Comparison of non-linear models to describe the growth in the Andalusian turkey breed

Figures & data

Figure 1. Andalusian turkey breed males and females according de feather colour. (A) Black female; (B) Black male; (C) Roan female; (D) Roan male.

Table 1. Recipe and chemical composition of experimental diets.

	Starter (0–4 weeks)	Grower (>4 weeks)
Recipe	Shelled toasted soybeans flour	Wheat
	Flaked wheat	Shelled toasted soybeans flour
	Corn	Corn
	Monocalcium phosphate	Monocalcium phosphate
	Calcium carbonate	Calcium carbonate
	Sodium bicarbonate	Sodium bicarbonate
	Soybean oil	Soybean oil
Analysed chemical composition (%)
Crude protein	20.50	18.00
Crude lipids	2.10	3.00
Crude fibre	2.80	3.00
Crude ash	6.30	5.70
Calcium	0.90	1.00
Phosphorus	0.69	0.50
Sodium	0.15	0.18
Methionine	0.48	0.32
Lysine	1.13	0.90
Analysed gross energy (kcal/kg)	4303.69	4530.20

Table 2. Mathematical description of growth models, biological parameters and growth evaluators.

	Mathematical expression	Inflection weight	Inflection age	Growth rate
Brody	y = a*(1−b*exp(−k*t))	–	–	$V_c=ka\left(1-\frac{y}{a}\right)$
Von Bertalanffy	y = a*(1−b*exp(−k*t))**3	$y_i=\frac{8a}{27}$	$t_i=\frac{ln(3b)}{k}$	$V_c=3ky\left[{\left(\frac{a}{y}\right)}^{1/3}-1\right]$
Verhulst	y = a/(1+b*exp(−k*t))	$y_i=\frac{a}{2}$	$t_i=\frac{ln(b)}{k}$	$V_c=ky\left(1-\frac{y}{a}\right)$
Logistic	y = a*(1 + exp(−k*t))**(−m)	$y_i=\frac{a}{2}$	$t_i=\frac{-ln(2^{\frac{1}{m}}-1)}{k}$	$V_c=mk\frac{y_i}{2}\left(\frac{e^{-kt}}{1+e^{-kt}}\right)$
Gompertz	y = a*exp (−b*exp(−k*t))	$y_i=\frac{a}{e}$	$t_i=\frac{ln(b)}{k}$	$V_c=\mathit{kyln}\left(\frac{a}{y}\right)$
Richards	y = a*(1−b*exp(−k*t))**m	$y_i=a{\left(\frac{m-1}{m}\right)}^m$	$t_i=k^{-1}\mathit{\text{ln mb}}$	$V_c=\frac{0.5amk}{(2m-1)}$
Sinusoidal	y = a1+a2*((sin (ct−θ))^n	a1	$t_i=\frac{\theta }{c}$

y = weight, in g, at age t; t = age in days; a, a₁, a₂, c, n, k, and m = parameters.

Table 3. Biological growth curve estimation parameters for each model by sex in Andalusian turkey.

SEX	Model	a (s.e)	b (s.e)	m (s.e)	k (s.e)	Pseudo-R^2	MSE	AIC	BIC	ICO
F	Brody	16,447.92 (1,702.55)	1.024 (0.004)	–	0.0018 (0.0002)	0.93	182,918.84	17,877.27	17,891.16	1.00
	Von Bertalanffy	5,706.38 (81.07)	0.943 (0.020)	–	0.0130 (0.0004)	0.94	144,569.52	17,530.23	17,544.12	4.75
	Verhulst	4,841.85 (36.57)	22.596 (1.068)	–	0.0296 (0.0006)	0.94	160,290.50	17,682.49	17,696.38	2.00
	Logistic	5,192.19 (50.00)	–	6.003 (0.140)	0.0193 (0.0004)	0.94	146,626.63	17,551.07	17,564.96	3.00
	Gompertz	5,328.39 (58.58)	4.625 (0.121)	–	0.0171 (0.0004)	0.94	145,118.49	17,535.82	17,549.71	4.00
	Richards	5,553.76 (119.71)	0.727 (0.173)	4.597 (1.604)	0.0144 (0.0010)	0.94	144,432.45	17,529.83	17,549.02	5.00
M	Brody	1,618,960.42 (10,126,234.52)	1.001 (0.004)	–	0.0000 (0.0002)	0.95	443,993.79	19,822.43	19,836.42	1.00
	Von Bertalanffy	13,304.69 (255.51)	0.989 (0.015)	–	0.0094 (0.0002)	0.97	258,779.78	18,999.73	19,013.71	2.75
	Verhulst	9,716.63 (75.16)	34.124 (1.162)	–	0.0265 (0.0004)	0.97	268,406.80	19,055.39	19,069.38	2.00
	Logistic	11,085.37 (124.53)	–	6.847 (0.110)	0.0155 (0.0002)	0.97	250,349.87	18,949.25	18,963.24	4.50
	Gompertz	11,559.01 (152.15)	5.270 (0.097)	–	0.0137 (0.0003)	0.97	250,764.45	18,951.78	18,965.76	3.75

F: female; M: male; s.e.: standard error; pseudo-R²: non-linear determinative coefficient; MSE: mean square error; AIC: Akaike information coefficient; BIC: Bayesian information criteria; ICO: combined selection index. Richards model for males and Sinusoidal model for both sexes did not converged.

Figure 2. Growth curves for both sexes of Andalusian turkey breed, observed and predicted with each model (F: female; M: male).

Table 4. Inflection weight, inflection age and growth rate at the inflection point of fitting models for the biological curve of Andalusian turkey breed.

Model		Inflection weight (g)	Inflection age (days)	Growth rate (g/day)
Brody	F	–	–	–
Brody	M	–	–	–
Von Bertalanffy	F	1,690.78	79.96	32.99
Von Bertalanffy	M	3,942.13	115.39	55.73
Verhulst	F	2,420.93	105.3	35.84
Verhulst	M	4,858.32	133.40	64.28
Logistic	F	2,596.10	108.80	16.41
Logistic	M	5,542.69	144.08	28.39
Gompertz	F	1,960.20	89.34	33.60
Gompertz	M	4,252.32	121.65	58.09
Richards	F	1,798.26	83.68	22.47
Richards	M	–	–	–
Sinusoidal	F	–	–	–
Sinusoidal	M	–	–	–

F: female; M: male.

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.