### INTRODUCTION

### MATERIALS AND METHODS

### Diets and experimental design

### Animals, feeding and sample collection

*N*sulfuric acid was used for urine collection. Feces and urine were collected daily, weighed, and all the feces and a 20% subsample of the urine were stored at −20°C until further analysis. All the collected samples were pooled per pig at the end of the experiment.

### Chemical analyses

### Calculations and statistical analysis

_{I}represents the dietary P (mg/d) or N (g/d) intake; and P

_{O}is the fecal P (mg/d) or N (g/d) output. Digested P or N (P

_{D}) is calculated by the difference between dietary P or N intake and fecal P or N output. The TTTD of P or N in SBM was determined by regressing P

_{D}against P

_{I}for diets with or without casein supplementation using the following model:

*t*-test (Zhai and Adeola, 2013). An α level of 0.05 was used to represent significance level.

### RESULTS

### DISCUSSION

^{32}P-labeled phosphates and the regression method have been used to measure the tandrue digestibility of P in assay ingredients and EPL for animals (Al-Masri and Günther, 1988; Al-Masri, 1995; Fan et al., 2001; Dilger and Adeola, 2006; Petersen and Stein, 2006; Akinmusire and Adeola, 2009). Because of disturbances in normal physiologic status of animals from the P-free diets and the rapid recycling of

^{32}P-labeled phosphates in the gut (Al-Masri and Günther, 1988; Al-Masri, 1995; Petersen and Stein, 2006), the regression method is widely used to estimate the TTTD of P in test ingredients and EPL for pigs. However, there were little information about dietary factors affecting the use of the regression mathematical model and limitations of this approach have been published previously. To our knowledge, the concentrations of P in experimental diets are lower than the requirements of pigs and dietary P levels being within the linear response range are the only reported conditions influencing the use of regression analysis (Poulsen et al., 1999; Fan et al., 2001; Dilger and Adeola, 2006). This is because of the digestibility of P in diets is depressed by excessive dietary phytate-P intake (Selle et al., 2009).

_{SBM}and TTTD

_{casein}represent the TTTD of P (%) in SBM and casein, respectively; P

_{SBM}and P

_{casein}is dietary P (mg/d) originate from SBM and casein, respectively; P

_{D}is digested P (mg/d); P

_{I}is dietary total P intake (mg/d), and EPL is EPL (mg/d). These equations indicate that the negative intercept is EPL+P

_{casein}× (TTTD

_{SBM}– TTTD

_{casein}) using a linear regression of P

_{D}on P

_{I}. However, the TTTD

_{SBM}is lower than TTTD

_{casein}. Therefore, the determined negative intercept representing for EPL is negative when adequate amounts of P derived from casein was supplemented in the basal diet. These equations suggested by Liu et al. (2014b), indicated that the P

_{D}is increased by graded P

_{I}derived from SBM because the increased dietary P intake is due to increasing inclusion of SBM. Therefore, it is reasonable that the estimates of slope representing for TTTD of P in SBM were not affected by constant casein addition in the basal diet. In the current study, the estimate of EPL associated with SBM in pigs is 66 mg/d, which is consistent with the 48 mg/d reported by Akinmusire and Adeola (2009). The values of EPL reported in previous studies ranged from 70 mg/kg of dry matter intake (DMI) (Dilger and Adeola, 2006; Pettey et al., 2006) to 670 mg/kg of DMI (Shen et al., 2002) by regression method. Using the P-free diet, an estimate of EPL at 139 mg/kg of DMI was also reported by Petersen and Stein (2006). Jongbloed et al. (1991) indicated that EPL is decreased when P intake is lower than the requirements for P. However, dietary concentration of P being lower than the requirements of the animal is a fundamental condition needed for using regression approach (Poulsen et al., 1999; Fan et al., 2001; Dilger and Adeola, 2006). Taken together, accurate EPL is not an essential requirement for reliable estimate of regression-derived TTTD of P in test feedstuffs.