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ANIMAL NUTRITION |
* Centre for Nutrition Modelling, Department of Animal and Poultry Science, University of Guelph, Ontario, N1G 2W1, Canada;
and
Animal Nutrition Group, Wageningen Institute of Animal Sciences, Wageningen University, 6709 PG, the Netherlands; and
Departamento de Produccion Animal, Universidad de León, 24071, Spain
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Abstract |
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 Top Abstract INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Key Words: endogenous phosphorus excretion • mathematical model • phosphorus balance • phosphorus maintenance requirement • pig
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INTRODUCTION |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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). In many countries, diets have been formulated traditionally to maximize growth without any consideration given to the amount of P excreted. However, there are economic and environmental reasons to reduce P excretion. The NRC (1998) suggested that P rather than N will limit land application of manure in intensive swine-producing areas, and the success of management strategies for reducing P excretion is 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.
Availability of P in feed ingredients for pigs is commonly evaluated using digestibility studies or the slope-ratio assay technique (Jongbloed et al., 1991). Digestibility studies estimate P availability by measuring its digestive utilization, whereas the slope-ratio assay provides a combined estimate of digestive and postabsorptive utilization of P at the tissue level (Jongbloed et al., 1991). Apparent digestibility values underestimate the true digestibility of P; therefore, true P digestibility values were recommended by Fan et al. (2001). In digestibility studies, determination of true P digestibility requires measurement of endogenous P excretion. Fan et al. (2001) developed a linear regression analysis approach to determine true P digestibility and endogenous P excretion that was subsequently applied to corn-based (Shen et al., 2002) and soybean meal-based (Ajakaiye et al., 2003) diets for growing pigs. A concern with this method is whether there is a linear relationship between endogenous P output and dietary P intake. Furthermore, Moughan et al. (1998) stated that endogenous estimates are constrained by the mathematical model fitted, which is accepted a priori, and estimated values tend to have high SE. However, little attention has been given to nonlinear models. Biological responses are rarely linear, and at high doses, nonlinearity of regression is almost inevitable for any kind of response (Finney, 1978).
The objectives of the current study were to collect data from P balance studies with growing pigs and to evaluate alternative mathematical functions to estimate biological determinants of P utilization with attention to endogenous P excretion, maintenance requirement, and efficiency of dietary P conversion into animal products. The null hypothesis was that the relationship between retained P and dietary P is linear.
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MATERIALS AND METHODS |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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The Database
A database containing P balance data for 350 pigs from 14 experiments was assembled from the literature. The database contained information on diet, dietary P intake, BW, P retention, and in some instances, available P content. In the studies that reported available P content, the values were based on the NRC (1998) bioavailability values for cornsoybean meal diets. Therefore, in this study, available P values are based on the NRC (1998) values for swine diets. For consistency and to minimize the effect of different types of diets on P utilization, we have selected studies that used diets based on corn and soybean meal. Table 1 shows details of the diet composition for the trials used to construct the database. The range of data included is summarized in Table 2.
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Various units are used to express the key parameters of P requirements in the literature. Rodehutscord et al. (1998) showed that endogenous P excretion was related to BW but not DMI; therefore, in this study, the analysis was conducted by scaling daily P intake (total and available) and P retention by metabolic BW (g/kg of BW0.75· d).
Candidate Functions
In addition to the traditional straight-line analysis used for determining P requirements, 3 other candidate functions were evaluated (Table 3). These were a function exhibiting diminishing returns behavior (monomolecular), a function exhibiting sigmoidal behavior with a fixed point of inflection (Gompertz), and a sigmoidal function with a flexible point of inflection (Richards, Table 3). The functions were specifically reparameterized for balance study analysis so that the parameters a, b, and c are positive entities, with ymax = a (upper asymptote) in the nonlinear models, and –b is the y-intercept [value of f(x) when x = 0] in all functions including the linear model (Kebreab et al., 2003). The Richards function has an extra parameter, n, which is a constant that determines the shape of the response curve (Thornley and France, 2007). The P requirement for maintenance was calculated by setting f(x) equal to zero and solving for x. Endogenous P excretion was estimated by the intercept on the y-axis. Figure 1 shows graphically the calculations of the key parameters using the monomolecular equation, which are discussed further below.
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) suggested that the monomolecular function was a good descriptor of the relationship between P retention (R) and available P intake (Ia). For example:
 | [1] |
where a = theoretical maximum P retention; b = endogenous P excretion; and c = a shape parameter. The instantaneous efficiency of conversion (kg) of available P to retained P at any given Ia is then:
 | [2] |
Available P intake at maintenance can be calculated by putting R = 0 into Eq. [1] and rearranging. The corresponding relationship between retained P and total P intake and the instantaneous efficiency (dR/dIt) are also given by equation forms 1 and 2, respectively.
The relationship between total P and available P intake was tested using the linear relationship:
 | [3] |
where 
= the intercept and ß = the slope (i.e., P availability coefficient). The PROC MIXED procedure (SAS Inst. Inc., Cary, NC) was used for regression to take account of the random effect of experiments. Equation [2] may be written:
 | [4] |
from Eq. [3], 
, and .
, thus, as an alternative to direct calculation, instantaneous efficiency of utilization of available P intake can be calculated indirectly by multiplying the instantaneous efficiency of utilization of total P intake by the factor 1/ß.
The average efficiency of conversion of available or total P to retained P (k) between 2 intakes (I and I + 
I, Figure 1) was calculated according to Darmani Kuhi et al. (2003):
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Statistical Analyses
The database contained information collected from several experiments, and in some instances, multiple observations were made on the same pig at different periods. Therefore, a meta-analytical approach was used for data analysis. Trial was coded as a random effect (because the experiments represent a random sample of a larger population), and random effects of pigs and period within experiments were added to the model. Pig breed, genotype, or both; sex; and year of study were added into the model as fixed-effect variables. Pig breed, genotype, or both, and year of study were not significant in the model, but sex was marginally significant, so it was left in the model. The PROC MIXED (for linear) and PROC NLMIXED (for nonlinear functions) procedures of SAS were used for analysis (Littell et al., 1996; SAS, 2000; St-Pierre, 2001).
Distribution of random effects was assumed to be normal and, the dual quasi-Newton technique was used for optimization with adaptive Gaussian quadrature as the integration method. Performance of the models was evaluated using the significance level of the parameters estimated, the variance of error estimate, and its approximate SE. Comparison of functions was made using Bayesian information criteria (BIC), which are model-order selection criteria based on parsimony and impose a penalty on more complicated models for inclusion of additional parameters. The BIC combine the maximum likelihood (data fitting) and the choice of model by penalizing the (log) maximum likelihood with a term related to model complexity, as follows:
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where 
= the maximum likelihood; K = the number of free parameters in the model; and N = the sample size (Leonard and Hsu, 2001). A smaller numerical value of BIC indicates a better fit when comparing models.
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RESULTS |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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The 4 functions were used on data set 1 to describe the relationship between P retained in the body and total P intake (Table 4). Invariably, there was a good relationship between P retention and total P intake. Based on BIC and SE of the models, the monomolecular equation gave the best fit followed by the Gompertz, Richards, and the straight line, respectively (Table 4). Two parameter estimates from the Richards and one from monomolecular and Gompertz equations were not significant.
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). The monomolecular equation estimate was 17 mg of P/kg of BW0.75· d, and the straight-line and Richards estimates were similar to this value. Estimates of total P requirement for maintenance ranged from 30 to 173 mg/kg of BW0.75· d, with values from Richards and the monomolecular at the lower end and Gompertz at the higher end. The P requirement for maintenance generated by this analysis also includes unavailable P. P Retention vs. Available P Intake
The 4 functions were fitted to the data on P retention and recorded available P intake (data set 2). The nonlinear functions showed a good fit to these data based on BIC and SE of the model and were all an improvement on the straight-line equation (Table 5). Parameters a and b can be ascribed biological meaning and refer to theoretical maximum P retention and endogenous P excretion, respectively. Parameters c and n are constants that determine the shape of the curve. The SE of parameter a was significant for all functions except the monomolecular, and parameter b was significant only for monomolecular and Gompertz equations. Parameter c was significant in all equations, but n was not significant for the Richards equation.
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). Available P requirement for maintenance ranged from 7 to 19 mg/kg of BW0.75· d. Average estimated efficiencies of conversion of available P to retained P over the total range of P intakes were close for the nonlinear functions evaluated, ranging from 54 to 65% (Table 5). Estimation of Available P from Total P
A mixed linear regression model given by Eq. [3] was applied to data set 2, and the following relationship was established:
 | [4] |
The intercept was not significantly different from zero, but the slope (measure of P availability) was highly significant. Based on Eq. [1] through [4], available P values were calculated for data points in which only total P was measured. Retained P was then regressed against calculated available P, and the parameter estimates from the monomolecular function were compared with the fit using reported available P values shown in Table 5. Parameters a, b, and c in the monomolecular function for data using calculated available P were 0.59 (SE = 0.24), 0.015 (SE = 0.005), and 1.61 (SE = 0.09), respectively. None of these parameter estimates were significantly different from those estimated using data set 2. The maintenance requirements and average efficiency values based on calculated available P intake were also similar (maintenance = 16 mg/kg of BW0.75· d); 
= 0.66).
Estimates of instantaneous efficiency of utilization kg based on the monomolecular equation are shown in Table 6. The estimates resulting from using calculated (i.e., Eq. [4]) and measured available P were in close agreement (Table 6).
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DISCUSSION |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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Endogenous P Excretion
Although there was evidence of nonlinearity, the lack of sufficient data above 0.7 g of total and 0.4 g of available P intake/kg of BW0.75· d indicated that parameter a was not well-estimated for the diminishing returns function and parameters b, c, and n for sigmoidal functions when retained P was regressed against total or available P intake. The case for the monomolecular as the most suitable candidate was strengthened, because as parameter n approaches particular values, the Richards equation encompasses other simpler models, such as the monomolecular (n = –1), Gompertz (n = 0), and logistic (n = 1). In our analysis, the parameter n was always negative, tending to the monomolecular.
We assumed that endogenous P excretion is equal to excretion at zero P intake. However, it is uncertain what happens when net retention becomes negative. There may be a different pattern of response from the body when its need for P is not met. However, it is expected that the efficiency of utilization will increase as digestion and absorption proportionally increase due to less supply of dietary P, thus creating greater utilization when the capacity for digestion and absorption, or both, is not reached. This would lead to a lower intercept on the y-axis due to a steeper slope. On the other hand, metabolism might decrease to spare the reserves, and the continuing recycling from body stores would lessen, leading to a decrease in endogenous excretion. This implies a greater intercept. This balance would further change if insufficient supply is continued for a prolonged time.
When P retained is regressed against P intake, endogenous P excretion is given by net retention at zero P intake. Estimates based on total P compared with available P would be expected to yield greater endogenous excretion, because the data from which it is derived would include undigestible P. Better estimates are achieved when available P is used to predict endogenous P excretion. The monomolecular equation predicted it to be 14 mg/kg of BW0.75· d, based on reported available P values and 17 mg/kg of BW0.75· d based on total P values, which, after accounting for metabolic BW, was close to the range suggested by Jongbloed (1987), who documented values of 2.9 to 24.5 mg/kg of BW· d for pigs weighing 15 to 140 kg (with P in the diet ranging from 0.33 to 0.83%). Variable endogenous P loss values were reported for growing pigs fed a semipurified diet (0.07 g/kg of DMI or 3.2 mg/kg of BW· d; Petersen and Stein, 2006; 7.3 to 9.3 mg/kg of BW0.75· d; Pettey et al., 2006), corn-based diet (0.67 g/kg of DMI or 30.2 mg/kg of BW· d; Shen et al., 2002), and soybean meal-based diet (0.45 g/kg of DMI or 20.3 mg/kg of BW· d; Ajakaiye et al., 2003). Our estimate was very close to that reported by Rodehutscord et al. (1998), who showed endogenous P excretion to be 15.5 mg of P/kg of BW0.75· d based on regression analysis of 66 P balance studies. Dilger and Adeola (2006) summarized estimates of endogenous P excretion values reported in the literature. They concluded that the endogenous P loss in pigs was likely to be less than 20 mg (kg of BW0.75· d), which agrees well with the results of our study based on the monomolecular equation. Estimates of endogenous P excretion predicted by the straight-line equation were close to estimates reported by Pettey et al. (2006) and Dilger and Adeola (2006), who also used a straight-line approach to estimate endogenous P excretion.
A nonlinear equation is expected to provide greater estimates of endogenous P excretion compared with standard straight-line analysis, because it assumes that the efficiency of P conversion to retained P is not fixed, as is the case with the straight-line analysis. The endogenous P excretion obtained by the monomolecular equation in this study included fecal endogenous P output and urinary metabolic endogenous loss. Total urinary P excretion accounted for only a small fraction of the whole-body total P excretion in growing pigs fed within P requirement levels (Rideout and Fan, 2004). Thus, it is conceivable that fecal endogenous P output is the primary component of endogenous P excretion estimated by the monomolecular equation in this study.
P Requirement for Maintenance
The functions predicted a range of available P values for P requirement for maintenance (Pm), with the best fitting model, the monomolecular equation, giving 15 and 16 mg/kg of BW0.75· d using either reported or calculated available P values, respectively. These values are slightly greater than basal endogenous P loss and therefore suggest that the maintenance requirement mostly accounts for the basal loss of P from the animal.
Despite the flexible nature of the function, the Richards function did not improve upon the variation explained by either of the simpler nonlinear models. This is partly because the Richards function appears over-parameterized for the data presented, which was illustrated by nonsignificant values of 2 of its 4 parameter estimates. Generally, the supply of other nutrients such as Ca and vitamin D are also known to influence P metabolism (NRC, 1998), thus influencing the behavior of the curve and maintenance requirement. The concentration of Ca and vitamin D was not considered in the present analysis. However, the supply of these nutrients was considered normal in the experiments examined to derive the data sets used for the parameterization of equations.
Calculations for assessing requirements of other nutrients including energy for growing pigs included separate estimates for maintenance and production. However, P requirements are usually expressed as the sum of obligatory loss (urine plus feces P) and retention (ARC, 1981; Jongbloed et al., 1999). Therefore, comparison of Pm values obtained in this study with other work is difficult due to the scarcity of reported Pm figures. Different recommendation tables (ARC, 1981; NRC, 1998; Jorgensen and Tybirk, 2005) only provide total P requirements and do not allocate it into maintenance and growth requirements. For example, the NRC (1998) recommends an available P requirement of 3.2 g/d for the 10- to 20-kg pig. This requirement includes maintenance P, which in our study was estimated to be 0.14 g/d for the 20-kg pig, and growth, which will be utilized at 65% efficiency according to our results. The estimated retention of approximately 2 g of available P/d is consistent with values reported by Hastad et al. (2004) for pigs with similar BW.
Efficiency of P Utilization
Greater efficiency coefficients are expected when using available rather than total P, because calculations based on total P also includes inefficiency or incomplete digestion or absorption of dietary P. Efficiency was generally greatest at low available P intake and became decreased as intake increased (Table 5 and 6). Changes in efficiency were greatest for the sigmoidal functions because of their inherent shape. Biologically, it is unlikely that there is a lag phase in which minimum changes in efficiency occur at lower intakes as predicted by the Gompertz equation. However, the monomolecular equation gives a diminishing return in efficiency as intake increases, which is biologically more sensible.
When total P intake was scaled by metabolic BW, average efficiency of P utilization was from 34 to 45%, which is in the range reported in the literature (Revy et al., 2004). For pigs fed corn and soybean-based diets, Adeola et al. (2004) reported efficiency of utilization of P in control animals was an average of 46%, which was close to estimates from the straight-line and Gompertz equations. Furthermore, Dilger and Adeola (2006) reported efficiency values ranging from 30 to 42%, which is within the range of estimates given by the straight-line, monomolecular, and Richards equations. Results for efficiency of conversion of dietary to retained P, evaluated at various intake ranges using the diminishing returns model, showed efficiency was greatest at low P intake followed by a decrease in efficiency as P intake increased. This was not the case for the sigmoidal function because of shallower slopes at the beginning of the curve, which rose sharply toward mid P intake values. In reality, this is an unlikely scenario, because the animals would have a greater efficiency when P is deficient, whereas more P would be excreted as their capacity to absorb P is saturated at high P intakes. However, it is difficult to say if the P retention curve shows sigmoidicity at dietary values very close to zero before following diminishing returns behavior after a low point of inflection. Nothing in the present data elucidates this.
Based on the meta-analyses conducted in this study, fitting the monomolecular equation to the data more accurately accounted for variation compared with fitting any of the other functions (including the straight line, which represented the null hypothesis in this study). Figure 2 shows the relationship between P retention and intake (both total and available) obtained with the monomolecular equation. Biologically, it is more plausible that efficiency of P utilization is greater when pigs consume P below their maintenance requirement and decreases as intake increases, which is the situation described by the monomolecular or Richards but not by the Gompertz equations. Scarcity of observations approaching the asymptote made estimating parameter a (maximum P retention) difficult, particularly in the analysis with available P. The monomolecular could also be used to investigate the effects of diets or Ca:P ratio, particularly if sufficient data on different weight groups were available.
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Footnotes |
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1 Corresponding author: Ermias_Kebreab{at}umanitoba.ca
Received for publication November 1, 2006. Accepted for publication April 13, 2007.
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LITERATURE CITED |
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TopAbstractINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONLITERATURE CITED |
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