Table 1.
Estimates of variance (block-diagonals), covariance (upper triangular blocks; in italic) and correlation (lower triangular blocks; in bold) among coefficients of reaction norm models (RNM) for the additive genetic effect of post-weaning weight gain (kg) in Nellore cattle, along with residual variance estimates and Akaike (AIC) and Bayesian (BIC) information criteria
| Modela | Coefficientb | b0 | b1 | b2 | b3 | b4 | ec | npd | AICe | BIC5 |
|---|---|---|---|---|---|---|---|---|---|---|
| RNM_homo | b0 (int) | 129.73 | 48.64 | 223.18 | 4 | 3,560,790 | 3,560,838 | |||
| b1 (slp) | 0.96 | 19.79 | ||||||||
| RNM_hete | b0 (int) | 89.80 | 16.33 | 5.55 | 5 | 3,559,272 (− 1518) | 3,559,332 (− 1506) | |||
| b1 (slp) | 0.86 | 3.99 | 0.23 | |||||||
| RNM_quad | b0 (int) | 95.90 | 11.53 | − 6.75 | 5.58 | 9 | 3,558,581 (− 2209) | 3,558,689 (− 2149) | ||
| b1 (slp) | 0.40 | 8.72 | 2.13 | 0.24 | ||||||
| b2 (qdr) | − 0.50 | 0.52 | 1.92 | − 0.06 | ||||||
| RNM_l-l | b0 (int) | 102.86 | 24.97 | − 1.00 | 5.60 | 9 | 3,558,765 (− 2025) | 3,558,873 (− 1965) | ||
| b1 (slp1) | 0.89 | 7.69 | 0.71 | 0.32 | ||||||
| b2 (slp2) | − 0.02 | 0.06 | 16.71 | 0.16 | ||||||
| RNM_q-q | b0 (int) | 98.03 | 24.51 | − 3.27 | − 1.55 | 0.82 | 5.55 | 20 | 3,558,372 (− 2418) | 3,558,611 (− 2227) |
| b1 (slp1) | 0.31 | 64.15 | 25.80 | − 33.82 | 17.93 | 0.06 | ||||
| b2 (qdr1) | − 0.09 | 0.91 | 12.50 | − 14.09 | 7.59 | − 0.18 | ||||
| b3 (slp2) | − 0.02 | − 0.48 | − 0.45 | 78.93 | − 28.23 | 0.20 | ||||
| b4 (qdr2) | 0.02 | 0.66 | 0.63 | − 0.93 | 11.63 | − 0.01 |
aRNM_homo: linear homoscedastic; RNM_hete: linear heteroscedastic; RNM_quad: quadratic heteroscedastic; RNM_l-l: spline linear–linear heteroscedastic; RNM_q-q: spline quadratic–quadratic heteroscedastic
bb0–b4 coefficients of the RNM for the additive genetic random effect [int: intercept; slp: slope; qdr: quadratic; slp1(2): slope segment 1(2); qdr1(2): quadratic segment 1(2)]
cResidual variance (RNM_homo) or residual coefficients associated with parameters of heteroscedastic RNM that were modeled using a log-residual function [25]
dNumber of estimated parameters
eNumbers in parenthesis refer to difference in comparison with RNM_homo