Table 2.

Estimated variance components, heritability, and comparison of statistics criteria of random regression models with various covariance functions for test-day semen traits in Thai native grandparent roosters.

Trait	Model		Variance Components/Heritability/Statistic Criteria
		${\mathsf{\sigma }}_{\mathbf{a}}^2$	${\mathsf{\sigma }}_{\mathbf{p}\mathbf{e}}^2$	${\mathsf{\sigma }}_{\mathbf{e}}^2$	${\mathbf{h}}^2$ (±SE)	$\mathbf{t}$ (±SE)	−2logL	AIC
Mass movement	KG	0.164	0.355	0.968	0.110 ± 0.02	0.349 ± 0.03	−2505	−2415
	WM	0.164	0.355	0.969	0.110 ± 0.02	0.349 ± 0.03	−2492	−2402
	LG2	0.164	0.352	0.968	0.111 ± 0.02	0.348 ± 0.03	−2870	−2684
	LG3	0.166	0.356	0.964	0.112 ± 0.02	0.351 ± 0.03	−2431	−2113
	LG4	0.163	0.356	0.964	0.110 ± 0.02	0.350 ± 0.03	−2088	−1602
Semen pH	KG	0.004	0.017	0.078	0.040 ± 0.01	0.212 ± 0.03	−2505	−2415
	WM	0.004	0.018	0.078	0.040 ± 0.01	0.220 ± 0.03	−2492	−2402
	LG2	0.004	0.016	0.074	0.043 ± 0.01	0.213 ± 0.03	−2870	−2684
	LG3	0.005	0.019	0.074	0.051 ± 0.01	0.245 ± 0.03	−2431	−2113
	LG4	0.005	0.020	0.073	0.051 ± 0.01	0.255 ± 0.03	−2088	−1602
Semen color	KG	0.016	0.033	0.124	0.092 ± 0.02	0.283 ± 0.03	−2505	−2415
	WM	0.016	0.033	0.124	0.092 ± 0.02	0.283 ± 0.03	−2492	−2402
	LG2	0.016	0.031	0.124	0.094 ± 0.02	0.275 ± 0.03	−2870	−2684
	LG3	0.017	0.032	0.126	0.097 ± 0.02	0.280 ± 0.03	−2431	−2113
	LG4	0.017	0.033	0.126	0.097 ± 0.02	0.284 ± 0.03	−2088	−1602
Semen volume	KG	0.018	0.037	0.025	0.225 ± 0.03	0.688 ± 0.06	−2505	−2415
	WM	0.018	0.037	0.025	0.225 ± 0.03	0.688 ± 0.06	−2492	−2402
	LG2	0.018	0.036	0.027	0.222 ± 0.03	0.667 ± 0.04	−2870	−2684
	LG3	0.018	0.036	0.028	0.220 ± 0.03	0.659 ± 0.05	−2431	−2113
	LG4	0.019	0.036	0.030	0.224 ± 0.03	0.647 ± 0.06	−2088	−1602
Sperm viability	KG	0.001	0.001	0.010	0.083 ± 0.01	0.167 ± 0.02	−2505	−2415
	WM	0.001	0.001	0.010	0.083 ± 0.01	0.167 ± 0.02	−2492	−2402
	LG2	0.001	0.001	0.010	0.083 ± 0.01	0.167 ± 0.02	−2870	−2684
	LG3	0.001	0.001	0.012	0.071 ± 0.01	0.143 ± 0.02	−2431	−2113
	LG4	0.001	0.001	0.013	0.067 ± 0.01	0.133 ± 0.02	−2088	−1602
Sperm abnormalities	KG	0.007	0.008	0.065	0.088 ± 0.01	0.188 ± 0.03	−2505	−2415
	WM	0.007	0.009	0.065	0.086 ± 0.01	0.198 ± 0.03	−2492	−2402
	LG2	0.008	0.007	0.070	0.094 ± 0.01	0.176 ± 0.03	−2870	−2684
	LG3	0.008	0.007	0.072	0.092 ± 0.01	0.172 ± 0.03	−2431	−2113
	LG4	0.009	0.007	0.075	0.099 ± 0.01	0.176 ± 0.03	−2088	−1602
Sperm concentration	KG	0.262	0.657	0.999	0.137 ± 0.02	0.479 ± 0.04	−2505	−2415
	WM	0.265	0.682	0.999	0.136 ± 0.02	0.487 ± 0.04	−2492	−2402
	LG2	0.266	0.660	0.998	0.138 ± 0.02	0.481 ± 0.04	−2870	−2684
	LG3	0.266	0.667	0.998	0.138 ± 0.02	0.483 ± 0.04	−2431	−2113
	LG4	0.266	0.669	1.043	0.134 ± 0.02	0.473 ± 0.04	−2088	−1602

KG = Koops and Grossman function, WM = Wilmink function, LG2 = second order Legendre polynomial functions, LG3 = third order Legendre polynomial functions, LG4 = fourth order Legendre polynomial function. ${\mathsf{\sigma }}_{\mathrm{a}}^2$ = additive genetic variance, ${\mathsf{\sigma }}_{\mathrm{p}\mathrm{e}}^2$ = permanent environmental variance, ${\mathsf{\sigma }}_{\mathrm{e}}^2$ = error variance, ${\mathrm{h}}^2$ = heritability, $\mathrm{t}$ = repeatability, −2logL = minus twice the logarithm of the likelihood, Akaike’s information criterion (AIC).