Parametrization of the Davis Growth Model using data of crossbred Zebu cattle

Biase, Adriele Giaretta; Dias, Carlos Tadeu dos Santos; Barioni, Luís Gustavo; Albertini, Tiago Zanett; Martorano, Lucieta Guerreiro; Oltjen, James W.; Lanna, Dante Pazzanese Duarte; Oliveira, Patrícia Perondi Anchão; Medeiros, Sérgio Raposo de; Torres, Roberto Augusto de Almeida

doi:10.1590/1678-992X-2015-0284

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Biometry, Modeling and Statistics • Sci. agric. (Piracicaba, Braz.) 74 (1) • Jan-Feb 2017 • https://doi.org/10.1590/1678-992X-2015-0284 copy

Parametrization of the Davis Growth Model using data of crossbred Zebu cattle

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT:

The system of differential equations proposed by Oltjen et al. [1986Oltjen, J.W.; Bywater, A.C.; Baldwin, R.L.; Garrett, W.N. 1986. Development of a dynamic model of beef cattle growth and composition. Journal of Animal Science 62: 86–97., named Davis Growth Model (DGM)] to represent cattle growth has been parameterized with data from Bos taurus (British) and Bos indicus (Nellore) breeds. The DGM has been successfully used for simulation and decision support in the United States. However, the effect of about 30 years of genetic improvement and the use of different breeds may affect the model parameter values, which also may need to be re-estimated for crossbred animals. The aim of this study was to estimate parameter values and confidence intervals for the DGM with growth and body composition data from Zebu crossbred animals. Confidence intervals and asymptotic distribution were generated through nonparametric bootstrap with data from a field experiment conducted in Brazil. The parameters showed normal probability distribution for most scenarios. The rate constant for deoxyribonucleic acid (DNA) synthesis had a minimum increase of 156 % and the maximum of 389 %, compared to the original values and the maintenance requirement had a minimum increase of 126 % and maximum of 160 % compared to the original values. Lower limits of 95 % confidence intervals for the parameters related to maintenance and protein accretion rates were higher than the original estimates of the DGM, evidencing genetic differences of the Zebu crossbred animals in relation to the original DGM parameters.

Keywords:
asymptotic distribution; calibrating; cattle growth; nonparametric bootstrap; ordinary differential equations

Previous weaning system	Measurements after experimental weaning
	Descriptive measures	Mean	SD	Min	Max
PS¹ 1 PS: Pasture System (n = 4 RCN);	BW_i³ 3 BWi: initial body weight, kg; , kg	293.75	25.33	267.00	328.00
	FP⁴ 4 FP: feedlot period, d; , d	90.00	50.95	47.00	147.00
	DMI⁵ 5 DMI: dry matter intake, kg DMI d−1; , kg DMI d⁻¹	7.40	1.12	6.35	8.99
	BWj_f⁶ 6 BWjf: final shrunk body weight, kg; , kg	386.00	27.60	347.00	412.00
	BWz_i⁷ 7 BWzi: initial empty body weight, kg; , kg	259.75	22.40	236.00	290.00
	BWz_f⁸ 8 BWzf: final empty body weight, kg; , kg	348.50	23.72	315.00	371.00
	PROT_BWz_i⁹ 9 PROT_BWzi: initial protein body weight, kg; , kg	44.47	3.86	40.40	49.70
	FAT_BWz_i¹⁰ 10 FAT_BWzi: initial fat body weight, kg; , kg	46.30	3.99	42.10	51.70
	PROT_BWz_f¹¹ 11 PROT_BWzf: final protein body weight, kg; , kg	58.05	3.70	53.00	61.90
	FAT_BWz_f¹² 12 FAT_BWzf: final fat body weight, kg. , kg	74.40	7.33	63.40	78.30
CS² 2 CS: Confined System (n = 4 RCN; n = 5 RN);	BW_i, kg	282.22	24.46	236.00	308.00
	FP, d	70.11	22.57	47.00	119.00
	DMI, kg DMI d⁻¹	7.69	0.86	6.21	9.15
	BWj_f, kg	368.33	25.56	323.00	413.00
	BWz_i, kg	249.33	21. 60	209.00	272.00
	BWz_f, kg	328.77	25.84	286.00	370.00
	PROT_BWz_i, kg	42.51	3.75	35.70	46.60
	FAT_BWz_i, kg	46.11	3.92	37.20	49.90
	PROT_BWz_f, kg	54.87	4.70	47.40	62.00
	FAT_BWz_f, kg	69.38	4.79	62.60	75.80

Previous weaning system	Measurements after experimental weaning
	Descriptive measures	Mean	SD	Min	Max
PS¹ 1 PS: Pasture System (n = 5 RCN);	BW_i³ 3 BWi: initial body weight, kg; , kg	320.80	44.99	268.00	388.00
	FP⁴ 4 FP: feedlot period, d; , d	132.60	32.19	75.00	147.00
	DMI⁵ 5 DMI: dry matter intake, kg DMI d−1; , kg DMI d⁻¹	8.69	1.10	7.67	10.14
	BWj_f⁶ 6 BWjf: final shrunk body weight, kg; , kg	483.60	52.65	428.00	568.00
	BWz_i⁷ 7 BWzi: initial empty body weight, kg; , kg	283.80	39.70	237.00	343.00
	BWz_f⁸ 8 BWzf: final empty body weight, kg; , kg	436.20	51.32	378.00	518.00
	PROT_BWz_i⁹ 9 PROT_BWzi: initial protein body weight, kg; , kg	50.10	7.02	41.90	60.60
	FAT_BWzi¹⁰ 10 FAT_BWzi: initial fat body weight, kg; , kg	38.92	5.47	32.50	47.10
	PROT_BWz_f¹¹ 11 PROT_BWzf: final protein body weight, kg; , kg	75.12	8.60	64.30	88.00
	FAT_BWz_f¹² 12 FAT_BWzf: final fat body weight, kg. , kg	75.10	12.95	67.50	98.10
CS² 2 CS: Confined System (n = 5 RCN; n = 4 RN);	BW_i, kg	329.00	30.75	270.00	366.00
	FP, d	108.55	31.51	75.00	147.00
	DMI, kg DMI d⁻¹	8.81	0.80	7.52	9.78
	BWj_f, kg	492.55	28.11	445.00	544.00
	BWz_i, kg	290.67	27.02	239.00	323.00
	BWz_f, kg	442.44	27.83	395.00	488.00
	PROT_BWz_i, kg	51.01	4.71	42.20	57.20
	FAT_BWzi, kg	42.85	5.67	32.80	51.00
	PROT_BWz_f, kg	75.81	4.69	67.90	83.90
	FAT_BWz_f, kg	78.90	6.16	69.00	85.70

Gender	Previous weaning system	Fixed Constants	Par.	Original sample	Bootstrap		p value KS	CI BCPB³ 3 Confidence interval of Biased Corrected Percentile Bootstrap;
Gender	Previous weaning system	Fixed Constants	Par.	Original sample	Mean	S.D.⁸ 8 Standard Deviation.	p value KS	Lower limit	Upper limit
F¹ 1 Females;	PS⁴ 4 Pasture System;	(k₂ = 0.0461)⁶ 6 Fixed values based by Oltjen et al. (1986);	k₁	0.0124	0.0167	0.0018	0.0460	0.0136	0.0187
		(k₃ = 0.1430)⁶ 6 Fixed values based by Oltjen et al. (1986);	α	0.1100	0.1082	0.0065	0.0894	0.0993	0.1185
		(DNA_max = 308)⁷ 7 DNAmax was based on direct and linear proportion of mature weight of the breed and gender of these animals;
	CS⁵ 5 Confined System;	(k₂ = 0.0461)⁶ 6 Fixed values based by Oltjen et al. (1986);	k₁	0.0092	0.0119	0.0020	0.7173	0.0079	0.0160
		(k₃ = 0.1430)⁶ 6 Fixed values based by Oltjen et al. (1986);	α	0.1216	0.1214	0.0022	0.9961	0.1171	0.1255
		(DNA_max = 308)⁷ 7 DNAmax was based on direct and linear proportion of mature weight of the breed and gender of these animals;
M² 2 Males;	PS⁴ 4 Pasture System;	(k₂ = 0.0461)⁶ 6 Fixed values based by Oltjen et al. (1986);	k₁	0.0061	0.0067	0.0017	0.1882	0.0035	0.0095
		(k₃ = 0.1430)⁶ 6 Fixed values based by Oltjen et al. (1986);	α	0.1360	0.1374	0.0024	0.1595	0.1311	0.1389
		(DNA_max = 462)⁷ 7 DNAmax was based on direct and linear proportion of mature weight of the breed and gender of these animals;
	CS⁵ 5 Confined System;	(k₂ = 0.0461)⁶ 6 Fixed values based by Oltjen et al. (1986);	k₁	0.0084	0.0096	0.0005	0.5842	0.0086	0.0108
		(k₃ = 0.1430)⁶ 6 Fixed values based by Oltjen et al. (1986);	α	0.1199	0.1204	0.0031	0.2023	0.1140	0.1255
		(DNA_max = 462)⁷ 7 DNAmax was based on direct and linear proportion of mature weight of the breed and gender of these animals;

			New calibrations¹ 1 Parameter fit in the current study;		Original parameters² 2 Based on parameters (k1, α) calculated in the Oltjen et al. (2000) study;
Clusters	Variables	Observed	Predicted	Bias	Predicted	Bias
Females	Protein (kg d⁻¹)	58.0500	57.9920	0.0579	53.8236	4.2264
PS³ 3 Pasture System;	Fat (kg d⁻¹)	74.4000	73.4140	0.9859	87.3991	−12.9991
Females	Protein (kg d⁻¹)	54.8777	54.9139	−0.0361	51.9247	2.9669
CS⁴ 4 Confined System.	Fat (kg d⁻¹)	69.3700	68.8142	0.5635	82.7235	−13.3535
Males	Protein (kg d⁻¹)	75.1200	74.4028	0.7171	53.8236	21.2964
PS³ 3 Pasture System;	Fat (kg d⁻¹)	75.1000	74.9045	0.1954	87.3991	−12.2991
Males	Protein (kg d⁻¹)	75.8111	75.5887	0.2223	67.8307	7.9804
CS⁴ 4 Confined System.	Fat (kg d⁻¹)	78.9000	79.4407	−0.5407	105.9546	−27.0546

Scenarios	Statistics	(New calibrations) Bootstrap¹ 1 Parameter fit in the current study;		Original parameters² 2 Based on parameters fit (k1, α) calculated in the Oltjen et al. (1986) study;
Scenarios	Statistics	Protein	Fat	Protein	Fat
Females Pasture System	MSEP³ 3 Mean square error of prediction (smaller is better);	2.1369	24.8920	20.9818	274.8000
	CCC⁴ 4 Concordance Correlation Coefficient (closer to 1 is better);	0.9539	0.9384	0.3481	0.3495
	p value⁵	0.9270	0.8352	0.6450	0.1160
	p value⁶	0.8283	0.2753	0.5678	0.0725
	p value⁷	0.7576	0.2889	0.2157	0.1021
	AIC⁸ 8 Akaike Information Criterion (smaller is better);	16.1524	16.1524	21.0760	21.0758
	BIC⁹ 9 Bayesian Information Criterion (smaller is better).	14.3113	25.2490	19.2347	26.2856
Females Confined System	MSEP³ 3 Mean square error of prediction (smaller is better);	7.6008	17.0037	17.3109	228.6716
	CCC⁴ 4 Concordance Correlation Coefficient (closer to 1 is better);	0.7053	0.7720	0.4810	0.2070
	p value⁵	0.0086	0.0046	0.1120	0.0079
	p value⁶	0.0095	0.0056	0.0925	0.0018
	p value⁷	0.0249	0.0199	0.0335	0.0000
	AIC⁸ 8 Akaike Information Criterion (smaller is better);	38.7718	38.7718	47.0016	47.0016
	BIC⁹ 9 Bayesian Information Criterion (smaller is better).	39.3634	45.9810	47.5933	54.1773
Males Pasture System	MSEP³ 3 Mean square error of prediction (smaller is better);	19.6221	40.9915	44.7486	1668.4700
	CCC⁴ 4 Concordance Correlation Coefficient (closer to 1 is better);	0.7600	0.8970	0.6340	0.2440
	p value⁵	0.4784	0.0878	0.2823	0.3543
	p value⁶	0.4822	0.1030	0.2215	0.0328
	p value⁷	0.8298	0.2844	0.1353	0.0031
	AIC⁸ 8 Akaike Information Criterion (smaller is better);	34.0756	32.9613	30.5307	35.5494
	BIC⁹ 9 Bayesian Information Criterion (smaller is better).	32.9039	31.7896	29.3590	34.3778
Males Confined System	MSEP³ 3 Mean square error of prediction (smaller is better);	3.8026	33.8657	67.2039	784.8868
	CCC⁴ 4 Concordance Correlation Coefficient (closer to 1 is better);	0.8170	0.9398	0.2830	0.1340
	p value⁵	0.5182	0.0354	0.0239	0.0224
	p value⁶	0.5691	0.0304	0.0080	0.0011
	p value⁷	0.2907	0.1094	0.0000	0.0000
	AIC⁸ 8 Akaike Information Criterion (smaller is better);	42.2798	56.9118	33.2404	52.8159
	BIC⁹ 9 Bayesian Information Criterion (smaller is better).	42.8714	57.5034	33.8321	53.4075

Zebu crossbred¹ 1 Parameter fit in the current study;					British (Bos taurus² 2 Based on parameters (k1, α) calculated in the Oltjen et al. (1986) study; )
Parameter fit	Females PS³ 3 Pasture System;	Females CS⁴ 4 Confined System.	Males PS³ 3 Pasture System;	Males CS⁴ 4 Confined System.	Steer
k₁	0.0167	0.0119	0.0067	0.0096	0.00429
α	0.1082	0.1214	0.1374	0.1204	0.0860
% of change	k₁ (389 %)	k₁ (214 %)	k₁ (156 %)	k₁ (223 %)	–
% of change	α (126 %)	α (141 %)	α (160 %)	α (140 %)	–

Zebu crossbred¹ 1 Parameter fit in the current study;					Nellore (Bos indicus² 2 Based on parameters (k1, α) calculated in the Sainz et al. (2006) study; )
Parameter fit	Females PS³ 3 Pasture System;	Females CS⁴ 4 Confined System.	Males PS³ 3 Pasture System;	Males CS⁴ 4 Confined System.	Bulls
k₁	0.0167	0.0119	0.0067	0.0096	0.00304
α	0.1082	0.1214	0.1374	0.1204	0.0768
% of change	k₁ (549 %)	k₁ (391 %)	k₁ (220 %)	k₁ (315 %)	–
% of change	α (141 %)	α (158 %)	α (178 %)	α (156 %)	–

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[1] *Corresponding author <ctsdias@usp.br>