Mathematical models to describe the growth curves of Vietnamese Ri chicken

Nguyen, T. H.; Nguyen, C. X.; Luu, M. Q.; Nguyen, A. T.; Bui, D. H.; Pham, D. K.; Do, D. N.

doi:10.1590/1519-6984.249756

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Brazilian Journal of Biology

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Original Article • Braz. J. Biol. 83 • 2023 • https://doi.org/10.1590/1519-6984.249756 copy

Mathematical models to describe the growth curves of Vietnamese Ri chicken

Modelos matemáticos para descrever as curvas de crescimento do frango Ri vietnamita

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Ri chicken is the most popular backyard chicken breed in Vietnam, but little is known about the growth curve of this breed. This study compared the performances of models with three parameters (Gompertz, Brody, and Logistic) and models containing four parameters (Richards, Bridges, and Janoschek) for describing the growth of Ri chicken. The bodyweight of Ri chicken was recorded weekly from week 1 to week 19. Growth models were fitted using minpack.lm package in R software and Akaike’s information criterion (AIC), Bayesian information criterion (BIC), and root mean square error (RMSE) were used for model comparison. Based on these criteria, the models having four parameters showed better performance than the ones with three parameters, and the Richards model was the best one for males and females. The lowest and highest value of asymmetric weights (α) were obtained by Bridges and Brody models for each of sexes, respectively. Age and weight estimated by the Richard model were 8.46 and 7.51 weeks and 696.88 and 487.58 g for males and for females, respectively. Differences in the growth curves were observed between males and female chicken. Overall, the results suggested using the Richards model for describing the growth curve of Ri chickens. Further studies on the genetics and genomics of the obtained growth parameters are required before using them for the genetic improvement of Ri chickens.

Keywords:
chicken; growth curve; body weight; Vietnam; indigenous breeds

Diets	Week 0-4	Week 5-8	Week 9-21
Gross energy (Kcal/kg)	2900	3000	2850
Protein (%)	20.0	18.0	16.0
Ash (%)	5.0	5.0	5.0
Calcium (%)	0.9	0.85	0.85
Phosphorus (%)	1.1	0.8	0.8
Methionine + Cystine (%)	0.75	0.7	0.7
Lysine (%)	1.0	0.8	0.85

Model	Equation	Parameters	Age at inflection	Weight of inflection
Logistic	$BWt = \frac{a}{β \times (1 + e^{- k t})}$	α, β and k	α/2	- ln(1/β)/ k
Gompertz	$BWt = a \times e^{- β \times e^{- k t}}$	α, β and k	α/e	ln(β)/ k
Brody	$BWt = a \times (1 - β \times e^{- k t})$	α, β and k
Bridges	$BWt = {BW}_{0} + a \times (1 - e^{- k t^{m}})$	α, BW₀, k and m	-	-
Janoschek	$BWt = a - (a - {BW}_{0}) \times e^{- k t^{m}}$	α, BW₀, k and m	-	-
Richards	$BWt = \frac{a}{{(1 - β \times e^{- k t})}^{\frac{1}{m}}}$	α, β, k and m	$\frac{a}{{(m + 1)}^{\frac{1}{m}}}$	- ln(m/β)/ k

Week		Male
Week	N	BW (g) (Mean ± SE)	SD	CV (%)	N	BW (g) (Mean ± SE)		SD		CV (%)
0*	46	25.74±0.31	2.09	8.12	57	25.67±0.24	1.8		7.01
1	44	63.44±0.91	6.03	9.51	57	61.01±0.89	6.72		11.01
2	45	110.37±1.8	12.06	10.93	55	107±2.25	16.65		15.56
3	45	173.12±3.06	20.52	11.85	56	160.18±20	14.96		9.34
4	45	252.94±4.71	31.58	12.49	57	235.03±3.34	25.24		10.74
5	46	344.07±6.79	46.04	13.38	57	314.7±4.94	37.28		11.85
6	46	465.68±9.14	62.01	13.32	56	417.22±7.14	53.47		12.82
7	46	617.84±11.81	80.13	12.97	57	535.99±7.94	59.91		11.18
8	46	786.32±14.22	96.46	12.27	57	659.89±9.54	72.01		10.91
9	46	960.91±18.01	122.15	12.71	57	772.55±11.23	84.82		10.98
10	46	1048.67±17.22	116.8	11.14	57	830.75±10.02	75.63		9.10
11	46	1144.95±16.79	113.89	9.95	57	886.84±9.71	73.29		8.26
12	46	1240.53±16.46	111.63	9.00	57	936.69±9.67	72.99		7.79
13	46	1331.87±15.54	105.4	7.91	57	989.59±10.06	75.98		7.68
14	46	1410.78±16.57	112.4	7.97	57	1043.33±10.66	80.47		7.71
15	46	1436.92±16.15	109.51	7.62	57	1069.82±11.13	84.05		7.86
16	46	1457.76±16.48	111.8	7.67	57	1090.28±11.18	84.42		7.74
17	45	1474.44±16.85	113.01	7.66	57	1106.37±11.23	84.79		7.66
18	36	1512.03±18.47	110.81	7.33	57	1119.06±11.54	87.15		7.79
19	36	1522.61±18.93	113.57	7.46	56	1124.2±11.79	88.2		7.85

Model	Degree of freedom	Male
		AIC	RMSE	BIC	Cor	AIC	MSE	BIC	Cor
Logistic	4	10612.37	90.10	12818.94	0.9994	12798.8	67.75	10631.56	0.9990
Gompertz	4	10632.73	92.13	12791.34	0.9992	12771.2	66.92	10651.91	0.9994
Brody	4	11193.74	126.01	13409.36	0.9863	13389.22	87.17	11212.92	0.9888
Bridges	5	10603.37	90.53	12789.89	0.9996	12764.71	66.67	10627.34	0.9994
Janoschek	5	10603.37	90.53	12789.89	0.9996	12764.71	66.67	10627.34	0.9994
Richards	5	10596.39	90.18	12776.06	0.9997	12750.89	66.27	10620.37	0.9996

Model	Sex	α (g)	β	k (g/week)	m	BW₀	Age at inflection (week)	Weight at inflection (g)
Logistic	Male	1516.7±7.89	38.75±2.11	0.41±0.01	-	-	8.95	758.35
	Female	1117.06±4.72	28.52±1.28	0.40±0.01	-	-	8.29	558.53
Gompertz	Male	1620.82±12.42	6.46±0.21	0.24±0	-	-	7.63	596.33
	Female	1181.7±6.9	5.54±0.15	0.25±0	-	-	6.91	434.77
Brody	Male	3238.72±186.76	1.08±0.01	0.04±0	-	-	-	-
	Female	1813.03±50.88	1.11±0.01	0.06±0	-	-	-	-
Bridges	Male	1480.59±14.66	-	5.79e-03±0.59e-04	2.53±0.06	34.81±8.82	-	-
	Female	1101.95±10.16	-	0.01±0	2.26±0.05	23.53±6.51	-	-
Janoschek	Male	1515.4±9.47	-	2.69e-03±0.34e-03	2.53±0.06	34.81±8.82	-	-
	Female	1125.48±6.04	-	0.01±0	2.26±0.05	23.53±6.51	-	-
Richards	Male	1550.8±12.96	8.96±3.3	0.33±0.02	0.54±0.1	-	8.46	696.88
	Female	1150.98±8.06	3.32±1.22	0.30±0.01	0.35±0.08	-	7.51	487.58

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