Modelling phosphorus and calcium requirements in swine

It has been estimated that the world population to exceed 9 billion people by 2050. This
will increase the demand for animal products, which will be challenging to meet without
intensification because very little room for land expansion exists. It is expected that the largest
growth will be in developing countries and will overtake developed countries in their
consumption of livestock products (FAO, 2011). Due to this increasing global demand for
livestock products, there are concerns over sustainable animal agriculture practices and
particularly environmental impacts of livestock production (Kebreab, 2013). The environment
can be impacted in several ways such as degradation of water quantity and quality, air emissions
and other emerging issues such as hormones, antibiotics and other chemical pollutants.
Minerals, particularly phosphorus (P) are expensive nutrients after carbohydrate and
protein in swine nutrition. Diets have traditionally been formulated to maximize growth without
any consideration given to the amount of minerals excreted. However, there are economic and
environmental reasons to reduce mineral excretion, particularly P, calcium (Ca) and heavy
metals. In the US, several states require regular analysis of manure and soil, inspections, and
operator education to avoid negative environmental impact of mineral excretion (von
Keyserlingk et al. 2013). The NRC (2012) suggested that P rather than nitrogen will limit land
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application of manure in intensive swine-producing areas, therefore, P excretion in manure
should be minimized. Management strategies to reduce P excretion are dependent on an accurate
estimate of P requirements for a given level of performance (Ekpe et al., 2002). Therefore, in
recent years, research has focused on improving efficiency of conversion of dietary P into animal
products and on accurate estimation of P requirement by the animal.
Several mathematical models have been used to estimate animal growth, nutrient intake
and excretion (e.g. Strathe et al., 2015a). Approaches to model P and Ca utilization in swine
production systems include factorial (e.g., NRC, 2012; Aarnink et al., 1992); dynamic and/or
mechanistic (e.g. Létourneau-Montminy et al., 2015, Symeou et al. 2014a), kinetic (e.g. Dias et
al., 2010) and empirical (Kebreab et al. 2007). The objective of this study is to summarize the
various approaches available to estimate mineral excretion and discuss the advantages and
disadvantages of each approach. Due to economic, environmental and policy importance more
weight will be given on P utilization.
Factorial models to estimate mineral utilization and excretion
Various versions of the US national nutrient requirement of swine (NRC, 1998; 2012)
have been used to estimate mineral utilization and excretion. Phosphorus requirement in the
NRC (2012) is predicted from maximum rates of whole-body P retention, P retention in
conceptus, P output in milk, basal endogenous gut P losses, miminum urinary P losses, marginal
efficiency of using standardized total tract digestible P (STTD P) intake for P retention, and P
requirements for maximum growth performance as a proportion of P requirements for maximum
whole-body P retention (for growing-finishing pigs). Calcium requirements are derived simply
and directly from STTD P requirements using fixed ratios. When animals are fed just below
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requirement, NRC (2012) assumes the maximum marginal efficiency of using digestible P intake
for whole-body P retention in groups of pigs to be 77% in all classes of pigs. Although some of
the assumption may be reasonable (e.g. relationship between milk nitrogen and P contents)
others may need further modification (e.g. developing variable efficiency values for gestating
sows, lactating sows and growing-finishing pigs instead of the current constant value).
Dynamic and mechanistic models of P utilization
Létourneau-Montminy et al. (2011) developed a model consisting of 3 compartments
associated with specific anatomical sections, i.e., stomach, proximal, and distal small intestine.
The model was developed to simulate dietary P and Ca utilization in a 40-kg pig. The model
contains 7 state variable within each compartments representing phytate and non-phytate P in
solubilized or non-solubilized forms, Ca in non-solubilized form from plant and animal
ingredients and Ca in solubilized form from mineral sources. The authors were able to simulate P
absorption in the proximal and distal part of the small intestine as a function of time after feed
intake and demonstrate the impact of additives such as phytase on P absorption and eventually
excretion. The model output were compared with observed values and for P the prediction
accuracy was high (R2 = 0.90) but less so for Ca (R2 = 0.78). Although the digestive processes
were well simulated, it was recommended that further model refinement need to include
metabolic flows of P and Ca to account for metabolic regulation of Ca and P absorption
(Létourneau-Montminy et al., 2011). Symeou et al. (2014 a,b) also took a similar approach in
developing a deterministic, dynamic model of P digestion, retention and excretion in growing
and finishing pigs of different pig genotypes but with different assumption. For example
Létourneau-Montminy et al. (2011) assumed that P is absorbed to the blood plasma according to
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active and passive mechanisms in the digestive tract while Symeou et al. (2014a) adopted a
constant digestibility coefficient of 0.8, which was consistent with experiment of Lopes et al.
(2009) and meta-analysis of Létourneau-Montminy et al. (2012). In representing Ca, Symeou et
al. (2014a) assumed a linear relationship between dietary Ca and phytate dephosphorylation but
do not consider interaction between Ca and P retention, which may limit its use in cases where
Ca may be limiting. In fact, evaluation of their model (Symeou et al., 2014b) showed that it
under-estimated the P excreted when phytase was supplemented at low Ca content diets, so
further representation of Ca digestion and interaction with P is warranted. For most ‘regular’
diets, the model was able to predict P utilization well.
Stathe et al. (2015a) and Hansen et al. (2014) developed a dynamic growth model for
prediction of nutrient partitioning and manure production in growing-finishing pigs and sows,
respectively. Their approach was different from those previously described because the
simulation model (Davis Swine Model) traced the fate of ingested nutrients and water through
digestion and intermediary metabolism into body protein, fat, water and ash with body protein
and fat representing the body constituent pools. Hansen et al. (2014) developed new equations to
estimate milk production which can be used to calculate P and Ca deposition in milk. Both
simulation models can be combined to run for a whole life cycle of pigs and nutrient utilization
and excretion calculated. Minerals were not explicitly represented in the model but it would be
straightforward to include some of the concepts on mineral utilization from other simulation
models described above. The advantage of such approach is that it gives a more complete picture
of the animal taking into account not only mineral utilization but also other nutrients and water,
which may affect P and Ca flow. Létourneau-Montminy et al. (2015) extended their previous
model that simulated digestive processes to represent metabolic utilization through digestion,
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soft tissue, and ash modules. The model was able to predict apparent total tract digestibility of P
well but was less accurate in simulating Ca digestibility and retention.
Kinetic models of P utilization
Models developed by Fernández (1995) and Dias et al. (2010) are based on radioactive
Ca and P flows and deal with P kinetics in the body of pigs. Phosphorus flows in four pools,
namely soft tissue, gut, plasma and bone were represented. The strength of the models was that
contribution of endogenous P sources to P excretion could be accurately determined and can be
incorporated in other simulation models. They are also unique in that P flows to and from bone
and soft tissue, turn over (accretion and mobilization) rates can be calculated. The models
indicated that there is indeed significant turnover of P in bone and soft tissue, and both P
resorption from bone and P mobilization from soft tissue contribute to maintain P levels in the
plasma for normal functions of the animal body (Fernández, 1995; Dias et al., 2010).
Empirical approach of P utilization
Several meta-analyses have been conducted to gain better understanding of the
relationship between P intake and P retention or excretion in swine production systems.
Létourneau-Montminy et al. (2012) conducted a meta-analysis to study the effect of dietary P, Ca
and exogenous phytase on P utilization by growing pigs: The authors reported that the amount of
phytate P leading to digestible P (g/kg) was estimated to be 21%, compared with 73% for nonphytate
P from plant ingredients and 80% from mineral and animal ingredients. The metaanalysis
of Schulin-Zeuthen et al. (2007) produced estimates of endogenous P excretion,
maintenance requirement and efficiency of P utilization in growing pigs. Kebreab et al. (2007)
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calculated average and instantaneous efficiency of P utilization, which can be used to predict the
pigs’ response to changes in intake and the potential to reduce excess P excretion. Metaanalytical
approaches are useful in obtaining estimates of parameters that can be used in more
complex simulation models. For example, the use of 80% as P digestibility coefficient in the
simulation model of Symeou et al. (2014a) was based on meta-analysis of Létourneau-Montminy
et al. (2012) who found that the flow of P from gut to blood was linear for a wide range of
dietary P intakes.
Modeling efficiency of P utilization and use of phytase
Kebreab et al. (2012) reported that there are several opportunities available to reduce
excess P excretion from livestock, which can be broadly divided in to two categories: improving
or optimizing P availability in feed, and increasing efficiency of livestock through increased P
incorporation in product or faster growth. Of these, the use of phytase has been researched
extensively (e.g. Lopes et al., 2009). Kebreab et al. (2011) used a nonlinear mixed effect
modeling approach to establish bioequivalence of diets offered by analyzing growth profiles of
pigs using growth functions, and investigate efficiency of P utilization in pigs offered a standard
diet or a P-amended diet (with phytase). They were able to show that the generalized MichaelisMenten
equation was appropriate for describing differences in P utilization between two diets.
On average, 56 g of supplemented inorganic P was consumed by a pig fed phytase supplemented
diet to reach market weight. In contrast, 309 g of supplemented inorganic P was consumed by the
group fed the standard diet to reach similar BW. They concluded that supplementing feed with
appropriate doses of phytase can result in economic benefit. Pigs fed the phytase supplemented
diet excreted 19% less P compared with those fed the standard diet. Nonlinear mixed model
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analysis (with repeated measures) is suitable for growth and efficiency analysis and particularly
useful in analyzing experimental results.
Opportunities for further work
Recommendations for mineral requirement of a population of pigs are often determined
based on an average animal without considering the between-animal variation. When these
recommendations are applied to populations exhibiting large between-animal variation, the
requirement of a certain percentage of the population may not be met, and the mean performance
of the group will be lower than expected. On the other hand, a significant amount of animals may
be over supplied with P and Ca resulting in excess excretion. Nutrient requirements vary greatly
between animals of a given population and each animal follows individual patterns over time
(Pomar et al., 2011). The mineral requirement may depend on the animal (e.g. genetics, age,
BW, and milk production), environment (e.g. temperature) and feeding factors. Therefore, it is
important to determine the mineral recommendations for pigs using a stochastic modeling
approach that integrates population variation and uncertainty of key parameters. Strathe et al.
(2015b) used Monte Carlo simulation techniques to determine the amino acid recommendations
for lactating sows using a stochastic modeling approach. Similar technique can be used in
conjunction with any of the simulation models discussed earlier to come up with new feeding
strategies by taking into account the variable requirement between groups of animals. The
inclusion of between-animal variation gives information on safety margins when developing new
dietary recommendations of minerals that would eventually result in lower P and Ca excretion
and optimize the swine production system.
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Conclusions
Phosphorus utilization is currently estimated using several types of mathematical
modeling approaches. The NRC (2012) is based on a factorial approach according to the
requirement for various body functions such as growth and lactation. Dynamic mechanistic
models include those developed by Létourneau-Montminy et al. (2011, 2015) that deal with the
fate of P intake in the digestive tract and metabolic processes of growing pigs and Symeou et al.
(2014a) that describe dynamic, mechanistic models of P utilization in the digestive tract of pigs
of different genotypes. Strathe et al. (2015a) and Hansen et al. (2014) also developed simulation
models of growing pigs and sows, respectively, that can be adapted to include P and Ca flows.
Kinetic and meta-analytical approaches have been used to calculate specific parameters such as
endogenous P excretion and rates of P and Ca resorption and deposition in bone. Non-linear
mixed effect modeling techniques have also been used to investigate the effect of mitigation
options such as inclusion of phytases in swine diets on P utilization.
Acknowledgements
The work was supported by the Sesnon Endowed Chair Program at UC Davis.
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