Statistical analyses

The effects of line and climate on feed requirements for BWG (i.e., the regression coefficients on BWG) were estimated based on the following mixed model that included all individual observations in all four TN and three HS periods:

were FI_i = average daily feed intake of individual i across all TN and HS periods, Line_j = effect of genetic line j (fixed effect; commercial, low RFI, high RFI), Climate_k = effect of climate k (fixed effect; TN, HS), Diet_l = effect of diet l (fixed effect; low fiber, high fiber), Room_m = effect of room m (fixed effect; room 1 and 2), Litter{Line_j}_n = effect of litter n nested within line j (random effect), Age_o = covariate effect of age o, BWi0.75 = covariate effect of metabolic body weight of individual i across all TN and HS periods, BWG_i = covariate effect of body weight gain of individual i across all TN and HS periods, BFT_i = covariate effect of backfat thickness of individual i, and e_i = error term of animal i across all TN and HS periods.

The SAS program (SAS Inst. Inc., Cary, NC) was used for the statistical analyses of all individual measured, calculated and estimated parameters. The following mixed model with a repeated statement was fitted to describe the data on BW, BWGperiod, FIperiod, RFI, and FCE.

where Y_ijklmnop = the phenotype measured on animal p, Line_i = effect of genetic line i (fixed effect; commercial, low RFI, high RFI), Climate_j = effect of climate j (fixed effect; TN, HS), Period{Climate_j}_k = effect of period k nested in climate j (fixed effect), Diet_l = effect of diet l (fixed effect; low fiber, high fiber), Room_m = effect of room m (fixed effect; room 1 and 2), Litter{Line_i}_n = effect of litter n nested within line i (random effect), Age_o = covariate effect of age o (regression coefficient), (Line × Climate)_ij = interaction effect between line i and climate j, (Line × Period{Climate_j})_ik = interaction effect between line i and period k (nested within climate j), (Line × Room)_im = interaction effect between line i and room m, (Line × Diet)_il = interaction effect between line i and diet l, (Diet × Climate)_lj = interaction effect between diet l and climate j, (Diet × Period{Climate_j})_lk = interaction effect between diet l and period k (nested within climate j), (Diet × Room)_lm = interaction effect between diet l and room m, (Room × Climate)_mj = interaction effect between room m and climate j, (Room × Period{Climate_j})_mk = interaction effect between room m and period k (nested within climate j), and e_ijklmnop = error term of animal p of genetic line i in climate j, in period k, on diet l, in room m, born in litter n, of age o, e_ijklmnop~NID(0, δe2). LossBWG and LossFI were analyzed with the same model (4) but excluding the effect of climate and its interactions. In addition, LEA and BFT were described by the same model (4) excluding the effect of climate and its interactions but including the covariate effect of BW. Interaction effects in model (4) with a p-value of 0.10 and larger were removed from the model (Table ​(Table2).2). Period was identified as the repeated effect in the model for each individual. “Period” corresponded to day 1, 8, 19, 23, 30, 34, 41, 45, and 52, for BW (9 periods), periods TN1 to TN4 for BWGperiod and FI_PERIOD (7 periods), periods HS1 to HS3 for LossBWG and LossFI (3 periods), and day 19 and 52 for LEA and BFT (2 periods). The following variance-covariance structures for repeated measures were evaluated to describe individual observations on a trait by trait basis (Table ​(Table2):2): Homogeneous Autoregressive(1) (AR(1)), Heterogeneous Autoregressive(1) (ARH(1)), Compound Symmetry (CS), Toeplitz (TOEP), and Unstructured (UN). The first two models also included the random effect of the individual. Analysis of BW was also evaluated with the spatial power variance components model (sp(pow)), which can be used if observations are not equally spaced in time. Model choice was based on evaluation of fit statistics [the (corrected) Akaike's information criterion and the Sawa Bayesian information criterion], and by using a likelihood ratio test to compare the two best fitting models (provided models were nested) with a chi-square test, using the difference in the −2 Res Log Likelihood and the difference in the number of covariance parameters estimated as test statistics.

Significance (p-values) for line, climate, period, diet, room, age and body weight (BW) and their interactions, on BW, body weight gain (BWGperiod), drop in body weight gain (LossBWG), feed intake (FIperiod), drop in feed intake (LossFI), residual feed intake (RFI), feed conversion efficiency (FCE), loin eye area (LEA), backfat thickness (BFT), percentage lean (%Lean), loin depth (LoinD), and hot carcass weight (HCW).

L, Line; D, Diet; C, Climate; P, Period; R, Room.

Variance-covariance structures used in model (4): Unstructured (UN), Toeplitz (TOEP), Heterogeneous Autoregressive(1) (ARH(1)), and the mixed model used in models (4) and (5) (MIXED).

The following random mixed model was used to evaluate the carcass traits LoinDepth and HCW:

where BW_m = covariate effect of body weight m, and all other effects are as given in model (4). In addition, %Lean was analyzed with the same model (5), but excluding the effect of BW. Interaction effects in model (5) with a p-value of 0.10 and larger were removed from the model (Table ​(Table22).

Results are presented as least squares means adjusted for the effects in models 4 and 5. Partial correlation coefficients among traits were estimated after correcting the phenotypes for the effects of line, diet, and room.