meta-analysis of phosphorus balance data from growing pigs

France M. Schulin-Zeuthen, E. Kebreab, W. J. J. Gerrits, S. Lopez, M. Z. Fan, R. S. Dias and J.

Meta-analysis of phosphorus balance data from growing pigs

published online Apr 27, 2007; J Anim Sci

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Meta-analysis of P balance data 1

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Meta-analysis of phosphorus balance data from growing pigs 3

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M. Schulin-Zeuthen,* E. Kebreab,*1 W. J. J. Gerrits,† S. Lopez,‡ M. Z. Fan,* R. S. Dias,* 5

and J. France* 6

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*Centre for Nutrition Modelling, Department of Animal and Poultry Science, University of 8

Guelph, ON, N1G 2W1, Canada; †Animal Nutrition Group, Wageningen Institute of Animal 9

Sciences, Wageningen University, 6709 PG Wageningen, The Netherlands; ‡Departamento de 10

Produccion Animal, Universidad de León, 24071 Leon, Spain 11

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1Corresponding author: [email protected] 18

Page 1 of 31 Journal of Animal Science

Published Online First on April 27, 2007 as doi:10.2527/jas.2006-715 by on May 14, 2011. jas.fass.orgDownloaded from

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ABSTRACT: Many studies have highlighted concerns over current methods of determining 19

endogenous phosphorus (P) losses and P requirements in growing pigs. Therefore, a database 20

containing observations on 350 pigs was assembled from various studies. Four functions for 21

analyzing P balance data were considered: straight line, a diminishing returns function 22

(monomolecular), a sigmoidal function with a fixed point of inflection (Gompertz), and a 23

sigmoidal function with a flexible point of inflection (Richards). The nonlinear functions were 24

specifically re-parameterized to assign biological meaning to parameters. Meta-analysis of the 25

data was conducted to estimate endogenous P excretion, maintenance requirement and efficiency 26

of utilization. Phosphorus retention was regressed against either available P intake or total P 27

intake (all variables scaled by metabolic BW (BW0.75)). There was evidence of nonlinearity in the 28

data and the monomolecular provided the best fit of the data. The Richards function did not fit 29

the data well and appeared over-parameterized. Estimates of endogenous P excretion of 14 and 30

17 mg/(kg BW0.75⋅ d) based on available and total P analysis, respectively, were predicted by the 31

monomolecular, which were within the range reported in the literature. Maintenance requirement 32

values of 15 mg available P/(kg BW0.75⋅ d) and 37 mg total P/(kg BW0.75⋅ d) were obtained, based 33

on the monomolecular function. Average efficiencies of conversion of dietary P to retained P 34

were 65 and 36% for available and total P, respectively, with greater efficiency values calculated 35

for low P intakes. Although the monomolecular fitted the data best, more observations at high P 36

intakes/kg BW0.75 are required to determine conclusively whether P retention scaled by metabolic 37

BW is linearly related to available or total P intake. 38

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Key words: endogenous P excretion, mathematical models, P balance, P maintenance 40

requirement, pigs 41

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INTRODUCTION 43

Phosphorus (P) is the third most expensive nutrient after carbohydrate and protein in swine 44

nutrition (Honeyman, 1993). In many countries, diets have been formulated traditionally to 45

maximize growth without any consideration given to the amount of P excreted. However, there 46

are economic and environmental reasons to reduce P excretion. The National Research Council 47

(1998) suggested that P rather than N will limit land application of manure in intensive swine 48

producing areas and the success of management strategies for reducing P excretion is dependent 49

on an accurate estimate of P requirements for a given level of performance (Ekpe et al., 2002). 50

Therefore, in recent years research has focused on improving efficiency of conversion of dietary 51

P into animal products and on accurate estimation of P requirement by the animal. 52

Availability of P in feed ingredients for pigs is commonly evaluated using digestibility 53

studies or the slope-ratio assay technique (Jongbloed et al., 1991). Digestibility studies estimate P 54

availability by measuring its digestive utilization; whereas, the slope-ratio assay provides a 55

combined estimate of digestive and post-absorptive utilization of P at the tissue level (Jongbloed 56

et al., 1991). Apparent digestibility values underestimate the true digestibility of P, therefore, true 57

P digestibility values were recommended by Fan et al. (2001). In digestibility studies, 58

determination of true P digestibility requires measurement of endogenous P excretion. Fan et al. 59

(2001) developed a linear regression analysis approach to determine true P digestibility and 60

endogenous P excretion that was subsequently applied to corn-based (Shen et al., 2002) and 61

soybean meal-based (Ajakaiye et al., 2003) diets for growing pigs. A concern with this method is 62

whether there is a linear relationship between endogenous P output and dietary P intake. 63

Furthermore, Moughan et al. (1998) stated that endogenous estimates are constrained by the 64



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mathematical model fitted, which is accepted a priori, and estimated values tend to have high 65

standard errors. However, little attention has been given to nonlinear models. Biological 66

responses are rarely linear and at high doses, nonlinearity of regression is almost inevitable for 67

any kind of response (Finney, 1978). 68

The objectives of the present study were to collect data from P balance studies with 69

growing pigs, and to evaluate alternative mathematical functions to estimate biological 70

determinants of P utilization with attention to endogenous P excretion, maintenance requirement, 71

and efficiency of dietary P conversion into animal products. The null hypothesis was that the 72

relationship between retained P and dietary P is linear. 73

MATERIALS AND METHODS 74

The Database 75

A database containing P balance data for 350 pigs in 14 experiments was assembled from 76

the literature. The database contained information on diet, dietary P intake, BW, P retention, and 77

in some instances available P content. In the studies that reported available P content, the values 78

were based on NRC (1998) bioavailability values for corn-soybean meal diets. Therefore, in this 79

study available P values are based on NRC (1998) values for swine diets. For consistency and to 80

minimize the effect of different types of diets on P utilization, we have selected studies that used 81

diets based on corn and soybean meal. Table 1 shows details of diet composition for the trials 82

used to construct the database. The range of data included is summarized in Table 2. 83

The database contained information where available P intake (i.e., the amount of P intake 84

that is potentially available for absorption by the animal) was not given. Therefore, 3 analyses 85

were conducted using 2 datasets. Dataset 1 contained all the data (n = 350) and Dataset 2 was a 86

subset containing only data where available P was reported (n = 76). In the first and second 87



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analyses, a relationship between retained, and total and available P using Datasets 1 and 2, 88

respectively, was established. In the third analysis, Dataset 2 was used to determine a relationship 89

between available and total P intake (i.e., the total amount of P fed to the animals and includes 90

both potentially available and unavailable P), and the resultant availability coefficient using in 91

conjunction with Dataset 1 to estimate instantaneous efficiencies at various P intakes. 92

Various units are used to express the key parameters of P requirements in the literature. 93

Rodehutscord et al. (1998) showed that endogenous P excretion was related with BW but not 94

DMI, therefore, in this study, the analysis was conducted scaling daily P intake (total and 95

available) and P retention by metabolic BW [g/(kg BW0.75⋅ d)]. 96

Candidate Functions 97

In addition to the traditional straight line analysis used for determining P requirements, 3 98

other candidate functions were evaluated (Table 3). These were a function exhibiting diminishing 99

returns behavior (monomolecular); a function exhibiting sigmoidal behavior with a fixed point of 100

inflection (Gompertz), and a sigmoidal function with a flexible point of inflection (Richards, 101

Table 3). The functions were specifically re-parameterized for balance study analysis so that the 102

parameters a, b, and c are positive entities, with ymax = a (upper asymptote) in the nonlinear 103

models, and -b is the y-intercept (value of f(x) when x = 0) in all functions including the linear 104

model (Kebreab et al., 2003). The Richards function has an extra parameter, n, which is a 105

constant that determines the shape of the response curve (Thornley and France, 2007). The P 106

requirement for maintenance was calculated by setting f(x) equal to zero and solving for x.107

Endogenous P excretion was estimated by the intercept on the y-axis. Figure 1 shows graphically 108

the calculations of key parameters using the monomolecular equation, which are discussed 109

further below. 110



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Comparison of candidate functions (discussed below, Table 3) suggested the 111

monomolecular was a good descriptor of the relationship between P retention (R) and available P 112

intake (Ia). For example: 113

( )e acIR a a b −= − + , [1] 114

where a is theoretical maximum P retention, b is endogenous P excretion and c is a shape 115

parameter. The instantaneous efficiency of conversion (kg) of available P to retained P at any 116

given Ia is then: 117

d ( ) edacI

ga

Rk a b cI−= = + [2] 118

Available P intake at maintenance can be calculated by putting R = 0 in Eq. [1] and re-arranging. 119

The corresponding relationship between retained P and total P intake and the instantaneous 120

efficiency dR/dIt are also given by equation forms [1] and [2], respectively. 121

The relationship between total P and available P intake was tested using the linear 122

relationship: 123

a tI Iα β= + , [3] 124

where α is the intercept and β is the slope (i.e. P availability coefficient). The MIXED procedure 125

(SAS, Inst., Inc., Cary, NC) was used for regression to take account of the random effect of 126

experiments. Equation [2] may be written: 127

d d dd d d

tg

a t a

R R Ik I I I= = × 128

From Eq. [3]: 129

dd

a

t

II β=130



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1dd

t

a

II β −∴ = ,131

thus, as an alternative to direct calculation, instantaneous efficiency of utilization of available P 132

intake can be calculated indirectly by multiplying the instantaneous efficiency of utilization of 133

total P intake by the factor 1/β.134

The average efficiency of conversion of available or total P to retained P ( k ) between 2 135

intakes (I and I + ∆I, Figure 1) was calculated according to Darmani Kuhi et al. (2003): 136

Rk I∆= ∆137

Statistical Analyses 138

The database contained information collected from several experiments, and in some 139

instances multiple observations were made on the same pig at different periods. Therefore, a 140

meta-analytical approach was used for data analysis. Trial was coded as a random effect (because 141

the experiments represent a random sample of a larger population) and random effects of pigs and 142

period within experiments were added to the model. Pig breed/genotype, sex, and year of study 143

were added into the model as fixed effect variables. Pig breed/genotype and year of study were 144

not significant in the model but sex was marginally significant so it was left in the model. The 145

MIXED (for linear) and NLMIXED (for nonlinear functions) procedures of SAS were used for 146

analysis (Littell et al., 1996; St-Pierre, 2001). 147

Distribution of random effects was assumed to be normal and the dual quasi-Newton 148

technique was used for optimization with adaptive Gaussian quadrature as the integration 149

method. Performance of the models was evaluated using significance level of the parameters 150

estimated, variance of error estimate and its approximate standard error. Comparison of functions 151

was made using Bayesian Information Criterion (BIC), which are model order selection criteria 152



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based on parsimony and impose a penalty on more complicated models for inclusion of 153

additional parameters. The BIC combines the maximum likelihood (data fitting) and the choice of 154

model by penalizing the (log) maximum likelihood with a term related to model complexity as 155

follows: 156

BIC = −2 log(Ĵ) + Klog (N), 157

where Ĵ is the maximum likelihood, K is the number of free parameters in the model and N is the 158

sample size (Leonard & Hsu, 2001). A smaller numerical value of BIC indicates a better fit when 159

comparing models. 160

RESULTS 161

P Retention vs. Total P Intake 162

The 4 functions were used on Dataset 1 to describe the relationship between P retained in 163

the body and total P intake (Table 4). In all cases, there was a good relationship between P 164

retention and total P intake. Based on BIC and SE of the models, the monomolecular equation 165

gave the best fit followed by the Gompertz, Richards, and the straight line, respectively (Table 4). 166

Two parameter estimates from the Richards and one from monomolecular and Gompertz 167

functions were not significant. 168

Estimates of endogenous P excretion ranged from 17 to 123 mg P/(kg BW0.75⋅ d) (parameter 169

b, Table 4). The monomolecular equation estimate was 17 mg P/(kg BW0.75⋅ d), and the straight 170

line and Richards estimates were similar to this value. Estimates of total P requirement for 171

maintenance ranged from 30 to 173 mg/(kg BW0.75⋅ d), with values from Richards and the 172

monomolecular at the lower end and Gompertz at the higher end. The P requirement for 173

maintenance generated by this analysis also includes unavailable P. 174

P Retention vs. Available P Intake 175



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The 4 functions were fitted to the data on P retention and recorded available P intake 176

(Dataset 2). The non-linear functions showed a good fit to these data based on BIC and SE of the 177

model and were all an improvement on the straight line function (Table 5). Parameters a and b178

can be ascribed biological meaning and refer to theoretical maximum P retention and endogenous 179

P excretion, respectively. Parameters c and n are constants that determine the shape of the curve. 180

The SE of parameter a was significant for all functions except the monomolecular and parameter 181

b was significant only for monomolecular and Gompertz functions. Parameter c was significant 182

in all equations but n was not significant for the Richards. 183

Estimates of endogenous P excretion (b) ranged from 3.8 to 14 mg/(kg BW0.75⋅ d; Table 5). 184

Available P requirement for maintenance ranged from 7 to 19 mg/(kg BW0.75⋅ d). Average 185

estimated efficiencies of conversion of available P to retained P over the total range of P intakes 186

were close for the non-linear functions evaluated, ranging from 54 to 65% (Table 5). 187

Estimation of Available P from Total P 188

A mixed linear regression model given by Eq. [3] was applied to Dataset 2 and the 189

following relationship was established: 190

Ia = 0.0006 (SE 0.005) + 0.47 (SE 0.095)It (r2 = 0.71) [4] 191

The intercept was not significantly different from zero, but the slope (measure of P 192

availability) was highly significant. Based on Eq. [1] through [4], available P values were 193

calculated for data points where only total P was measured. Retained P was then regressed 194

against calculated available P and the parameter estimates from the monomolecular function were 195

compared to the fit using reported available P values shown in Table 5. Parameters a, b, and c in 196

the monomolecular function for data using calculated available P were 0.59 (SE = 0.24), 0.015 197

(SE = 0.005) and 1.61 (SE = 0.09), respectively. None of these parameter estimates were 198



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significantly different from those estimated using Dataset 2. The maintenance requirements and 199

average efficiency values based on calculated available P intake were also similar (maintenance = 200

16 mg/(kg BW0.75⋅d); k = 0.66). 201

Estimates of instantaneous efficiency of utilization kg based on the monomolecular equation 202

are shown in Table 6. The estimates resulting from using calculated (i.e. Eq. [4]) and measured 203

available P were in close agreement (Table 6). 204

DISCUSSION 205

In this study, linearity of the relationship between P retention and dietary P intake was 206

challenged by comparing 4 candidate functions. Available P was not always reported for the 207

literature data collected, so it was necessary to use 2 datasets; one containing total P intake 208

(reported with or without available P) and another limited to those values with reported available 209

P only. Using the candidate functions, first, a relationship between retained P and total P intake 210

was established. Second, retained P was related to available P and third, available P was 211

regressed against total P intake. Finally, information obtained using dataset 2 was applied to the 212

composite data in order to extract information on key determinants of P requirement and the 213

nature of the relationship between P retention and intake. 214

Endogenous P Excretion 215

Although there was evidence of nonlinearity, the lack of sufficient data above 0.7 g of total 216

and 0.4 g of available P intake/(kg BW0.75⋅d) indicated that parameter a was not well estimated 217

for the diminishing returns function and parameters b, c, and n for sigmoidal functions when 218

retained P was regressed against total or available P intake. The case for monomolecular as the 219

most suitable candidate was strengthened because as parameter n approaches particular values, 220

the Richards equation encompasses other simpler models, such as the monomolecular (n = –1), 221



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Gompertz (n = 0) and logistic (n = 1). In our analysis, the parameter n was always negative, 222

tending to the monomolecular. 223

We assumed that endogenous P excretion is equal to excretion at zero P intake. However, it 224

is uncertain what happens when net retention becomes negative. There may be a different pattern 225

of response from the body when its need for P is not met. However, it is expected that the 226

efficiency of utilization will increase as digestion and absorption proportionally increase due to 227

less supply of dietary P, thus creating greater utilization is achieved when the capacity for 228

digestion and absorption, or both is not reached. This would lead to a lower intercept on the y-229

axis due to a steeper slope. On the other hand, metabolism might decrease in order to spare the 230

reserves and the continuing re-cycling from body stores would lessen, leading to a decrease in 231

endogenous excretion. This implies a greater intercept. This balance would further change if 232

insufficient supply is continued for a prolonged time. 233

When P retained is regressed against P intake, endogenous P excretion is given by net 234

retention at zero P intake. Estimates based on total P compared to available P would be expected 235

to yield greater endogenous excretion because the data from which it is derived would include 236

undigestible P. Better estimates are achieved when available P is used to predict endogenous P 237

excretion. The monomolecular equation predicted it to be 14 mg/(kg BW0.75⋅ d), based on 238

reported available P values and 17 mg/(kg BW0.75⋅ d) based on total P values, which after 239

accounting for metabolic BW was close to the range suggested by Jongbloed (1987) who 240

documented values of 2.9 to 24.5 mg/(kg BW⋅d) for pigs weighing 15 to 140 kg (with P in the 241

diet ranging from 0.33 to 0.83%). Variable endogenous P loss values were reported for growing 242

pigs fed a semi-purified diet (0.07 g/kg DMI or 3.2 mg/(kg BW⋅d), Petersen and Stein, 2006; 7.3 243

to 9.3 mg/(kg BW0.75⋅ d), Pettey et al., 2006), corn-based diet (0.67 g/kg DMI or 30.2 mg/(kg 244



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BW⋅d), Shen et al., 2002) and soybean meal-based diet (0.45 g/kg DMI or 20.3 mg/(kg BW⋅d), 245

Ajakaiye et al., 2003). Our estimate was very close to that reported by Rodehutscord et al. (1998) 246

who showed that endogenous P excretion to be 15.5 mg of P/(kg BW0.75⋅d) based on regression 247

analysis of 66 P balance studies. Dilger and Adeola (2006) summarized estimates of endogenous 248

P excretion values reported in the literature. They concluded that the endogenous P loss in pigs 249

was likely to be less than 20 mg (kg BW0.75⋅ d) which agrees well with the results of our study 250

based on monomolecular function. Estimates of endogenous P excretion predicted by the 251

straight-line function was close to estimates reported by Pettey et al. (2006) and Dilger and 252

Adeola (2006) who also used a straight line approach to estimate endogenous P excretion. 253

A nonlinear equation is expected to provide greater estimates of endogenous P excretion 254

compared to standard straight line analysis because it assumes that the efficiency of P conversion 255

to retained P is not fixed as is the case with the straight line analysis. The endogenous P excretion 256

obtained by the monomolecular equation in this study included fecal endogenous P output and 257

urinary metabolic endogenous loss. Total urinary P excretion accounted for only a small fraction 258

of the whole body total P excretion in growing pigs fed within P requirement levels (Rideout and 259

Fan, 2004). Thus, it is conceivable that fecal endogenous P output is the primary component of 260

endogenous P excretion estimated by the monomolecular equation in this study. 261

Phosphorus Requirement for Maintenance (Pm)262

The functions predicted a range of available Pm values, with the best fitting model, the 263

monomolecular function, giving 15 and 16 mg/(kg BW0.75⋅d) using either reported or calculated 264

available P values, respectively. These values are slightly greater than the basal endogenous P 265

loss and therefore suggest that the maintenance requirement mostly accounts for the basal loss of 266

P from the animal. 267



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Despite the flexible nature of the function, the Richards did not improve upon the variation 268

explained by either of the simpler nonlinear models. This is partly because the Richards appears 269

over-parameterized for the data presented, which was illustrated by non-significant values of 2 of 270

its 4 parameter estimates. Generally, the supply of other nutrients such as Ca and vitamin D are 271

also known to influence P metabolism (NRC, 1998) thus influencing the behavior of the curve 272

and maintenance requirement. The concentration of Ca and vitamin D was not considered in the 273

present analysis. However, the supply of these nutrients was considered normal in the 274

experiments examined to derive the data sets used for the parameterization of equations. 275

Calculations for assessing requirements of other nutrients including energy for growing pigs 276

included separate estimates for maintenance and production. However, P requirements are 277

usually expressed as the sum of obligatory loss (urine plus feces P) and retention (ARC, 1981; 278

Jongbloed et al. 1999). Therefore, comparison of Pm values obtained in this study with other work 279

is difficult due to the scarcity of reported Pm figures. Different recommendation tables (NRC, 280

1998; ARC, 1981, Jorgensen & Tybirk, 2005) only provide total P requirements and do not 281

allocate it into maintenance and growth requirements. For example, NRC (1998) recommends an 282

available P requirement of 3.2 g/d for the 10- to 20-kg pig. This requirement includes 283

maintenance P, which in our study was estimated to be 0.14 g/d for the 20-kg pig, and growth 284

which will be utilized at 65% efficiency according to our results. The estimated retention of 285

approximately 2 g available P/d is consistent with values reported by Hastad et al. (2004) for pigs 286

with similar BW. 287

Efficiency of P Utilization 288

Greater efficiency coefficients are expected when using available rather than total P because 289

calculations based on total P also includes inefficiency or incomplete digestion or absorption of 290



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dietary P. Efficiency was generally greatest at low available P intake and became decreased as 291

intake increased (Table 5 and 6). Changes in efficiency were greatest for the sigmoidal functions 292

because of their inherent shape. Biologically, it is unlikely that there is a lag phase where 293

minimum changes in efficiency occur at lower intakes as predicted by the Gompertz equation. 294

However, the monomolecular function gives a diminishing return in efficiency as intake 295

increases, which is biologically more sensible. 296

When total P intake was scaled by metabolic BW, average efficiency of P utilization was 297

between 34 and 45%, which is in the range reported in the literature (e.g., Revy et al., 2004). For 298

pigs fed corn and soybean based diets, Adeola et al. (2004) reported efficiency of utilization of P 299

in control animals was an average of 46% which was close to estimates from the straight line and 300

Gompertz functions. Furthermore, Dilger and Adeola (2006) reported efficiency values ranging 301

from 30 to 42% which is within the range of estimates given by the straight line, monomolecular, 302

and Richards functions. Results for efficiency of conversion of dietary to retained P, evaluated at 303

various intake ranges using the diminishing returns model, showed efficiency was greatest at low 304

P intake followed by a decrease in efficiency as P intake increased. This was not the case for the 305

sigmoidal function because of shallower slopes at the beginning of the curve, which rose sharply 306

towards mid P intake values. In reality, this is an unlikely scenario as the animals would have a 307

greater efficiency when P deficient while more P would be excreted as their capacity to absorb P 308

is saturated at high P intakes. However, it is difficult to say if the P retention curve shows 309

sigmoidicity at dietary values very close to zero before following diminishing returns behavior 310

after a low point of inflection. Nothing in the present data elucidates this. 311

Based on the meta-analyses conducted in this study, fitting the monomolecular equation to 312

the data more accurately accounted for variation compared with fitting any of the other functions 313



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(including the straight line, which represented the null hypothesis in this study). Figure 2 shows 314

the relationship between P retention and intake (both total and available) obtained with the 315

monomolecular equation. Biologically, it is more plausible that efficiency of P utilization is 316

greater when pigs consume P below their maintenance requirement and decreases as intake 317

increases, which is the situation described by the monomolecular or Richards, but not by the 318

Gompertz. Scarcity of observations approaching the asymptote made estimating parameter a319

(maximum P retention) difficult, particularly in the analysis with available P. The monomolecular 320

could also be used to investigate the effects of diets or Ca:P ratio, particularly if sufficient data on 321

different weight groups were available. 322

In summary, a meta-analytical approach to evaluating various functions describing the 323

relationship between P retention and available P (and total P) in growing pigs revealed that the 324

monomolecular equation consistently described the data better than linear, Gompertz and 325

Richards equations. The monomolecular indicated that endogenous P excretion was 14 mg/(kg 326

BW0.75⋅ d) based on available P analysis. Maintenance requirements was 15 mg available P/(kg 327

BW0.75⋅ d). Average efficiencies of utilization above maintenance were 65 and 36% for available 328

and total P, respectively. Therefore, requirements can be estimated by adding the P needed for 329

maintenance and body retention, assuming normal ranges of dietary Ca:P ratios and vitamin D 330

concentrations. 331



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Table 1. Diet composition, number of pigs and references for the trials used to construct the database412

Trial n Main diet ingredients1 Pig breed Weight

range

(kg)

Reference

1 4 Corn and soybean meal with different levels of P C-15 × Canabrid 54 Ekpe et al. (2002)

2 7 Corn diet supplemented with different protein sources

(soybean meal, whey protein and blood meal) with sodium

and dicalcium phosphate added to adjust P levels

Yorkshire-Landrace

Duroc

30 Veum et al. (2002)

3 7 As in trial 2 Yorkshire-Landrace ×

Duroc

37 to 42 Veum et al. (2001)

4 5 Corn and soybean meal with different levels of P Yorkshire-Landrace ×

Duroc

20 Spencer et al. (2000)

5 6 Corn and soybean meal with 2 levels of Ca and P Yorkshire × Hampshire 76 Carter et al. (1999)

6 2 Corn and soybean meal with different levels of dicalcium

phosphate

Yorkshire × Landrace 30 D. Vitti (CENA, Sao

Paulo, SP, personal

communication)


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7 27 Corn and barley with soybean meal with 3 levels of Ca:P

ratio

Landrace × Yorkshire 38 to 97 Jongbloed (1987)

8 15 As in trial 7 but with high and low levels of feeding2 Landrace × Yorkshire 42 to 94 Jongbloed (1987)

9 32 Corn, barley and soybean meal with 2 levels of energy

supply

Landrace × Yorkshire 27 to 94 Jongbloed (1987)

10 32 Corn, barley and soybean meal with 4 levels of lysine

concentration in diet

Nieuw Dalland ×

Landrace

35 to 98 Jongbloed (1987)

11 63 As in trial 10 Yorkshire × Landrace 35 to 99 Jongbloed (1987)

12 45 Corn, barley and various combinations of dietary fat and Ca

levels

Pure Yorkshire 39 to 97 Jongbloed (1987)

13 36 Corn, barley with soybean meal and 4 levels of dietary fibre Landrace × Yorkshire 42 to 98 Jongbloed (1987)

14 69 Corn, barley with soybean meal and 4 levels of Ca:P ratio Landrace × Yorkshire 39 to 95 Jongbloed (1987)1Unless otherwise stated the animals had ad libitum access to feed.413

2One half of the animals were fed at high level of feeding (average 1.86 kg/d) and the other were on 80% of the high level of414

feeding.415

416


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Table 2. Summary statistics for the data used in the study 417

Mean SD Minimum Maximum

Animal data

DMI, g/d 1784 449 585 2825

BW, kg 59.2 27.1 20.0 99.0

P measurements (g/d)

P intake 10.8 4.21 1.79 25.1

Available P intake 5.26 1.48 1.68 8.19

P retention 3.70 1.27 0.32 8.13

P measurements (g/(kg BW0.75⋅ d))

P intake 0.49 0.12 0.19 0.84

Available P intake 0.23 0.06 0.10 0.50

P retention 0.17 0.06 0.03 0.39



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Table 3. The functional forms used to describe the relationship between retained P, y(x), and P 418

intake, x419

Function1 y(x) Value of x when y = 0

Straight line ax b− /b a

Monomolecular ( )e−− + cxa a b 1ln[( ) / ]c a b a− +

Gompertz 2exp[(1 e )ln ] 2cx a bb bb

− +− − 1 ln[( 2 ) / ]ln{ }ln[( 2 ) /(2 )]a b bc a b b

− ++

Richards { }1/( 2 ) 2

( 2 ) e nn n n cxb a b b

b a b b −+ − + + −

1 2 [( 2 ) ]ln ( 2 ) (2 )

n n n

n na b bc a b b

− + − + − 1The parameters a, b and c are positive entities, n ≥ −1, and in nonlinear models ymax = a420

and ymin = −b.421



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Table 4. Parameter estimates and goodness of fit for the different equations fitted to P retention 422

vs. total P intake [g/(kg BW0.75⋅ d)] using Dataset 1. Standard errors are given in brackets. 423

Equations

Item Straight line Monomolecular Gompertz Richards

Parameter1

a 0.42 (0.03) 0.71 (0.36) 0.34 (0.03) 0.39 (0.03) b 0.023 (0.002) 0.017 (0.006) 0.123 (0.15) 0.019 (0.114) c 0.64 (0.061) 3.38 (0.39) 1.59 (1.3) n -1.00 (0.08)

σ (model)2 0.000701 0.000625 0.000633 0.000631 BIC3 -482.3 -508.7 -503.2 -501.2 r2 0.75 0.81 0.78 0.78 k 4 0.42 0.36 0.45 0.34

)45.00( −k 5 0.41 0.76 0.45

)9.045.0( −k 6 0.31 0.33 0.23 Pm6 0.056 0.037 0.173 0.030

1Parameters a and b refer to theoretical maximum P retention and endogenous P 424

excretion, respectively and are expressed in g/(kg BW0.75⋅d). Parameter c is a constant expressed 425

in (kg BW0.75⋅d)/g and parameter n is a dimensionless constant. Parameters c and n determine the 426

shape of the curve. 427

2Standard error of model. 428

3Bayesian information criteria. 429

4Average efficiency of conversion of dietary P intakes from 0 to 0.9 g/(kg BW0.75⋅ d) to 430

retained P. 431

5Average efficiency of conversion of dietary P intakes from 0 to 0.45 g/(kg BW0.75⋅ d) to 432

retained P. 433



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6Average efficiency of conversion of dietary P intakes from 0.45 to 0.9 g/(kg BW0.75⋅ d) to 434

retained P. 435

7Total P requirement for maintenance [g/(kg BW0.75⋅ d)]. 436



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Table 5. Parameter estimates and goodness of fit for the different equations fitted to P retention 437

vs. available P intake [g/(kg BW0.75⋅ d)] using Dataset 2. Standard errors are given in brackets 438

Equations

Item Straight line Monomolecular Gompertz Richards

Parameter1

a 0.76 (0.12) 0.63 (0.31) 0.27 (0.02) 0.32 (0.03) b 0.005 (0.03) 0.014 (0.006) 0.0038 (0.008) 0.011 (0.12) c 1.44 (0.08) 10.3 (2.4) 5.1 (1.88) n -0.5 (0.37)

σ (model)2 0.000669 0.000625 0.00063 0.000635 BIC3 -418.2 -436.4 -434.3 -433.2 r2 0.74 0.80 0.78 0.78 k 4 0.76 0.65 0.54 0.58

)25.00( −k 5 0.75 0.82 0.78

)5.025.0( −k 6 0.54 0.27 0.39 aPm7 0.007 0.015 0.017 0.019

1Parameters a and b refer to theoretical maximum P retention and endogenous P 439

excretion, respectively and are expressed in g/(kg BW0.75⋅ d). Parameter c is a constant expressed 440

in (kg BW0.75⋅d)/g and parameter n is a dimensionless constant. Parameters c and n determine the 441

shape of the curve. 442

2Standard error of model. 443

3Bayesian information criteria. 444

4Average efficiency of conversion of available dietary P intakes from 0 to 0.5 g/(kg 445

BW0.75⋅ d) to retained P. 446

5Average efficiency of conversion of available dietary P intakes from 0 to 0.25 g/(kg 447




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6Average efficiency of conversion of available dietary P intakes from 0.25 to 0.5 g/(kg 449


7Available P requirement for maintenance [g/(kg BW0.75⋅ d)]. 451



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Table 6. Instantaneous efficiency values at various intake levels for available and total P based 452

on the monomolecular equation 453

Measured

Instantaneous efficiency1 available P2 total P Calculated available P3

kgm 0.90 0.45 0.96

kg1 0.80 0.40 0.84

kg2 0.69 0.34 0.72

kg3 0.51 0.25 0.52 1kgm = instantaneous efficiency at maintenance, kg1 to kg3 = instantaneous efficiency at 454

total P intake levels of 0.1, 0.2, and 0.3 g/(kg BW0.75⋅ d), respectively. 455

2Data from Dataset 2 only is used in the analysis. 456

3Available P calculated indirectly by dividing the instantaneous efficiency for total P by the 457

factor 0.47 given by Eq. [4]. 458



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Figure legends: 459

460

Figure 1. Schematic representation of endogenous P excretion, P requirement for maintenance 461

and efficiencies of P conversion using the monomolecular equation. Axes are in units of g/(kg 462

BW0.75⋅ d). 463

464

Figure 2. Relationship between P retention and available P intake scaled by metabolic BW 465

(BW0.75) in growing pigs using the monomolecular function. The solid line is given by the 466

equation 0.63 – (0.63 + 0.014)e-1.44(available P intake) 467



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Figure 1. Schulin-Zeuthen et al. 468

469

Col 1 vs Col 2 Col 1 vs Col 2

Monomolecular

Intake, I0.20 0.40 0.60 0.80

Reten

tion,R

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Instanteneous efficiencyof conversion at intake I = dR/dI

P requirement for maintenance

Endogenous Pexcretion

Average efficiency of conversion between intakes I and I + ∆I = ∆R/∆I

∆R

∆I

470 471



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Figure 2. Schulin-Zeuthen et al. 472

473

available P intake, g/kg BW0.75 per d0.0 0.1 0.2 0.3 0.4 0.5

Pret

entio

ng/kg

BW0.7

5pe

rd

0.0

0.1

0.2

0.3

474



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