a biological background and it has been repeatedly suggested that this approach should be non-linear.
This was confirmed by Rodehutscord and Pack (1999), who undertook an extensive review of different non-linear dose-response functions on the basis of 37 amino acid experiments conducted in either growing broilers or rainbow trout. It was very clear from their comparison of three non-lin ear response models versus the Broken Line model, that each of the non-linear curves was a better fit than the Broken Line. Among the non-linear models, the saturation kinetics and the four-parameter logistic functions gave the best fit, if the range in dietary amino acid concentration was very wide, i.e. from very deficient to adequate. For cases with a more narrow set of data closer to adequate supply, the exponential function gave a similar fit and has the advantage of a somewhat simpler equation, which facilitates handling and evaluation of data sets. Also, it has frequently been shown to give a good and realistic prediction of amino acid responses in monogastric animals. Therefore, exponential response curves as described by Rodehutscord and Pack (1999) or Gahl et al. (1994) will be used in the present survey to evaluate responses.
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