Analysis of growth of broilers with restricting and unrestricting initial body weight in Gompertz-Laird model in different environments

Abstract

The objectives of the present study were twofold. The first objective was to compare the original Gompertz-Laird model with two other versions of the Gompertz-Laird models where the model parameter of the initial body weight (BW₀) was restricted in two different ways: 1) BW₀ was set to be the mean of the observed initial body weights, 2) BW₀ was allowed to vary within an interval of ±3σ_p around the mean of the initial observed body weights. The second objective was to estimate growth curve parameters for live weight of broilers using the selected form of the model, then to investigate the effect of environmental fluctuations on the model parameters.

Data were obtained from the 278 broilers that were reared in diverse environments where temperature, sex, and feeding regimes were the factors creating the environmental diversity. Models were compared using coefficients of determination (R²), correlation between the observed and the estimated growth curves (r), residual standard deviation (RSD), and the estimated mature body weight (BW_a).

The restrictions applied on BW₀ did not improve the fitting of Gompertz-Laird model, and resulted in estimating model parameters that are out of the parameter space. The unrestricted form of the Gompertz-Laird model was, however, observed to be suitable for explaining the growth of broilers. Broilers subjected to 21°C reached the age of maximum growth about 3 days later than the broilers subjected to 30°C. The initial specific growth rate (L) and the rate of exponential decay (K) of the initial specific growth rate were lower in 21°C than 30°C. The model parameters of BW₀, L, and K were affected by differences in feeding regimes.

Keywords:

• Gompertz-Laird model
• Broiler
• Restriction on model parameters
• Growth.

Introduction

Growth trajectory measured as body mass or body weight has been described by mathematical functions fitted to growth curves, particularly in poultry (Laird, 1966; Tzeng and Becker, 1981; Ricklefs, 1985; Barbato, 1991, 1992; Remignon, 1993; Mignon-Grasteau et al., 2000; Maruyama et al., 2001; Aggrey, 2002; Reddish and Lilburn, 2004; Norris et al., 2007). Growth curve models provide a set of parameters that are used to describe growth pattern over time, and to estimate the expected weight of animals at a specific age (Tzeng and Becker, 1981; Yakupoglu and Atil, 2001b). In addition, the parameters obtained from growth curve functions are highly heritable and have been used in selection studies (Merrit, 1974; Mignon-Grasteau et al., 2000).There is a set of growth curve functions used to determine age-weight relationship of poultry. The functions have different properties and different mathematical limitations. Among these functions, the Laird form (Laird et al., 1965) of the Gompertz model (Gompertz, 1925) has been the model used to analyse chicken data (Tzeng and Becker, 1981; Anthony et al., 1991; Barbato, 1991; Mignon-Grasteau et al., 1999; Aggrey, 2002). The original Gompertz model is a function of mature body weight, whereas the Laird form (Laird et al., 1965) of Gompertz model is a function of initial body weight and inflection point (Barbato, 1991). The performance of the Gompertz-Laird model can be improved by some constraints on the initial body weight (Grossman and Bohren, 1982), or by weighting initial body weight by the inverse of the variance (Pasternak and Shalev, 1994). Moreover, initial body weight can be set within two standard deviation of mean initial body weight as suggested by Mignon-Grasteau et al.(1999). The effect of constraining initial body weight on the other model parameters to improve fitting of data is yet to be investigated (Aggrey, 2002).

Therefore, the purposes of the present study were to investigate the effect of constraining initial body weight on the general fitting of Gompertz-Laird model, and to investigate the effect of environmental changes on the parameters of the model.

Materials and methods

Experimental design

From a commercial hatchery of Ross 308 chicks, 200 males and 200 females were obtained. All birds were wing-tagged and weighed at 3 days of age. Two experiments were carried out in an environmentally controlled house capable of ±1°C temperature control. The broilers were brooded and reared on pine wood shavings litter. Lighting was continuous (24 hours), as access to feed and water. Room temperature was 30.0°C the first 7 days, 27.0 0C the second 7 days and 24.0°C the third 7 days. During the first 21 days, birds were fed on a crumbled starter diet. Thereafter, chicks were subjected to the experimental treatments. Two experiments were carried out, experiment 1 and experiment 2. In experiment 1, 36 males and 36 females were reared in 36 pens with two birds of the same sex in one pen under a temperature regimen of 21.0°C from 21 to 42 days; another 36 males and 36 females were reared under a temperature regimen of 30.0°C from 21 to 42 days. Birds for the experiments were selected in such way that each pen (0.5×0.5 m) of two birds were weighed and pen weights were adjusted by replacing individual birds to provide pen weights within 1σ_p of pen weights for all treatments. Experiment 1 consisted of 3 dietary treatments per temperature, repeated six times with male and female, 2 broilers of the same sex per pen, that is to say, there were about 12 males and 12 females for each temperature-diet subclass. Five diet formulations were used in both trials. For Diet 1, 2, and 4 (based on maize and soybean) the nutrient specifications were set to meet or exceed NRC (1994) requirements. Diet 3 was essentially Diet 2 without supplemental methionine so that the calculated level of methionine in the feed was 3.1 g/kg. Similarly, Diet 5 was essentially Diet 4 without supplemental methionine so that the calculated level of methionine in the feed was 2.9 g/kg. The ingredients used and the calculated nutrient content of the five diet formulations used in this study are shown in Table 1.

Table 1 The ingredient- and calculated nutrient composition of diets.

	Diet 1	Diet 2	Diet 3	Diet 4	Diet 5
	0–3 wk	4–6 wk	4–6 wk	7th wk	7 th wk
	(%)	(%)	(%)	(%)	(%)
Ingredients
Yellow corn (7.57 % CP)	46.24	57.44	57.40	64.56	64.54
Soybean meal (46.36 % CP)	41.85	33.68	33.77	28.25	28.29
Sunflower oil	8.09	5.68	5.70	4.42	4.42
Limestone	1.34	1.40	1.40	1.31	1.31
Dicalcium phosphate	1.60	1.15	1.15	0.93	0.93
NaCl	0.46	0.33	0.33	0.26	0.26
Vit/Min. Premix^*	0.25	0.25	0.25	0.25	0.25
DL-Methionine	0.17	0.07	-	0.03	-
Calculated nutrient composition^°
Crude protein	23.0	20	20	18	18
Calculated nutrient composition^#
Calcium	1.00	0.90	0.90	0.80	0.80
Total phosphorus	0.45	0.35	0.35	0.30	0.30
Sodium	0.20	0.15	0.15	0.12	0.12
Methionine	0.52	0.38	0.32	0.32	0.29
Cystine	0.38	0.34	0.34	0.31	0.31
Methionine + Cystine	0.90	0.72	0.66	0.63	0.60
Lysine	1.31	1.10	1.10	0.96	0.96
Threonine	0.90	0.78	0.78	0.70	0.70
Tryptophan	0.27	0.23	0.23	0.20	0.20
Arginine	1.61	1.37	1.38	1.21	1.21
Isoleucine	1.00	0.86	0.86	0.76	0.76
Leucine	1.94	1.75	1.75	1.61	1.61
Valine	1.08	0.94	0.94	0.85	0.85
Histidine	0.64	0.56	0.56	0.51	0.51
Energy (kcal ME/kg)	3200	3200	3200	3200	3200

* The composition of vitamins and minerals in the premix provided the following amounts in 2.5 kilogram: vitamin A, 15,000,000 U; vitamin D₃, 2,500,000 U; vitamin E, 40,000 mg; niacin, 40,000 mg; pantothenic acid, 10,000 mg; vitamin B₂, 7000 mg; vitamin K₃, 5000 mg; vitamin B₁, 3000 mg; vitamin B₆, 5000 mg; vitamin B₁₂, 20 mg; folic acid, 1000 mg; biotin, 70 mg; iron, 60,000 mg; cobalt, 200 mg; manganese, 80,000 mg; copper, 5000 mg; zinc, 60,000 mg; iodine, 1000 mg; selenium, 150 mg; choline cloride, 300,000 mg.

° Calculations are based on analyzed values for corn and soybean meal.

# Based on NRC 1994 values for corn and soybean meal.

The diets given to birds in weekly bases and experimental treatments (Trt1, Trt2, Trt3) are shown in Table 2. Water was supplied from 2000 mL plastic water bottles fitted with nipples at the base. Each pen was equipped with one hanging feeder and an individual bottle. Feed and water were consumed ad libitum. Incandescent lights were used to provide the birds with 24 hours of light per day. Body weights of each bird were measured at 3 and 7, 14, 21, 28, 35, and 42 days of age.

Table 2 Diets given to birds in weekly bases.

		4–6 week	7th week
Experiment 1	Trt1	Diet 2 with normal water	-
Trt2	Diet 3 with 0.050% methionine in drinking water	-
Trt3	Diet 3 with 0.075% methionine in drinking water	-
Experiment 2	Trt1	Diet 2 with normal water	Diet 4 with normal water
Trt2	Diet 3 with 0.050% methionine in drinking water	Diet 5 with 0.050% methionine in drinking water
Trt3	Diet 3 with 0.075% methionine in drinking water	Diet 5 with 0.075% methionine in drinking water

0–3 week: all the birds fed with the Diet 1. Trti: ith dietary-treatment.

Experiment 2 was a duplicate of experiment 1, except that birds’ body weight was measured at 49 days of age as well.

Preliminary analyses showed that there was no significant difference in parameter estimates for comparing experiment 1 and experiment 2. Therefore, data obtained from the two experiments were combined and used for growth curve parameters estimation. Thus, a total of 278 birds (142 males and 136 females) had complete growth data.

Data analysis

The Laird form of the Gompertz model was fit to the data. The Gompertz-Laird growth curve is described by the following equation: where BW_w is the weight of birds at week w, BW₀ is the initial body weight, L is the initial specific growth rate per week, K is the rate of exponential decay of the initial specific growth rate. At the inflection point, the following parameters were derived: where t_i is the inflection point as week, and BW_a is the asymptotic body weight.

Since consecutive or repeated measurements are usually auto-correlated, the growth models were fitted to individual birds in order to remove possible bias in the statistical inference on the growth parameters. The model was run three times for each individual birds in the following manner; in the 1^st run, no constrain was applied on BW₀, in the 2^nd run, BW₀ was constrained as the observed initial body weight, that is, the mean of observed initial body weight of all birds was put in the model as a constant, and finally, in the 3^rd run, BW₀ was allowed to vary within a ±3σ_p interval around the mean of observed initial body weight of all birds.

Models were compared on the basis of coefficient of correlation (R²), residual standard deviation (RSD), correlation (r) between the observed and the predicted growth curves, and estimates of asymptotic body weights (BW_a). The comparisons were made by t-test. Subsequently, growth curve parameters of the selected model were discussed. Calculations were carried out using the non-linear regression option of the statistical software package SPSS (version 5.0.1). The Levenberg-Marquart estimation method was applied. Convergence criterion was the relative reduction between successive residual sums of squares, and was set to 1.0E-08.

Results and discussion

Overall means and standard errors of body weight (BW) for both sexes in relation to environmental changes are represented in Table 3. In all environments, standard errors increased with age in both sexes. Differences in BWs of males and females were significant at week two and thereafter (P<0.05). Males were heavier than females throughout the experiment regardless of the environmental differences. The effect of treatment became apparent at week 4 and remained evident thereafter. The differences in BWs for both males and females were significant (P<0.05) in Trt2 in comparison to those in Trt1 and Trt3. Males and females in Trt1 and Trt3 were heavier than those in Trt2 throughout the experiment. The effect of temperature first appeared at week 5, and stayed significant thereafter. Males and females reared in 21°C were heavier (P<0.05) than those in 30°C. There was no significant interaction between the environmental conditions, and only the main environmental conditions were effective on BW.

Table 3 Means, standard errors in grams, and number of observations for body weight (BW) at different ages in relation to environments for male and female broilers.

Te Trt			1		21°C 2		3		1		30°C 2		3
	Age wk	N		N		N		N		N		N
M	0	24	57.0±0.98	22	56.0±1.02	25	55.8±0.85	24	56.3±1.00	21	53.7±0.97	26	54.4±0.95
1	24	139.3±4.01	22	139.9±3.62	25	139.4±3.14	24	143.9±3.99	21	137.6±4.17	26	136.7±3.34
2	24	384.0±9.73	22	386.3±9.28	25	386.6±8.37	24	393.8±8.40	21	385.2±8.72	26	379.5±8.44
3	24	732.2±13.90	22	733.8±14.85	25	740.1±13.36	24	770.2±14.14	21	724.3±17.07	26	718.9±15.08
4	24	1272.9±22.92	22	1248.3±28.49	25	1286.4±24.52	24	1323.6±24.27	21	1204.4±25.71	26	1250.0±25.64
5	24	1891.3±36.82	22	1861.6±41.83	25	1913.4±33.04	24	1900.1±35.32	21	1714.2±34.13	26	1830.7±32.77
6	24	2538.5±47.45	22	2496.4±53.68	25	2563.6±44.26	24	2485.0±44.29	21	2232.1±39.09	26	2441.1±39.92
7	12	3300.6±92.16	11	3226.3±77.54	13	3221.2±63.40	12	3113.6±46.32	9	2759.1±58.10	14	2953.1±60.46
F	0	22	55.7±0.93	23	56.2±0.77	20	56.3±0.96	23	54.7±1.05	27	55.8±0.96	21	56.5±0.94
1	22	137.4±2.84	23	140.9±2.87	20	139.2±3.08	23	132.6±3.13	27	137.5±3.35	21	144.1±3.77
2	22	372.4±6.41	23	373.6±7.42	20	365.8±8.02	23	362.2±6.44	27	370.0±7.90	21	376.4±7.50
3	22	695.5±8.99	23	682.9±12.48	20	674.2±13.08	23	680.2±10.07	27	681.6±12.84	21	685.2±12.60
4	22	1150.3±18.53	23	1107.1±27.49	20	1142.8±25.96	23	1133.3±16.76	27	1122.8±20.38	21	1145.9±21.58
5	22	1683.4±27.92	23	1591.8±38.64	20	1689.4±34.18	23	1628.8±22.87	27	1594.0±30.36	21	1643.3±26.33
6	22	2178.1±47.21	23	2101.5±48.05	20	2229.4±42.10	23	2136.4±28.59	27	2067.9±38.85	21	2130.9±32.19
7	10	2804.9±46.78	11	2738.1±46.40	8	2816.9±67.72	11	2599.8±29.04	15	2563.9±35.39	9	2668.8±49.17

Te: temperature.

Trt 1: Diet 1 (0–3 wk) + Diet 2 with normal water (4–6 wk) for the experiment 1. Trt 1: Diet 1 (0–3 wk) + Diet 2 with normal water (4–6 wk) + Diet 4 (wk 7) for the experiment 2. Trt 2: Diet 1 (0–3 wk) + Diet 3 with 0.050% methionine in drinking water (4–6 wk) for the experiment 1. Trt 2: Diet 1 (0–3 wk) + Diet 3 with 0.050% methionine in drinking water (4–6 wk) + Diet 5 with 0.050% methionine in drinking water (wk 7) for the experiment 2. Trt 3: Diet 1 (0–3 wk) + Diet 3 with 0.075% methionine in drinking water (4–6 wk) for the experiment 1. Trt 3: Diet 1 (0–3 wk) + Diet 3 with 0.075% methionine in drinking water (4–6 wk) + Diet 5 with 0.075% methionine in drinking water (wk 7) for the experiment 2.

M:males, F:females.

In accordance to the choice made about the form of Gompertz-Laird model used (i.e. whether the unrestricted form or one of the restricted ones), differences between the goodness of fit criteria were tested by using t-test procedures. The estimates of the comparison criteria and standard errors in relation to the environmental condition are shown in Table 4.

Table 4 Coefficients of determination (R²), residual standart deviation (RSD), correlation between observed and the predicted growth curves (r), and asymptotic body weight (BW_a) values of Gompertz-Laird model restricted in three different ways.

			No.	Restriction on BW0 Observed	±3σp of Obs
R-Square	Temp	21°C	0.9997±0.0001^*	0.9975±0.0001	0.9983±0.0001
30°C	0.9998±0.0000	0.9971±0.0001	0.9980±0.0001
Trt	1	0.9998±0.0000	0.9971±0.0002	0.9980±0.0001
2	0.9997±0.0000	0.9974±0.0001	0.9983±0.0001
3	0.9997±0.0014	0.9972±0.0001	0.9982±0.0001
Sex	M	0.9997±0.0000	0.9973±0.0001	0.9982±0.0001
F	0.9998±0.0000	0.9972±0.0001	0.9982±0.0001
RSD	Temp	21°C	20.46±0.872	70.54±1.224	56.79±1.156
30°C	18.56±0.866	74.22±1.416	60.58±1.324
Trt	1	19.07±0.973	75.60±1.635	61.66±1.556
2	19.28±0.975	67.79 ±1.495	54.58±1.359
3	20.12±1.243	73.89 ±1.673	59.94±1.606
Sex	M	21.83±0.993a	75.42±1.380	61.52±1.311
F	17.04±0.656b	69.30±1.231	55.81±1.142
r	Temp	21°C	0.9997±0.0001	0.9982±0.0001	0.9987±0.0001
30°C	0.9997±0.0000	0.9979±0.0001	0.9985±0.0000
Trt	1	0.9997±0.0000	0.9979±0.0001	0.9985±0.0001
2	0.9997±0.0000	0.9982±0.0001	0.9987±0.0001
3	0.9997±0.0001	0.9980±0.0001	0.9986±0.0001
Sex	M	0.9997±0.0000	0.9981±0.0001	0.9986±0.0001
F	0.9997±0.0000	0.9980±0.0001	0.9986±0.0001
Bwa	Temp	21°C	6344±167a	25776±2845	14636±798
30°C	5027±88b	48533±32570	11347±948
Trt	1	5593±170a	19002±1799	12191±670
2	5585±206a	20489±32001	11916±823
3	5838±146a	73092±50242	14781±1559
Sex	M	6350±159a	58499±32599	15720±1133
F	4963±89b	15370±991	10070±371

* Numbers in each row (for R2, RSD, and r) are significantly different from each other (P<0.05). BW₀: initial (hatching) body weight in grams, No: no restriction applied on BW₀, Observed: BW₀ restricted to be the mean of observed initial body weights in grams, ±3σ of Obs.: BW₀ restricted to stay within 3 standart deviation around the mean of the observed initial body weights in grams. Temp: temperature, Trt: treatment. Trt 1: Diet 1 (0–3 wk) + Diet 2 with normal water (–6 wk) for the experiment 1. Trt 1: Diet 1 (0–3 wk) + Diet 2 with normal water (–6 wk) + Diet 4 (wk 7) for the experiment 2. Trt 2: Diet 1 (0–3 wk) + Diet 3 with 0.050% methionine in drinking water (–6 wk) for the experiment 1. Trt 2: Diet 1 (0–3 wk) + Diet 3 with 0.050% methionine in drinking water (–6 wk) + Diet 5 with 0.050% methionine in drinking water (wk 7) for the experiment 2. Trt 3: Diet 1 (0–3 wk) + Diet 3 with 0.075% methionine in drinking water (–6 wk) for the experiment 1. Trt 3: Diet 1 (0–3 wk) + Diet 3 with 0.075% methionine in drinking water (–6 wk) + Diet 5 with 0.075% methionine in drinking water (wk 7) for the experiment 2.

Sex: M=males and F=females.

R² values were decreased significantly (P<0.05) when the restriction applied on BW₀ become more rigid. For example, when the BW₀ was not allowed to vary, that is, when BW₀ was set to the mean of the observed initial body weights, R² values varied from 0.9971 to 0.9974, however, when BW₀ was allowed to vary in an ±3σ_p interval around the mean of the observed initial body weight, R² values varied from 0.9980 to 0.9983. Moreover, when BW₀ was not restricted, R² values varied from 0.9997 to 0.9998, and were higher than those obtained from each of the restricted form of the model (P<0.05). In agreement with these findings, high R² values were also reported in a study on growth using unrestricted Gompertz model in broilers (Yakupoglu and Atil, 2001b) and in Venda and Naked Neck chickens (Norris et al., 2007).

Residual standard deviations (RSD) and standard errors are presented in Table 4. RSDs were larger for the model in which the BW₀ was set to the observed mean value than for the models with BW₀ restricted to vary in an interval. The smallest RSD (P<0.05) was obtained from the model without restriction on BW₀. Previous study by Aggrey (2002) has also reported similar RSD for Gompertz-Laird model without any restriction on BW₀. The estimates of correlation (r) between observed and predicted growth curves are presented in Table 4. Similarly to R² values, r values also decreased when the restriction applied on BW₀ became more rigid. From the unrestricted form of the model, significantly larger (P<0.05) r values were obtained than from restricted forms of the model.

Another comparison criterion used in the present study was the estimate of asymptotic body weight (BW_a) (Table 4). Restricted forms of the model produced very high values of BW_a. The estimates were far beyond the acceptable region of the broiler mature body weight. Restriction applied on BW₀ forced BW₀ to take larger values than the model could produce, and since BW_a is a function of BW₀, it caused BW_a become larger.

Previous studies have suggested ways of improving the fitting of the data. Thus, some restrictions could be put on the initial body weight (Grossman and Bohren, 1982). The observed initial body weight could be used as a constant in the model (Barbato, 1990), or BW₀ could be weighted by the inverse of the variance (Pasternak and Shalev, 1994). In addition, Mignon-Grasteau et al. (1999) constrained BW₀ to stay within two standard deviations of mean of BW₀, and reported a correlation of 0.98 between the observed and the predicted initial body weights. In the present study, we compared the original Gompertz-Laird model with restricted Gompertz-Laird models in which BW₀ was restricted in two different ways. Analyses showed that the any restriction on BW₀ alone in the Gompertz-Laird model forces the other model parameters to take the values out of parameter space. For example, in cases when BW₀ was restricted, asymptotic body weight (BW_a) (Table 4) derived by using the estimates of BW₀, L, and K, has taken very large values, ranging from 10.1 kg to 73.1 kg. The same situation was observed also for the parameter ti. Consequently, this caused a decrease of the estimation power of the model, which can be seen by examining the RSD, R², and the correlation (r) between the observed and the estimated growth curves (Table 4). The values of r obtained from the unrestricted Gompertz-Laird model were different and significantly larger (P<0.05) than the r values obtained from the restricted forms of the model.

The estimates of BW₀ obtained from the restricted forms of Gompertz-Laird models were not reported here because the estimates were identical and the smallest possible value for all individuals. For example, when the BW₀ was restricted to be the mean of the observed initial body weights, naturally all the individuals had the same estimate of BW₀. Similarly, when the BW₀ was allowed to vary within an interval of ±3σ_p around the mean of the observed initial body weights, all the individuals had the lowest possible estimate of BW₀ and that was the lowest bound of the interval. Without any restriction on BW₀, the model significantly (P<0.01) underestimated the observed BW₀ in every level of each environmental condition (Table 5). However, considering the other goodness of fit criteria, the unrestricted Gompertz-Laird model performed well, that is, the highest R², the highest correlation (r) between the observed and the estimated growth curves, the smallest RSD, and the reasonable estimates of BW_a were obtained by the model (Table 4).

Table 5 Growth curve parameters of broilers obtained by the unrestricted form of the Gompertz-Laird model.

		BW0	L	K	ti	r(L,K)
Temp	21°C	10.92±0.452^a	1.82±0.043^a	0.27±0.004^a	6.82±0.078^a	0.947^a
30°C	8.79±0.399^b	1.98±0.032^b	0.30±0.003^b	6.20±0.058^b	0.935^b
Trt	1	8.90±0.467^a	1.98±0.061^a	0.29±0.005^a	6.40±0.081^a	0.959^a
2	11.29±0.636^b	1.81±0.038^b	0.28±0.004^a	6.54±0.105^a	0.920^b
3	9.28±0.440^a	1.90±0.039a^b	0.28±0.004^a	6.57±0.079^a	0.955^a
Sex	M	9.69±0.461^a	1.92±0.036^a	0.28±0.003^a	6.68±0.079^a	0.949^a
F	9.97±0.404^a	1.88±0.042^a	0.29± 0.003^a	6.32±0.063^b	0.946^a

Numbers not containing common superscript in each column within an environment are significantly different from each other (P<0.05). BW₀: initial (hatching) body weight in grams, L: initial specific growth rate, K: the rate of exponential decay of the initial specific growth rate, ti: the inflection point as week, r(L,K): correlation between the observed and the predicted growth curves. Temp: temperature. Trt 1: Diet 1 (0–3 wk) + Diet 2 with normal water (4–6 wk) for the experiment 1. Trt 1: Diet 1 (0–3 wk) + Diet 2 with normal water (4–6 wk) + Diet 4 (wk 7) for the experiment 2. Trt 2: Diet 1 (0–3 wk) + Diet 3 with 0.050% methionine in drinking water (4–6 wk) for the experiment 1. Trt 2: Diet 1 (0–3 wk) + Diet 3 with 0.050% methionine in drinking water (4–6 wk) + Diet 5 with 0.050% methionine in drinking water (wk 7) for the experiment 2. Trt 3: Diet 1 (0–3 wk) + Diet 3 with 0.075% methionine in drinking water (4–6 wk) for the experiment 1. Trt 3: Diet 1 (0–3 wk) + Diet 3 with 0.075% methionine in drinking water (4–6 wk) + Diet 5 with 0.075% methionine in drinking water (wk 7) for the experiment 2.

Sex: M=males and F=females.

On the basis of the comparison criteria of R², RSD, r, and BW_a, used in the present study, the unrestricted form of the Gompertz-Laird model seemed to be the most appropriate model to describe the association between age and live weight, and to explain the growth trajectory of broilers. Based on the above assessments, the unrestricted form of the Gompertz-Laird model was further used to assess the parameters of the growth curves of broilers raised in different environments.

Since consecutive or repeated measurements are usually auto-correlated, the growth models were fitted to individual birds to remove possible bias in the statistical inference on the growth parameters. Then the estimated parameters were averaged over each main effect of the environmental conditions. Comparisons were made within environments using t-test procedure. The levels of interaction of environmental conditions are not reported here because the all interaction effects were insignificant.

The values estimated for the parameters BW_a, r, RSD, and R2 are given in Table 4 (the first column). The other model parameter estimates are shown in Table 5. The results obtained here can be compared with those reported on broiler genotypes by Hancock et al. (1995) and Gous et al. (1999). The mature live weight estimate of 6.4 kg for males in this work (Table 4) is larger than those of broilers in earlier reports (Knizetova et al., 1991; Hancock et al., 1995; Gous et al., 1999). Similarly, the estimated mature live weight of females of 5.0 kg is larger than the range of 4.3 to 4.7 kg reported by Hancock et al. (1995), but they were equal to the estimates reported by Knizetova et al. (1991) and Gous et al. (1999).

The value of initial growth rate parameter, L, was similar in two sexes, 1.92±0.036 and 1.88±0.042 in males and females, respectively (Table 5). These values were larger than those reported in literature (Tzeng and Becker, 1981; Barbato, 1991; Mignon-Grasteau et al., 1999; Aggrey, 2002). By contrast, L values reported in earlier studies (Mignon-Grasteau et al., 1999; Aggrey, 2002), were smaller for both sexes than the findings in the present work. The same authors also reported different K values for males and females. The rate of maturation, K, was similar in both sexes (Table 5), and was consistent with the studies by Yakupoglu and Atil (2001a). However, Hancock et al. (1995) did not observe any sexual dimorphism in K when the Gompertz model was fitted, in agreement with the findings in this study. Among the growth parameters predicted by the model, a highly positive correlation was found between L and K (Table 5), which are close to the correlation reported by Barbato (1991) and Aggrey (2002).

The estimated ages at maximum growth (t_i) are represented in Table 5. Females reached ti faster than males. The differences in ti for males and females were small (0.36 w), but significant (P<0.05). These findings are in contrast with earlier studies (Yakupoglu and Atil, 2001a), in which males and females reached ti about a week earlier (in 5.7 w). Aggrey (2002) stated that individuals with higher mature BW_a reach the age at maximum growth later than individuals with lower mature BW_a provided that BW_a differs among sexes. The results obtained in the present study confirm this statement as males had higher mature BW_a and reached the age at maximum growth about 0.36 w later than females.

The effect of temperature on all growth parameters was significant (P<0.05) (Table 5). The estimates of BW₀ and ti were larger for broilers subjected to 21°C than that for broilers subjected to 30°C. Broilers in 21°C reached the maximum growth rate 4.2 days (i.e. 0.6 w) later than those in 30°C. In high temperature, initial growth rate (L) was high, thus, birds grew fast in the first period of growth trajectory. However, the rate of exponential decay of the initial specific growth rate (K) was also high, thus, the speed of growth of individual birds slowed down in the second period. Consequently, birds in 30°C reached the age at maximum growth earlier (Table 5) and had smaller mature body weight than those subjected to 21°C (Table 4). In the latter group (21°C), the rate of exponential decay of the initial specific growth rate (K) was slow which prolonged the time needed to reach the age at maximum growth (t_i) (Table 5). It is generally expected, when the Gompertz-Laird model is fitted, that individuals with higher initial growth rate would reach the age of maximum growth later, consequently, show a lower exponential decay than individuals with lower initial growth rate (Aggrey, 2002). However, the results in the present study revealed that this general expectation does not hold when there is some fluctuation in the environmental conditions. For example, the individual birds in 21°C in this experiment had lower L than those in 30°C, thus, they reached the age of maximum growth later (Table 5). Moreover, regardless of the level of treatment (Trt1, 2, or 3), individuals with different L values reached the age of maximum growth at the same time (Table 5). Thus, the results indicate that the exponential decay, K, is the factor affecting the time to reach the age of the maximum growth.

Conclusions

In conclusion, the Gompertz-Laird model without any restriction on initial body weight (BW₀) is appropriate for describing the agelive weight relationship in broilers. The results showed evidence that restricting BW₀ results in having very high estimates of the other model parameters. The initial specific growth rate (L), the rate of exponential decay (K) of the initial specific growth rate, and the relationship between L and K vary as the environmental conditions change. The model parameters of BW₀, L, and K were also affected by different feeding regimes. Based on the results in this study, it will be necessary to take into account environmental factors in future studies on growth of broilers.

Acknowledgments

the authors extend special thanks to undergraduate students who participated in all phases of this work, and to Katalin Vajda for kindly help in spelling check.

Financial assistance of the HR.U. Scientific Research Foundation (Project Number: HUBAK-697) is greatly acknowledged.