D.1 Milk Yield

D.1 Holstein: Milk Yield

D.1.1: Full Period: 1985-2023

Model Summary

A. parametric coefficients	Estimate	Std. Error	t-value	p-value
(Intercept)	17.8235	0.6916	25.7716	\(< 0.0001\)
parityprimiparous	-3.4189	0.0129	-264.1612	\(< 0.0001\)
year1986	0.3265	0.3478	0.9389	0.3478
year1987	0.1965	0.5377	0.3654	0.7148
year1988	0.0287	0.6610	0.0435	0.9653
year1989	0.5588	0.8363	0.6682	0.5040
year1990	0.8289	0.8270	1.0024	0.3162
year1991	0.9862	0.8085	1.2198	0.2226
year1992	1.3033	0.7913	1.6470	0.0996
year1993	1.3348	0.7892	1.6912	0.0908
year1994	1.2533	0.7838	1.5990	0.1098
year1995	1.5410	0.7860	1.9605	0.0499
year1996	1.7461	0.7837	2.2280	0.0259
year1997	2.2454	0.7879	2.8498	0.0044
year1998	2.8965	0.7939	3.6483	0.0003
year1999	2.8606	0.8275	3.4567	0.0005
year2000	3.0084	0.7605	3.9561	0.0001
year2001	3.1575	0.7423	4.2539	\(< 0.0001\)
year2002	3.5520	0.7379	4.8134	\(< 0.0001\)
year2003	3.9766	0.7361	5.4026	\(< 0.0001\)
year2004	4.3994	0.7339	5.9945	\(< 0.0001\)
year2005	4.8325	0.7330	6.5926	\(< 0.0001\)
year2006	4.9189	0.7324	6.7165	\(< 0.0001\)
year2007	4.7073	0.7264	6.4805	\(< 0.0001\)
year2008	5.0081	0.7264	6.8946	\(< 0.0001\)
year2009	5.4514	0.7225	7.5456	\(< 0.0001\)
year2010	6.0077	0.7211	8.3318	\(< 0.0001\)
year2011	6.2726	0.7234	8.6706	\(< 0.0001\)
year2012	6.2564	0.7278	8.5960	\(< 0.0001\)
year2013	5.9409	0.7442	7.9826	\(< 0.0001\)
year2014	6.5407	0.7493	8.7297	\(< 0.0001\)
year2015	6.9626	0.7412	9.3935	\(< 0.0001\)
year2016	7.3016	0.7404	9.8618	\(< 0.0001\)
year2017	7.5165	0.7399	10.1585	\(< 0.0001\)
year2018	8.0975	0.7432	10.8957	\(< 0.0001\)
year2019	8.2939	0.7587	10.9316	\(< 0.0001\)
year2020	8.7453	0.7749	11.2863	\(< 0.0001\)
year2021	9.2780	0.7623	12.1713	\(< 0.0001\)
year2022	9.4385	0.7518	12.5551	\(< 0.0001\)
year2023	9.9865	0.7507	13.3024	\(< 0.0001\)
B. smooth terms	edf	Ref.df	F-value	p-value
s(thi_mean_t0_3d):paritymultiparous	8.3629	8.3629	517.3513	\(< 0.0001\)
s(thi_mean_t0_3d):parityprimiparous	6.5585	6.5585	48.0496	\(< 0.0001\)
s(days_in_milk_t):paritymultiparous	14.5992	14.5992	120213.0040	\(< 0.0001\)
s(days_in_milk_t):parityprimiparous	14.0843	14.0843	14232.8232	\(< 0.0001\)

Table D.1: Holstein: Milk Yield - 1985-2023 - GAMM model summary without random effect terms.

Smooth Term Fixed Effect	Est.	SE	z	p
s(thi_mean_t0_3d):multiFx1	0.4424	0.1070	4.14	\(<1e-04\)
s(thi_mean_t0_3d):primiFx1	0.3466	0.1162	2.98	0.0028
s(days_in_milk_):multiFx1	5.0429	0.5387	9.36	\(<1e-20\)
s(days_in_milk_):primiFx1	4.8631	0.6608	7.36	\(<1e-12\)
Variance Component	Estimated \(\sigma\)
\(\sigma_\alpha\)	3.1230
\(\sigma_\iota\)	1.0079
\(\sigma_\phi\)	3.1247
s(thi_mean_t0_3d):multi	2.3664
s(days_in_milk_):primi	9.0384
s(days_in_milk_):multi	10.9130
s(thi_mean_t0_3d):primi	1.2902
Residual	3.7902

Table D.2: Holstein: Milk Yield - 1985-2023 - Mixed Model Summary - Smooth Terms and Random Effects.

Model Diagnostics

Figure D.1: Holstein: Milk Yield - 1985-2023 - Diagnostic Plot

THI Effect and Lactation Curve

Figure D.2: Holstein: Milk Yield - 1985 - 2023 - THI Effect and Lactation Curve

D.1.2: Split Period: Until 2010 - After 2010

D.1.2.1 Split Period: 1985 - 2010

Model Summary

A. parametric coefficients	Estimate	Std. Error	t-value	p-value
(Intercept)	17.4723	0.4846	36.0518	\(< 0.0001\)
parityprimiparous	-2.9636	0.0135	-218.8244	\(< 0.0001\)
year1986	0.1529	0.1767	0.8655	0.3868
year1987	-0.0051	0.3698	-0.0139	0.9889
year1988	-0.0538	0.4676	-0.1151	0.9084
year1989	0.5836	0.5228	1.1162	0.2643
year1990	1.0427	0.5324	1.9586	0.0502
year1991	1.2681	0.5365	2.3638	0.0181
year1992	1.5385	0.5405	2.8462	0.0044
year1993	1.7418	0.5397	3.2271	0.0013
year1994	1.7286	0.5424	3.1867	0.0014
year1995	2.0734	0.5756	3.6019	0.0003
year1996	2.2707	0.5748	3.9506	0.0001
year1997	2.7340	0.5549	4.9272	\(< 0.0001\)
year1998	3.3217	0.5222	6.3608	\(< 0.0001\)
year1999	3.4296	0.5187	6.6121	\(< 0.0001\)
year2000	3.6071	0.5113	7.0543	\(< 0.0001\)
year2001	3.9367	0.5104	7.7127	\(< 0.0001\)
year2002	4.2369	0.5132	8.2562	\(< 0.0001\)
year2003	4.7670	0.5144	9.2674	\(< 0.0001\)
year2004	5.2638	0.5135	10.2511	\(< 0.0001\)
year2005	5.7675	0.5124	11.2567	\(< 0.0001\)
year2006	5.9112	0.5147	11.4841	\(< 0.0001\)
year2007	5.8929	0.5097	11.5607	\(< 0.0001\)
year2008	6.2882	0.4996	12.5867	\(< 0.0001\)
year2009	6.9956	0.5079	13.7748	\(< 0.0001\)
year2010	7.7149	0.5678	13.5864	\(< 0.0001\)
B. smooth terms	edf	Ref.df	F-value	p-value
s(thi_mean_t0_3d):paritymultiparous	8.5121	8.5121	747.8886	\(< 0.0001\)
s(thi_mean_t0_3d):parityprimiparous	7.1550	7.1550	77.0589	\(< 0.0001\)
s(days_in_milk_t):paritymultiparous	14.4063	14.4063	130999.6058	\(< 0.0001\)
s(days_in_milk_t):parityprimiparous	13.8961	13.8961	17856.8448	\(< 0.0001\)

Table D.3: Holstein: Milk Yield - 1985-2010 - GAMM model summary without random effect terms.

Smooth Term Fixed Effect	Est.	SE	z	p
s(thi_mean_t0_3d):multiFx1	-0.5301	0.1141	-4.65	\(< 1e-05\)
s(thi_mean_t0_3d):primiFx1	-0.3337	0.1241	-2.69	0.0072
s(days_in_milk_):multiFx1	2.4075	0.5902	4.08	\(< 1e-04\)
s(days_in_milk_):primiFx1	2.9462	0.6274	4.70	\(< 1e-05\)
Variance Component	Estimated \(\sigma\)
\(\sigma_\alpha\)	2.9738
\(\sigma_\iota\)	0.9483
\(\sigma_\phi\)	2.7446
s(thi_mean_t0_3d):multi	2.7246
s(days_in_milk_):primi	7.6254
s(days_in_milk_):multi	9.4602
s(thi_mean_t0_3d):primi	1.5465
Residual	3.4568

Table D.4: Holstein: Milk Yield - 1985-2010 - Mixed Model Summary - Smooth Terms and Random Effects.

Model Diagnostics

Figure D.3: Holstein: Milk Yield - 1985-2010 - Diagnostic Plot

THI Effect and Lactation Curve

Figure D.4: Holstein: Milk Yield - 1985 - 2010 - THI Effect and Lactation Curve

D.1.2.2 Split Period: 2010 - 2023

Model Summary

A. parametric coefficients	Estimate	Std. Error	t-value	p-value
(Intercept)	23.8289	0.3841	62.0385	\(< 0.0001\)
parityprimiparous	-3.5815	0.0143	-250.7346	\(< 0.0001\)
year2012	-0.1435	0.4281	-0.3352	0.7375
year2013	-0.4446	0.4293	-1.0358	0.3003
year2014	0.1502	0.4291	0.3501	0.7263
year2015	0.4723	0.4308	1.0965	0.2728
year2016	0.7635	0.4567	1.6718	0.0946
year2017	1.1762	0.4488	2.6207	0.0088
year2018	1.7098	0.4437	3.8535	0.0001
year2019	1.9267	0.4429	4.3500	\(< 0.0001\)
year2020	2.4354	0.4451	5.4719	\(< 0.0001\)
year2021	2.6773	0.4567	5.8617	\(< 0.0001\)
year2022	2.5650	0.4533	5.6584	\(< 0.0001\)
year2023	2.9380	0.4808	6.1102	\(< 0.0001\)
B. smooth terms	edf	Ref.df	F-value	p-value
s(thi_mean_t0_3d):paritymultiparous	8.3215	8.3215	484.5057	\(< 0.0001\)
s(thi_mean_t0_3d):parityprimiparous	7.0657	7.0657	29.5389	\(< 0.0001\)
s(days_in_milk_t):paritymultiparous	14.6827	14.6827	114849.4858	\(< 0.0001\)
s(days_in_milk_t):parityprimiparous	13.9847	13.9847	12129.3973	\(< 0.0001\)

Table D.5: Holstein: Milk Yield - 2011-2023 - GAMM model summary without random effect terms.

Smooth Term Fixed Effect	Est.	SE	z	p
s(thi_mean_t0_3d):multiFx1	-0.5663	0.1050	-5.39	\(< 1e-07\)
s(thi_mean_t0_3d):primiFx1	-0.4351	0.1310	-3.32	0.0009
s(days_in_milk_):multiFx1	6.2500	0.5244	11.92	\(< 1e-32\)
s(days_in_milk_):primiFx1	3.9576	0.6407	6.18	\(< 1e-09\)
Variance Component	Estimated \(\sigma\)
\(\sigma_\alpha\)	3.1563
\(\sigma_\iota\)	1.1935
\(\sigma_\phi\)	3.7462
s(thi_mean_t0_3d):multi	2.2598
s(days_in_milk_):primi	8.5279
s(days_in_milk_):multi	12.0097
s(thi_mean_t0_3d):primi	1.6772
Residual	3.9639

Table D.6: Holstein: Milk Yield - 2011-2023 - Mixed Model Summary - Smooth Terms and Random Effects.

Model Diagnostics

Figure D.5: Holstein: Milk Yield - 2011-2023 - Diagnostic Plot

THI Effect and Lactation Curve

Figure D.6: Holstein: Milk Yield - 2010 - 2023 - THI Effect and Lactation Curve