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Cuban Journal of Agricultural Science

Print version ISSN 0864-0408On-line version ISSN 2079-3480

Cuban J. Agric. Sci. vol.49 no.3 Mayabeque July.-Sept. 2015




Modeling of live weight per age in fattening bovines under a silvopastoral system with Leucaena leucocephala


Modelación de peso vivo por edad en bovinos de engorde en silvopastoreo con Leucaena leucocephala



J. Iraola,I Yenny García,I E. Muñoz,I L.M. Fraga,I M. Barros-Rodríguez,II J.L. Hernández,I E. Moreira,I

IInstituto de Ciencia Animal, Apartado Postal 24, San José de las Lajas, Mayabeque, Cuba.
Facultad de Ciencias Agropecuarias, Universidad Técnica de Ambato, Ecuador.




The modeling of the curve of live weight per age in non-castrated male bovines under a silvopastoral system with Leucaena leucocephala during four productive cycles was evaluated. For that purpose, four genetic groups were used: Zebu, crossbred Zebu, crossbred Zebu and dairy crossbreds, with 74, 80, 90 and 90 animals, respectively. Monthly weighing was carried out in all the cycles. For deciding the goodness of fit, the following criteria were proposed: mean square of the error, fitted R2, model significance, parameter significance and graphic distribution of residues. The non-linear models (Gompertz and Logistic) were only fitted in the second and third productive cycle under the specific conditions of the study. The simple linear model showed adequate adjustments in every cycle, and showed lower values of mean square of the error than the non-linear models in the second and third cycles. There were no marked differences of liveweight increase among the four genetic groups evaluated, with daily mean gains around and superior to 0.700 kg. This indicates the need of developing specific strategies for the ending stages of male bovines under silvopastoral conditions. Further studies on modeling with higher liveweight at sacrifice of Zebu and crossbred animals are suggested, which will allow to predict the productive performance of these animals. Interpreting the results and controlling the indicators, like food balance and management, could substantially improve the indicators of liveweight at sacrifice in a silvopastoral system with leucaena and grasses.

Key words: linear and non-linear model, bovines, silvopastoral system.


Se evaluó mediante la modelación la curva de peso vivo por edad de bovinos machos, sin castrar, en silvopastoreo con leucaena (Leucaena leucocephala) durante cuatro ciclos productivos. Se utilizaron para ello los siguientes grupos genéticos: Cebú, Cebú mestizos, Cebú mestizos y mestizos lecheros, con 74, 80, 90 y 90 animales, respectivamente. Se realizaron los pesajes mensualmente en todos los ciclos. Para la decisión de bondad de ajuste de los modelos, se propusieron los criterios siguientes: cuadrado medio del error, R2 ajustado, significación del modelo, significación de los parámetros y distribución gráfica de los residuos. Los modelos no lineales (Gompertz y Logístico) solo se ajustaron en el segundo y el tercer ciclo productivo en las  condiciones específicas de estudio. El modelo lineal simple presentó adecuados ajustes en todos los ciclos, y mostró menores valores del cuadrado medio del error que los modelos no lineales en el segundo y tercer ciclo. No se encontraron marcadas diferencias de incremento de peso vivo entre los cuatro grupos genéticos evaluados, con ganancias medias diarias cercanas y superiores a 0.700 kg. Esto indica la necesidad de desarrollar estrategias específicas para la finalización de bovinos machos en silvopastoreo. Se sugiere profundizar en estudios de modelación con mayor peso vivo de sacrificio en animales Cebú y mestizos, lo que permitiría predecir el comportamiento productivo de estos animales. Con la interpretación de los resultados y el control de indicadores, como el balance alimentario y el manejo, se pudieran mejorar sustancialmente los indicadores de peso vivo al sacrificio en silvopastoreo con leucaena y gramíneas.

Palabras clave: modelo lineal y no lineal, bovinos, silvopastoreo.




Modeling researches of liveweight per age are very important in animal production, mainly from the economical point of view. According to Agudelo et al. (2008), Nogales (2009) and Posada et al. (2011), different prediction models can be used that will allow to plan the management and decision-making. In this case, the models will be linear and non-linear (Gompertz 1825, Brody 1945, Bertalanffy 1957 and Nelder 1961), among others. The use of these models, as well as other methodologies, appears frequently in the references.

In Cuba, since Menchaca (1990) carried out modeling studies in fattening cattle, the application of models gained importance, which had the purpose of using them under production conditions. Díaz (2008) evaluated the weighted growth of dairy crossbred, Zebu and Charolais from Cuba genotypes, in the categories of pre-fattening and growth-finishing, in a system established with herbaceous legumes and silvopastoral conditions with leucaena in 100 % of the area. This author referred that linear and non-linear models (Gompertz and Logistic) has a good fit in the evaluated genotypes. However, in the pre-fattening category with Charolais from Cuba, only the simple regression linear model was fitted. Nevertheless, it confirmed the usefulness of growth curves because they allow the dynamic fit of requirements per categories regarding the increase of liveweight with age. In addition, its use will allow to predict and reduce losses in technological costs of opportunities and decision-making, as a guarantee for improving meat productivity (Iraola 2013). The objective of this research was to deepen and evaluate the estimation of curves of liveweight per age in male non-castrated bovines, during the growth and finishing stages under silvopastoral conditions.



The study was developed in areas of the Institute of Animal Science from Cuba, located at 22° 53' N and 82° 02' W and 92 m o.s.l. Four production cycles with non-castrated male bovines were evaluated. The monthly weighings per production cycle were performed: 5 (2008), 8 (2009), 10 (2010) and 10 (2011), respectively. The following genetic groups were used in each cycle: Zebu, crossbred Zebu, crossbred Zebu and dairy crossbreds, with 74, 80, 90 and 90 animals, respectively. A rotational grazing took place under silvopastoral conditions with leucaena, associated with a mixture of natural and improved grasses, without irrigation and without fertilization. The inclusion of leucaena reached 50% of the area. An amount of 50 g of salt per animal per day was provided.

The period evaluated in the first productive cycle was the finishing stage. The remaining cycles included growth and finishing stages. Three models were selected for studying the adjustment of liveweight curve (table 1). For estimating the parameters, the modified method of Gauss-Newton was used, available at the proc NLIN SAS, version 9.1 (2007). For the selection of models, some criteria defined by Guerra et al. (2003) and Torres et al.(2012) were considered. These are the following criteria:

1. R2 fitted to the degrees of freedom of the model

2. The value of the mean square of the prediction error (MSE)

3. Test of model significance

4. Test of parameter significance

5. Amount of iterations, determining the high or low convergence difficulty (Brown et al. 1976)

6. Graphic distribution of residues



Table 2 shows the results obtained after fitting the different models used for all the productive cycles. The models were significant in every case, as well as the parameters of curves.  

In the first productive cycle, the linear model presented appropriate fit, according to the analyzed criteria. There was a fitted coefficient of determination of 96%, accompanied by the mean square of the error (21.32). In the second and third productive cycle, the three models (linear, logistic and Gompertz) were fitted. The mean square of the error of the three models in the second cycle was small and was higher in the third, with regard to non-linear models analyzed. In the logistic model, the asymptotic weight (a) was inferior and maturity rate (c) was superior in the second and third cycle. However, the integration coefficient (b) was inferior in both. Finally, in the curve of the fourth productive cycle, the simple linear model showed appropriate approaches to the curve observed with the adj. R2 of 99%. This indicated that the simple linear model explained best the weight per age relationship in the life phases included on the research, for all the productive cycles, because it showed the lowest values of MSE with respect to non-linear models in the second and third cycle.

Modeling of liveweight per age for the four productive cycles, referring to the daily mean gain (DMG) that ranged between 649 and 769 g (table 3), could be described by the suitable fit of the models used in accordance with the evaluated growth-finishing phases and the stability of the four productive cycles.

Regarding the first cycle, the curve of liveweight showed linear tendency almost until the last weighing. However, the linear model overestimated the liveweight at some points of the observed curve. This could be explained by the lack of metabolic energy that showed the system to meet the animal requirements at the finishing stage. Obviously, it could be important because it affected the individual daily gain. The energy deficit in this cycle was confirmed with the exercises of food balance performed after using the requirement tables (table 4) of Martin and Palma (1999). In the practice, the food balance relationship for fattening animals, mainly the energy-protein balance, daily mean gain and growth prediction with the use of different models (McPhee 2009), among other productive elements, would allow to correct, with technology and management decisions, the losses of weight gains in different genotypes during a determined growth stage in grazing, according to the season and different productive conditions. 

In the second cycle, linear functions and Gompertz and logistic models described the observed curve with ascending tendency, and, in the final phase, they had a similar performance to the previously described cycle, which did not show a stable phase. According to Rodríguez et al. (2011), the results confirmed the ability of these genetic animals to obtain liveweight at slaughtering superior to 400 kg, which would allow to improve carcass meat yield. Bittante et al. (2011) stated that this animal performance depends on the weight and age relationship, under normal production conditions.  

 Likewise, in the third cycle, the linear, logistic and Gompertz models were fitted. All had some difficulties to describe the curvature change, from the third weighing up to the seventh, time that coincided with the transition from dry to rainy season, although there were no marked differences related to individual gain, which was slightly higher at 0.086 kg in this last period. This explained the performance in this study. However, unlike the previous fattening cycle, the final phase of the curvature showed a slight stability, which might be related to weight at slaughtering, superior to the rest of the analyzed cycles.

The fourth cycle showed a similar performance to the previous cycles. The linear function described a good accompaniment in all phases of the observed curve, although the animals were sacrificed with the lowest body weight.

In the calculation of food balance based on grasses, with the exception of the first cycle, included in the finishing phase, which was strategically supplemented, there was an increase of crude protein (CP) in the contribution of the system, resulting in an excess in the balance. Chongo (1988) stated that an excess of CP can produce an additional energy cost for its removal as urea. Therefore, this study allows to infer that, even though the energy covered the requirements for the estimated gain, an important part of it was used to counteract the excess of protein, and could limit the performance of animals, based on the daily mean gain. In addition, the energy would not be enough, according to the balance performed in this system to increase daily mean gains superior to 0.800 kg. These results agree with those reported by Díaz et al. (2009) and Iraola (2013), who refer that metabolizable energy is a limiting factor for obtaining higher daily gains in a silvopastoral system with leucaena, which could be corrected with sources of soluble sugars, in order to search for greater energy-protein ruminal synchronism.

The results of this study confirm those of Tedeschi et al. (2000) in the Latin American context, as well as those reported by Díaz (2008) and Iraola et al. (2014) in Cuba, under similar conditions. These results, according to Fernández (1996), Agudelo et al. (2008) and Grimm et al. (2010), are very related to the evolution of animal liveweight in the time. Therefore, under normal feeding conditions, growth speed tends to be linear and it can be maintained until animals reach their adult individual weight and stop growing. Generally, fat deposition in muscles increases, as well as the percentage of bones in the carcass. In this sense, the control of food balance contributes to finding feeding deficiencies in the system and avoiding problems in the individual gain of animals (Iraola 2014).  

Therefore, the evaluated growth and finishing stages favored the suitable adjustment of the linear model in each cycle. Some results reported by Menchaca (1991ab), Cañeque and Sañudo (2005) and Jones (2014) could help to confirm the results obtained in that study with beef cattle for these growth stages.

Residues indicated normal distribution of their values for all cycles (figure 1a, b, c and d). In the simple linear model, values ranged from -20 to 20, and in the non-linear models, between -150 and 150. The development of biomass production, from the second production cycle, contributed to stabilize the estimated daily mean gain, without marked problems, according to the season, with a favorable productive performance for tropical conditions. This allowed a mean duration in grazing during the growth-fattening stage, from the second cycle of eight and nine months, in order to obtain mean liveweight at slaughtering between 380 and 416 kg with these genetic groups (table 3).

The results support a linear performance in the evaluated genetic groups. This indicates that commercial arguments are needed in order to maximize profitability in these genotypes, because if the animals finish fattening stage under silvopastoral conditions with leucaena and a mixture of improved and natural grasses, genetic and non-genetic factors (climate, management, and some others) should be considered to achieve better productive indicators (Justin et al. 2012). Therefore, control should be together with some indicators, such as food balance per season, and others related to management, so as to ensure animal productivity in the real context of each productive system.

It can be concluded that the model of linear growth was fitted in all fattening cycles. The non-linear (Gompertz and logistic) models were fitted in the second and third cycle in the life phases evaluated in this study. This indicates the need to develop specific strategies for the finishing stage of male cattle in silvopastoral systems with leucaena. Further studies on growth models with superior liveweight at slaughtering in Zebu and crossbred animals are suggested, which would predict the productive performance over time. Interpreting results, control indicators such as food balance and management, could substantially improve the indicators of liveweight at slaughtering, under silvopastoral conditions with leucaena and grasses.



Thanks to the workers from the fattening unit “Ayala” and to the Department of Animal Genetics from the Institute of Animal Sciences.



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Received: July 9, 2014
Accepted: March 31, 2015



J. Iraola, Instituto de Ciencia Animal, Apartado Postal 24, San José de las Lajas, Mayabeque, Cuba. Email:

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