### INTRODUCTION

### MATERIALS AND METHODS

### Animal management and data collection

^{2}of floor space to provide 0.635 m

^{2}/pig with 12 pigs/pen. Each pen was randomly assigned to either the high (HE) or low (LE) energy diets (Table 1) and to either light or heavy market weight. The LE and HE diets were phase fed from the test date to completion of test. For replicates 1 to 6, the target BWs were 117.9 and 131.5 kg. In replicates 7 to 10, the target BWs were 127 and 140.6 kg. Individual pig BWs were recorded for each pig every 28 to 30 d until the pig achieved its target BW. Pen feed intake data was collected each weigh day and when one or more pigs achieved its target BW and was removed from the pen and marketed. Pigs were transported and harvested at a commercial pork processing plant.

### Statistical analyses

_{i},

_{t}= ((WT

_{o}K

^{C})+( WF t

^{C}))/(K

^{C}+t

^{C})+e

_{i,t}or WT

_{i,t}= WT

_{o}+((WF−WT

_{o})(t/K)

^{C}))/(1+(t/K)

^{C}))+e

_{i,t}where WF is mean mature BW, WT

_{o}is the mean birth BW, t is days of age, K is a parameter equal to the days of age in which one-half WF is achieved and C is a unit less parameter related to changes in proportional growth and shape of the growth curves (Lopez et al., 2000). In this function, each pig’s actual birth BW (WT

_{i,o}) was used. This function has an inflection point age (IP, d) = K ((C−1)/(C+1))

^{(1/C)}and the BW at the IP = ((1+(1/C))WT

_{o}+(1−(1/C))WF)/2. In this function, WF, K and C were considered as random effects.

_{i}as a linear function of wf

_{i}(c

_{i}= b wf

_{i}) or k

_{i}(c

_{i}= b k

_{i}). In these analyses, the fixed parameter C was replaced by C+c

_{i}(C+b wf

_{i}) or (C+b k

_{i}). These analyses allowed for a pig specific value of c

_{i}to be predicted based upon a population wide linear relationship of the predicted random effect for c

_{i}and wf

_{i}.

^{®}(SAS Institute, Inc., Cary, NC). Random effects were added in a step-wise order based on Akaike’s Information Criteria (AIC) values. The addition of a predicted random effect for c

_{i}as a linear function of wf

_{i}was evaluated for each equation by comparing the AIC values. The R

^{2}values were calculated as squared correlations between the predicted and actual observations. The RSD was calculated with the equation

*e*

*is the residual value of the i*

_{i,t}^{th}pig at age

*t*, n is the number of observations, and p is the number of parameters in the model. The NLMIXED procedure provided predicted values for the random effect of each pig, variance estimates for each random effect, covariance estimates for each pair of random effects, and the residual variance.

_{i,BW}= C(1−exp(−M BW

^{A})) +e

_{i, BW}was proposed by Bridges et al. (1986). Here BW is mid-BW (kg) of the i

^{th}pen, C is the average mature DFI, ME, or NE intake, M is the exponential growth decay constant and A is the kinetic order constant. Since the exponential decay parameter was close to zero, the model was reparamaterized (M′ = log M)) with the form, DFI

_{i,BW}= C(1−exp(−exp(M′)BW

^{A})) (Craig and Schinckel, 2001; Schinckel et al., 2009b). In this function, the BW in which the rate in which daily feed, ME or NE intake changes from being increasing to decreasing relative to BW is called the inflection point (IP) and is equal to DFI times F where F = 1−exp((1/A)−1). The age at the IP = (A M/(A−1))

^{(−1/A)}. In this function, C, M′ and A were considered as pen specific effects. After preliminary analyses were completed and no solution was obtained for the three random effects models, alternative analyses were completed using each equation. The alternative analyses predicted a random effect for a

_{i}as a linear function of c

_{i}(a

_{i}= b c

_{i}) and

*m*

*′ as a linear function of c*

_{i}_{i}. In these analyses, the fixed parameter A was replaced by A+a

_{i}(A+b

_{i}c

_{i}) or M′ replaced by M′+b

_{2}c

_{i}. These analyses allowed for a pen specific value of c

_{i}to be predicted based upon a population wide linear relationship of the predicted random effect for c

_{i}. The inclusion of the pen specific random effects into the Bridges function relating feed or energy intake to BW allows the prediction of pen specific feed and energy intake curves.

### RESULTS

### Body weight growth

_{i}and k

_{i}for barrows and wf

_{i}and c

_{i}for gilts) increased the R

^{2}values and reduced the residual standard deviations. Inclusion of the two random effects in the GMM function produces individual pig BW growth curves that differ in their shape (Schinckel et al., 2009a).

### Daily feed and energy intakes

^{2}and decreased the RSD values of the Bridges functions.

### Measures of feed and energetic efficiency

### DISCUSSION

^{2}per pig to reflect commercial conditions. The floor space allowance required for maximum growth is a function of K times BW

^{0.667}(Gonyou et al., 2006). Based upon the K values of Gonyou et al. (2006), the pigs’ ADG was reduced by the 0.635 m

^{2}stocking density at 89 to 102 kg BW. At heavier BWs, as the fastest gaining pigs reached their target BWs, the ADG of the remaining pigs likely increased in comparison to if no pigs were removed (DeDecker et al., 2005).

^{0.70}than muscle mass (Noblet et al., 1999). Pigs fed the HE diets had both greater dietary lipid intake and lipid accretion. The HE, high fat diets may have an advantage in that the direct deposition of dietary fat to lipid accretion is an energetically efficient process (about 90%; Whittemore, 1997; Birkett et al., 2001c; Noblet and Milgen, 2004). Nutrient flow models which consider the animals’ ultimate use of the nutrients (protein, starch, fat) and the increased endogenous secretions produced by some feedstuffs and their impact on maintenance requirements could better account for the differences in pig performance observed in this trial (Birkett and de Lange, 2001a, b).