Low phosphorus (P) digestibility combined with intensive pig production can increase P diffuse pollution and environmental load. The aim of this paper was to develop a deterministic, dynamic model able to represent P digestion, retention and ultimately excretion in growing and finishing pigs of different genotypes, offered access to diets of different composition. The model represented the limited ability of pig endogenous phytase activity to dephosphorylate phytate as a linear function of dietary calcium (Ca). Phytate dephosphorylation in the stomach by exogenous microbial phytase enzymes was expressed by a first order kinetics relationship. The absorption of non-phytate P from the lumen of the small intestine into the blood stream was set at 0.8 and the dephosphorylated phytate from the large intestine was assumed to be indigestible. The net efficiency of using digested P was set at 0.94 and assumed to be independent of BW, and constant across genotype and sex. P requirements for both maintenance and growth were made simple functions of body protein mass, and hence functions of animal genotype. Undigested P was assumed to be excreted in the feaces in both soluble and insoluble forms. If digestible P exceeded the requirements for P then the excess digestible P was excreted through the urinary flow; thus the model represented both forms of P excretion (soluble and insoluble) into the environment. Using a UK industry standard diet, model behaviour was investigated for its predictions of P digestibility, retention and excretion under different levels of inclusion of microbial phytase and dietary Ca, and different non-phytate P : phytate ratios in the diet, thus covering a broad space of potential diet compositions. Model predictions were consistent with our understanding of P digestion, metabolism and excretion. Uncertainties associated with the underlying assumptions of the model were identified. Their consequences on model predictions, as well as the model evaluation are assessed in a companion paper.Keywords: modelling, phosphorus, phytase enzymes, phytate, pig ImplicationsCurrently there is some disagreement about the phosphorus (P) requirements of pigs of different genotypes and how digestible P contents of pig diets are calculated, especially for diets that include different amounts of phytate and nonphytate P. Achieving a balance between meeting digestible P requirements for optimum growth and health, and avoiding excess P intake would lead to a reduction in diffuse P levels in manure and effluents, and environmental impact from pig systems. A simulation model that predicts P intake, digestion, retention and excretion is the first, necessary step towards achieving this aim. IntroductionPhosphorus (P) is an important mineral for both the metabolism and skeletal development of the growing pig (NRC, 2012).In pig diets, P is the third most expensive nutrient required, after carbohydrates (energy) and protein. The high cost of P is due to the low digestibility of plant dietary P, which results in the need to sup...

There is a global imperative to reduce phosphorous (P) excretion from pig systems. In this study, a previously validated deterministic model was modified to be stochastic, in order to investigate the consequences of different management strategies on P excretion by a group of growing pigs. The model predicts P digestion, retention and excretion from feed composition and growth parameters that describe a specified pig phenotype. Stochasticity was achieved by introducing random variation in the latter. The strategies investigated were: (1) changing feed composition frequently in order to match more closely pig digestible P (digP) requirements to feed composition (phase feeding) and (2) grouping pigs into light and heavy groups and feeding each group according to the requirements of their group average BW (sorting). Phase feeding reduced P excretion as the number of feeding phases increased. The effect was most pronounced as feeding phases increased from 1 to 2, with a 7.5% decrease achieved; the increase in phases from 2 to 3 was associated with a further 2.0% reduction. Similarly, the effect was more pronounced when the feed targeted the population requirements for digP at the average BW of the first third, rather than the average requirements at the mid-point BW of each feeding sequence plan. Increasing the number of feeding phases increased the percentage of pigs that met their digP requirements during the early stages of growth and reduced the percentage of pigs that were supplied <85% of their digP requirements at any stage of their growth; the latter may have welfare implications. Sorting of pigs reduced P excretion to a lesser extent; the reduction was greater as the percentage of pigs in the light group increased from 10% to 30% (from 1.5% to 3.0% reduction, respectively). This resulted from an increase in the P excreted by the light group, accompanied by a decrease in the P excreted by the remaining pigs. Sorting increased the percentage of light pigs that met their dig P requirements, but only slightly decreased the percentage of heavy pigs that met these requirements at any point of their growth. Exactly the converse was the case as far as the percentage of pigs that were supplied <85% of their digP requirements were concerned. The developed model is flexible and can be used to investigate the effectiveness of other management strategies in reducing P excretion from groups of pigs, including precision livestock feeding.

Low P digestibility combined with intensive pig production can lead to water pollution. The aim of this paper was to develop a model able to represent P digestion in pigs across diets and contribute towards the reduction of P excretion. Phosphorus in plant feedstuffs includes some nonphytate P (NPP) that is readily digested but is mostly as organic phytate P (oP) that is indigestible unless it is dephosphorylated. The ability of pigs to dephosphorylate oP using endogenous phytase enzymes is limited and is a function of Ca intake. The effect of Ca (g/kg diet) on the proportion of oP dephosphorylated (kg/kg) in the small intestine (SI) and large intestine (LI) was determined as 0.26 - (0.015 × dietary Ca) and 0.69 - (0.059 × dietary Ca), respectively. The dephosphorylated oP in the LI was assumed to be indigestible and was excreted. Proportion of oP dephosphosphorylation (kg/kg) by microbial and plant phytase activity (FTU) in the stomach was estimated to be 0.56 × [1 - exp(-0.001 × FTU)] and 0.38 × [1 - exp(-0.002 × FTU)], respectively. Phosphorus digestibility (kg/kg) of NPP and dephosphorylated oP in the SI was assumed to be constant at 0.8. The model was used to predict P digestibility in 2 experiments by Stein et al. (2011) and Poulsen et al. (2010) and compare the predictions with experimental outcomes. The model successfully predicted the P digestibility to a range of dietary Ca concentrations and for 2 levels of supplementation with microbial phytase. However, the predictions overestimated P digestion systematically but always within a 10% margin of the observed values. The model could be a useful tool for formulating strategies to improve the efficiency of P digestion and reduce soluble P excretion in pigs.

A deterministic, dynamic model was developed, to enable predictions of phosphorus (P) digested, retained and excreted for different pig genotypes and under different dietary conditions. Before confidence can be placed on the predictions of the model, its evaluation was required. A sensitivity analysis of model predictions to ±20% changes in the model parameters was undertaken using a basal UK industry standard diet and a pig genotype characterized by British Society Animal Science as being of 'intermediate growth'. Model outputs were most sensitive to the values of the efficiency of digestible P utilization for growth and the non-phytate P absorption coefficient from the small intestine into the bloodstream; all other model parameters influenced model outputs by <10%, with the majority of the parameters influencing outputs by <5%. Independent data sets of published experiments were used to evaluate model performance based on graphical comparisons and statistical analysis. The literature studies were selected on the basis of the following criteria: they were within the BW range of 20 to 120 kg, pigs grew in a thermo-neutral environment; and they provided information on P intake, retention and excretion. In general, the model predicted satisfactorily the quantitative pig responses, in terms of P digested, retained and excreted, to variation in dietary inorganic P supply, Ca and phytase supplementation. The model performed well with 'conventional', European feed ingredients and poorly with 'less conventional' ones, such as dried distillers grains with solubles and canola meal. Explanations for these inconsistencies in the predictions are offered in the paper and they are expected to lead to further model development and improvement. The latter would include the characterization of the origin of phytate in pig diets. Keywords: mathematical model, phosphorus, phytate, pig, sensitivity analysis ImplicationsThe model developed in the companion paper (Symeou et al., 2014) and evaluated here predicts adequately the P digestion, retention and excretion of growing-finishing pigs for a wide range of dietary compositions and for pigs of different genotypes. Consequently, the model can be applied to develop feeding strategies to optimize phosphorus (P) utilization and minimize the different forms of P excreted to the environment. The model can be further improved, by considering 'reactive' as opposed to total phytate content of the diet, as well as experimentally establishing the net efficiency of digestible P utilization for growth and the non-phytate P absorption coefficient from the small intestine into the bloodstream, for pigs offered access to different diets.

Simulation models of nutrient utilisation ignore that variation in pig system components can influence the predicted mean and variance of the performance of a group of pigs. The objective of this study was to develop a methodology to investigate how variation in feed composition would (a) affect the outputs of a nutrient utilisation model and (b) interact with variation that arises from the traits of individual pigs. We used a P intake and utilisation model to address these characteristics. Introduction of stochasticity gave rise to a number of methodological challenges -for example, how to generate variation in both feed composition and pigs and account for correlations between ingredients when modelling variation associated with feed mixing efficiency. Introducing variation in feed composition and pig phenotype resulted in moderate decreases in mean digested, retained and excreted P predicted for a population of pigs and an increase in their associated CV. A lower percentage of pigs in the population were predicted to meet their requirements during the feeding period considered, by comparison with the no-variation scenario. Variation in feed ingredient composition contributed more to performance variation than variation due to mixing efficiency. When variations in both feed composition and pig traits were considered, it was the former rather than the latter that had the dominant influence on variability in pig performance. The developed framework emphasises the consequences of random variability on the predictions of nutrient utilisation models. Such consequences will have a significant impact on decisions about management strategies such as feeding that are subject to variation.Key words: Co-products: Feed mixing: Phosphorus: Pigs: Populations: Stochastic modelsApart from a few notable exceptions, most simulation models of nutrient utilisation are deterministic -that is, they deal with the performance of the average animal, offered a diet of a certain composition, while maintained in a relatively constant environment. Some models deal with variation between individual pigs and in aspects of the environment (1)(2)(3) , but none has dealt with uncertainty in feed composition at a particular point in time or over time. There are several reasons why the latter may be important. Feed ingredients may vary substantially in nutrient composition, due to growing conditions, hybrid or variety differences, planting and harvest dates and storage and feed out conditions (4) . In addition variation in feed composition may arise from the feed manufacturing process, such as mixing and processing, including, for example, the drying process in the production of distillers dry grain solubles (DDGS) (5)(6)(7) . Although several authors have identified such uncertainty in feed composition as a significant contributor to variation in performance (8)(9)(10)(11) , it is surprising that none has taken it into account in nutrient utilisation models.In this study, we used a previously published, deterministic model that predicts...