# Diet formulation: making use of non-linear functions

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2 Energy Correction (MJ/kg) (Teeter et al., 2012) and this could also be quantified. An example of a simple regression model for fat inclusion into a broiler diet is shown in figure 1. Table 1 Adjustment factors for the AME n of (added?) fat together with calculated and correction factors use in the model (Data from Leeson and Summers, 2005). Added Fat Inclusion Level (g/kg) Relative Energy Level (%) Calculated Energy Levels (MJ/kg) Energy Correction (MJ/kg) Figure 1: A model for correcting the energy contribution of added dietary fat to a broiler feed y = x x x R² = Added Dietary Fat (g/kg) Using LP it is impossible to reduce the energy contribution of an ingredient (in this case added fat) as its inclusion in a diet increases. The way the regression model derived above can be included into a standard feed formulation system is shown below. Note that for formulation purposes, the energy correction is the product of the energy correction factor (as determined by the model) and the physical amount of fat added to the diet. An adjustment is required to convert the result from g/kg to the percent inclusion in the diet, which is how LP is usually configured. The correction factor is then added to (or subtracted from) the ME constraint (the right-hand side) of the LP. Correction = (( f f f) X a) X f))/100 Where: Correction for fat inclusion is expressed in MJ/kg f = the g/kg of added fat. a = the age factor A model such as this needs to be validated, and to this end, a formulation exercise was carried out using a standard broiler grower diet. The control diet is a standard least cost diet formulated using Soya oil with

5 the more efficacious phytase is likely to be. It has been reported that increasing the dietary calcium to phosphorus ratio (Amerah et al., 2014)) will reduce the efficacy of supplemental phytase, while simply increasing the level of Ca inhibits IP hydrolysis (Tamim and Angel, 2003). Until recently, nutritionists have not been able to adequately formulate diets using these relationships, so there has been no need for the suppliers of enzymes to present data of this nature. Rather, this relationship has had to be modelled for the purpose of this paper. The response curve published by DSM (2013) was used as a starting point for this exercise. Under practical conditions, it is unlikely that phytase will release more than 70% of the IP contained in a diet (Plumstead, 2014) so this value was set as the maximum yield to be expected of the phytase. By calculation, the percentage yields for the other levels of phytase inclusion were determined. The final yield of phosphorus was then derived by multiplying the percentage digestibility brought about by the phytase with the level of IP in the diet. In this example, it is assumed that the digestibility of IP is of a linear nature although this is unlikely. The model that was finally determined is: Phosphorus yield = ( p p p ) x i (r 2 = 0.934) Where: p = is the level of phytase in the diet in g/ton. i = the inclusion of IP in the diet in g/kg Figure 2: A model of expected phosphorus yield where both the level of dietary inositol phosphate and the level of phytase enzyme applied vary. As was done previously, this model was also validated by doing some practical examples. Although the Format system does allow for multiple non-linear relationships to be added to a formulation, it was decided to remove the relationship that calculates the energy contribution for phytase because it made it far more difficult to understand what was happening in each formulation. Thus, in the examples below, only digestible phosphorus and calcium have been considered.

6 The first challenge given to the model was to demonstrate how it would react to differences in the price ratio of inorganic phosphorus (MCP) to phytase (Ronozyme Hi-Phos). One would expect the amount of phytase used to decrease as its price relative to inorganic phosphorus increased. From table 4, it can be seen that this is indeed what happened. In the second exercise, the levels of IP in the diet were manipulated by forcing the inclusion of low IP-containing ingredients into the formulation. As can be seen from Table 5, the amount of phytase included in the formulation decreases as the levels of substrate are reduced. The standard feed used in this example is the same diet that was used in the first example as the 1:100 diet. This model is based on the assumption that all phytate is equally digestible, which may not be true, but which is a factor that could be considered when the data becomes available. Table 4: The impact of the inorganic phosphorus price on the inclusion of phytase in a typical broiler grower diet. Price Ratio MCP:Hi-Phos 1:1000 1:100 1:10 Cost/Ton Yellow Maize 7.5% Extruded Full Fat Soya 36% Soya O/C 46% Sunflower O/C 38 % Limestone Monocalcium Phos Salt Soya Oil HiPhos AME (MJ/kg) Crude Protein (g/kg) Fat (g/kg) Crude Fibre (g/kg) Calcium (g/kg) Total Phosphorus (g/kg) Digestible Phosphorus (g/kg) Sodium (g/kg) Available Lysine (g/kg) Available Methionine (g/kg) Dietary Inositol Phosphate (g/kg) Model phosphorus yield (g/kg) Phytase (g/ton) Adjusting nutrient digestibility and other examples Amerah et al., (2014) presented data which clearly demonstrates that the amino acid digestibility of a broiler diet is impacted upon by both phytase inclusion in the diet and the calcium to the available phosphorus ratio. Only a single level of phytase was used for this experiment (although a curvilinear response would be expected had more been used) making it a simple matter to add a relationship that adjusts amino acid digestibility (lysine in this case) to a changing calcium to phosphorus ratio.

7 Additional Lysine yielded (g/kg) = (( (0.0084*(Ca/AvlP)))x a) Where Ca = the dietary calcium level (g/kg) AvlP = the dietary available phosphorus level (g/kg) a = the average % increase in lysine digestibility when using phytase. Table 5: The impact of dietary inositol phosphate level on the inclusion of phytase in a typical broiler grower diet. Animal Standard No Sunflower Animal Protein Protein No Sunflower Cost Wheat Yellow Maize 7.5% Extruded Full Fat Soya 36% Soya O/C 46% Sunflower O/C 38 % Carcass Meal 55% Local Fish 65% Poultry By-Prod 50% Limestone Monocalcium Phos Salt Soya Oil DL Methionine L Threonine L Valine Lysine HCL Premix and Additives HiPhos AME (MJ/kg) Crude Protein (g/kg) Fat (g/kg) Crude Fibre (g/kg) Calcium (g/kg) Total Phosphorus (g/kg) Digestible Phosphorus (g/kg) Sodium (g/kg) Available Lysine (g/kg) Available Methionine (g/kg) Dietary Inositol Phosphate (g/kg) Model phosphorus yield (g/kg) Phytase (g/ton)

9 dos Santos, T. T., Walk, C. L. and Srinongkote, S., Influence of phytate level on broiler performance and the efficacy of 2 microbial phytases from 0 to 21 days of age. J. Appl. Poult. Res. 23 : DSM (2013). Kaiseraugst, Switzerland Format International (2013). Woking, United Kingdom. Leeson, S. and Summers, J.D Commercial poultry nutrition (3rd edn). University Books, Guelph, Ontario, Canada. Le tourneau-montminy, M.P, Narcy, A. Lescoat, P., Bernier, J.G., Magnin, M., Pomar, C., Nys,.Y., Sauvant, D., and Jondreville, C., (2010). Meta-analysis of phosphorus utilisation by broilers receiving bcorn-soya bean meal diets: influence of dietary calcium and microbial phytase. Animal, 4:11, pp Plumstead, P.W., (2014). Pers.comm. Selle, P. H. and Ravindran, V. (2007). Microbial phytase in poultry nutrition. Animal Feed Science and Technology, 135: Selle, P.H. Cowieson, A.J., Cowieson, N.P., and Ravindran, V., (2012). Protein phytate interactions in pig and poultry nutrition: a reappraisal. Nutrition Research Reviews,25, pp 1?17 Tahir, M., Shim, M.Y., Ward, N.E., Smith, C., Foster, E., Guney. A.C. and Pesti, G. M. (2012). Phytate and other nutrient components of feed ingredients for poultry. Poult Sci : Tamim, N.M., Angel, R. and Christman, M. (2004). Influence of dietary calcium and phytase on phytate phosphorus hydrolysis in broiler chickens. Poult Sci 83: Teeter, R., Beker, A., Brown, C., Broussard, C., Newman, L. and Ward, N Production and managerial considerations influencing the calorific efficiency of growing broilers. Proceedings of the Arkansas Nutrition Conference.

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