Unraveling genetic sensitivity of beef cattle to environmental variation under tropical conditions

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

Model^a	Coefficient^b	b0	b1	b2	b3	b4	e^c	np^d	AIC^e	BIC⁵
RNM_homo	b0 (int)	129.73	48.64				223.18	4	3,560,790	3,560,838
RNM_homo	b1 (slp)	0.96	19.79				223.18		3,560,790	3,560,838
RNM_hete	b0 (int)	89.80	16.33				5.55	5	3,559,272 (− 1518)	3,559,332 (− 1506)
RNM_hete	b1 (slp)	0.86	3.99				0.23		3,559,272 (− 1518)	3,559,332 (− 1506)
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

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