Description of growth in sheep creole ( Ovis aries ) in two populations from Córdoba , Colombia Descripción del crecimiento de ovinos criollos ( Ovis aries ) en dos poblaciones de Córdoba , Colombia

Objective. Evaluate the model that best described the growth in sheep creole in the Department of Cordoba. Materials and methods. Weights of 55 Criollos sheep were used to select the model that best fit the data. Brody, Logistic, Gompertz and Von Bertalanffy models were evaluated. The parameters of the models were estimated using the NLIN procedure of SAS. The selection of the curve that best described the growth was done considering the Aikaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), the Determination Coefficient (R2), and the Percentage of Convergent Curves (CCP). For the model that best described the growth curve, the percentage of maturity at 4 (M4) and 6 (M6) months of age and age at 75 (AM75) and 95% (AM95) at maturity was estimated. Results. The Brody model presented the best fit. Sex effect was significant (p≤0.05) for β2, M4, M6, EM75 and EM95. While the Farm effect had only a significant effect (p≤0.05) for β2. Conclusions. The Brody model best described growth of the studied sheep populations, its estimated values for maturity and age at maturity were low.


INTRODUCCIÓN
La producción de ovinos de pelo en Colombia, tradicionalmente se ha considerado como una actividad secundaria de la ganadería vacuna.Para lograr un incremento de la competitividad del sector, se requiere de la incorporación del conocimiento como factor producción y generador de ventajas competitivas mediante sistemas de gestión de conocimiento que se adapten a las condiciones de la producción primaria de un país en desarrollo como Colombia (1).

INTRODUCTION
The production of hair sheep in Colombia has traditionally been considered a secondary activity to cattle farming.To achieve an increase in the competitiveness of this sector, it is necessary to incorporate knowledge as a production factor and generate competitive advantages through knowledge management systems that adapt to the conditions of primary production in developing countries such as Colombia (1).
Currently, technology transfer processes are being generated from different places, which are unrelated to the production conditions of the Colombian tropics, so that at a certain moment, they may become obstacles to achieving the much sought-after competitiveness, by generating unplanned undesirable events, instead of real solutions to livestock production (2).The above suggests that it is necessary to deepen the different aspects associated with their production to allow improving productive indexes (1,3).On the other hand, sheep production has characteristics that make this exploitation system profitable in the short term, because sheep are a rustic species, with high fertility, prolificacy and longevity (3).
Based on the above, it is necessary to carry out studies in Colombia that provide a greater knowledge of sheep production.In this sense, the study of growth curves is essential to initiate a selection and genetic improvement program in sheep, destined to increase the precocity of this species (4).These measures have been used by some researchers to describe animal growth (4).Hence, the importance of this research in the evaluation of different non-linear growth models, managed under grazing conditions in the Department of Córdoba, to provide relevant information to producers, for the selection of animals with performance according to the objectives of production.

MATERIALS AND METHODS
Location.This study was conducted in two sheep production systems, located in the municipalities of Montería (Farm 1) and Sahagún (Farm 2).The municipality of Monteria is located at 08°45' North latitude and 75°53' West longitude, altitude of 18 meters above sea level, average annual temperature of 28°C, average annual rainfall of 1,225 mm and relative humidity of 80%.The municipality of Sahagún is located at 08°56 'North latitude and 75°26' West longitude, height of 75 masl, average annual temperature 27°C, average annual rainfall of 1,395 mm and relative humidity of 80%.latitud Norte y 75°26' longitud Oeste, altura de 75 msnm, temperatura media anual 27°C, precipitación media anual de 1.395 mm y humedad relativa de 80%.
Además, se calculó el porcentaje de madurez a los cuatro (M4) y seis meses (M6) de edad y la edad promedio para alcanzar el 75 (EM75) y 95% (EM95) de madurez, para el modelo Brody, que fue el que mejor describió el crecimiento de los ovinos de las poblaciones estudiadas, de acuerdo a las siguientes formulas: Management, animals and nutrition.Fiftyfive Creole sheep from single births, belonging to two different production systems born from single births between November 2013 and April 2014, were used.Weigh-ins were carried out every 15 days from birth to 6 months of age (since this is the age at which producers market animals for slaughter).Each production system had a JAZ-DINA L150 digital scale with a capacity of 150 kg, to carry out the weighing of the animals, with at least 10 weigh-ins for each animal and a maximum of 13.The animals were managed under grassland grazing conditions of Bothriochloa pertusa, with water and mineral salt availability at will; during the dry season the animals of farm 1 were supplemented with corn silage and grain and those of farm 2 with Pennisetum purpureum silage.

Growth curves.
With the weighing data, a database for the study of the growth curves was elaborated by means of the following non-linear regression models: Where: yt represents the weight of the animal at time t; β0 represents the asymptotic weight of the animal when «t» tends to infinity, it is generally interpreted as a percentage of maturity compared to adult weight; β1 is an adjustment parameter when y ≠ 0 or t ≠ 0; β2 is a maturity index or measure of precocity, expressed as a percentage proportion of the maximum growth compared to the adult weight of the animal, the higher it is, indicates a faster growth rate (9)(10)(11).
In addition, the percentage of maturity was calculated at four (M4) and six months (M6) of age and the average age to reach 75 (EM75) and 95% (EM95) maturity, for the Brody model, which was the one that best described the growth of the sheep in the populations studied, according to the following formulas: Where: %M= percentage of maturity estimated at 4 or 6 months; t = time to reach a percentage of maturity (4 or 6 months).

Statistical analysis.
The parameters of the growth curves were estimated using the SAS NLIN procedure (12).For the selection of the best model, the Akaike information criterion (AIC), the Bayesian information criterion (BIC), the coefficient of determination (R2) and the percentage of convergent curves (PCC) were considered.To determine if there was statistical difference between genders and farms for model parameters, percentage of maturity and age at maturity, a variance analysis of was performed using the GML procedure of the SAS.It should be noted that the assumptions of normality and independence of the errors were validated.

RESULTS
Table 1 shows the estimates of parameters β 0 , β 1 , β 2 , R 2 , AIC, BIC and PCC of the different models studied.All models evaluated had 100% PCC.However, the Brody model presented a lower AIC and BIC compared to the other models, although its R 2 was smaller, but met three of the four criteria for model selection.This allows us to affirm that the Brody model fits satisfactorily to the growth of Creole sheep.Como el modelo Brody fue el que mejor describió el crecimiento de los ovinos Criollos.
En la literatura consultada no se encontró información sobre los porcentajes y edad a la Inés sheep evaluating the Brody, Von Bertalanffy, Logistic, Gompertz and Richards models, found that the Logistic model was the one that best described growth.As is noticed, each specific population has a particular model to describe its growth, since according to the literature consulted, the growth of the same breed can be adjusted to different non-linear models, so that environmental conditions, feeding systems and handling are determinants in the generation of information for the adjustment of the models; without leaving aside the effect of the breed or breeds involved.
The estimated values of (β 0 =46.As the Brody model was the one that best described the growth of Creole sheep.When considering the sex effect, males reached a greater weight and maturity rate during adulthood than females.These results agree with that reported by Sarmento et al (11) and Oliveira et al (18), who found that the sex effect of the animals significantly influenced parameters β0 and β2.The superiority of males compared to females may be related to sexual dimorphism, due to the anabolic effect of testosterone acting as a growth promoter, represented by a higher weight of males in adulthood (18,31).When considering the farm effect, the animals in farm 1 reached a greater weight and maturity rate at madurez.Al comparar los efectos sexo y finca, se encontró que los machos tuvieron un mayor porcentaje de madurez a los 4 y 6 meses de edad y una menor edad para alcanzar el 75 y 95% de la madurez que las hembras, debido al dimorfismo sexual en esta especie, y que los animales de la finca 1 tuvieron un mayor porcentaje de madurez a los 4 y 6 meses de edad y una menor edad para alcanzar el 75 y 95% de la madurez que los animales de la finca 2 (Tabla 2).
El porcentaje de madurez a los seis meses es de gran importancia, ya que es el referente en los rebaños de la región como la edad apropiada para llevar a sacrificio los corderos y las hembras a la reproducción.De acuerdo a los parámetros estimados y a los valores de edad a la madurez y porcentaje de madurez, se debe mejorar la alimentación de los animales en los sistemas de producción estudiados, con el fin de que sean más precoces en su crecimiento, es decir, que alcancen un mayor peso a una edad más temprana.Para obtener efectos positivos, es necesario garantizar un suministro constante de alimento en la cantidad adecuada y de un valor nutricional que cumpla con las exigencias metabólicas de los animales (32).Además, se hace necesario la implementación de un programa de selección para las características de crecimiento en los sistemas de producción de carne Ovina.
De acuerdo a los resultados obtenidos, se puede afirmar que los animales de la finca 1 presentan un mayor peso a la edad adulta y mayor precocidad que los de la finca 2, debido a que tienen mayor β 0 que representa el peso adulto, y mayor β 2 que indica una mayor velocidad de crecimiento.La posible explicación de esto, se mencionó en un párrafo anterior.
adult age than the animals in farm 2, perhaps due to the type of food used, since farm 1 in the dry season is supplemented with corn silage with grain, which is of higher nutritional content than the Pennisetum purpureum silage used in farm 2.
In addition, farm 1 is part of the mid Sinu valley, where the soil has better nutritional quality than savannah soils, where farm 2 is located.
In the literature consulted, no information was found on the percentages and age of maturity.
When comparing sex and farm effects, males had a higher percentage of maturity at 4 and 6 months of age and a lower age to reach 75 and 95% maturity than females, due to the sexual dimorphism in this species, and that the animals in farm 1 had a higher percentage of maturity at 4 and 6 months of age and a lower age to reach 75 and 95% maturity than the animals in farm 2 (Table 2) .
The percentage of maturity at six months is of great importance, since it is the reference in the herds of the region as the appropriate age to slaughter lambs, and females for reproduction.
According to the estimated parameters and the age values at maturity and percentage of maturity, the feeding of the animals in the studied production systems must be improved, in order for them to grow faster, that is to say, to achieve greater weight at a younger age.
To obtain positive effects, it is necessary to guarantee a constant food supply in the proper amount and a nutritional value that meets the metabolic requirements of the animals (32).In addition, it is necessary to implement a selection program for growth characteristics in sheep meat production systems.
According to the results obtained, the animals from farm 1 have a greater weight at adult age and higher precocity than those from farm 2, because they have higher β0 representing adult weight, and higher β2 which indicates a higher growth rate.The possible explanation for this was mentioned in the previous paragraph.
Animals with higher values of β 2 , are faster in growth, compared with individuals of lower values of β 2 and similar initial weight, so that variations between the values of β 2 represent, with fair precision, the variations in the relative speed with which the animal grows (33).This is corroborated by the ages and percentages of maturity in the farms studied (Table 3).Texeitra et al (13), affirm that it is necessary to evaluate all the parameters together to decide which is the best growth curve model applied to a certain production model, so that there is a model of the growth curve that best fits for each production system.
It can be concluded that the Brody model was the one that best adjusted to the growth curve in the Creole sheep of the Colombian tropics.Male animals have a higher percentage of maturity at 4 and 6 months of age and a lower age to reach 75 and 95% maturity than females.In the production systems, the feeding of the animals must be improved in order to achieve a higher growth rate, in order to reach slaughter at a younger age.

Acknowledgment
The authors thank Mauricio Buelvas and Rafael Vergara, owners of the sheep production systems where the study was developed, for allowing us to use the facilities and animals.In addition, to the Research Office of the Universidad de Córdoba, for financing this project.
Se puede concluir que el modelo Brody fue el que mejor se ajustó a la curva de crecimiento en los ovinos Criollos del trópico colombiano.Los animales machos presentan un mayor porcentaje de madurez a los 4 y 6 meses de edad y una menor edad para alcanzar el 75 y 95% de la madurez que las hembras.En los sistemas de producción se debe mejorar la alimentación de los animales con el fin de lograr una mayor tasa de crecimiento, para alcanzar una edad menor al sacrificio.

Figure 1 .
Figure 1.Growth curve of Creole sheep using the Brody model (8).

Figure 2
Figure2and 3 show the behavior of the growth curves, according to gender and farm, using the model proposed by Brody(8).Table3shows the percentage of maturity at four (M4) and six (M6) months of age and age at 75 (EM75) and 95% (EM95) maturity for the Brody model in Creole sheep.The percentage of maturity according to the Brody model was 44.9 ± 18.7% at 4 months of age and 55.7±20.6% at 6 months of age.According to this model, the animals reached an average of 75% maturity at 414.2±285.5 days and reached 95% maturity at 920.9±615.6 days.

Figure 2 .
Figure 2. Growth curves of Creole sheep according to sex using the model proposed by Brody (8).

Figure 3 .
Figure 3. Growth curves of Creole sheep according to the farm using the model proposed by Brody (8)

Table 2
shows the average values estimated for the parameters studied, considering gender and farm effects for the Brody model in Creole sheep.There was no significant effect (p>0.05) for gender and farm on parameters β 0 and β 1 , while there was a For a given effect, equal letters in the same column indicate that there was no significant difference (p>0.05)

Table 2 .
Estimates for the parameters studied, according to the Brody model, as per gender and farm in Creole sheep.

Table 3
shows the percentage of maturity at four (M4) and six (M6) months of age and age at 75 (EM75) and 95% (EM95) maturity for the Brody model in Creole sheep.The percentage of maturity according to the Brody model was 44.9 ± 18.7% at 4 months of age and 55.7±20.6% at 6 months of age.According to this model, the animals reached an average of 75% maturity at 414.2±285.5 days and reached 95% maturity at 920.9±615.6 days.
(8))nes estudiaron los modelos Brody, Von Bertalanffy, Richards y Gompertz, y encontraron que el modelo Brody fue el que mejor describió el crecimiento.Mientras que, Dorper × Longtail and Dorper × Santa Inés), found that the Gompertz model was the one that best described growth.Keskin et al(20)found that the Quadratic and Gompertz models were the ones that best described the growth of the sheep when evaluating the Quadratic, Cubic, Gompertz and Logistic models in sheep of the Konya Merino breed.Estimados para porcentaje de madurez y edad a la madurez en ovinos Criollos, de acuerdo al modelo propuesto por Brody(8).
(30)valores de estimados (β 0 = 33.82;β 1 = 0.907) del presente estudio, en los ovinos Criollos, utilizando el modelo Brody, fueron superiores a los reportados por Souza et al(25)(β 0 =28.96;DISCUSSIONTheresults of the growth curves in the present study were similar to those reported by Teixeira et al(13), Gbangboche et al(14)and Bahreini et al(15)in Santa Ines, West African and Baluchi sheep respectively, who studied the Brody, Von Bertalanffy, Richards and Gompertz models, and found that the Brody model was the one that best described growth.While, Lupi et al (16) using the Brody, Von Bertalanffy, Logístico and Gompertz models in sheep of Segureña race, found that the Von Bertalanffy model was the one that best described growth.Ullah et al(17)also reported that the Von Bertalanffy model was the one that best adjusted to the growth curve in sheep.Oliveira et al(18)and Sarmento et al(11)using the Brody, Von Bertalanffy, Logistic, Gompertz and Richards models to describe growth in Santa Ines sheep, reported the Gompertz model as the best fit.Similarly, Malhado et al(19), when evaluating the same models in sheep (Dorper×Morada Nova, used the Brody, Logistic and Richards models in sheep of the Bergamácia race, to describe their growth, being the Logistic model the one they recommended; likewise Daskiran et al(23)when evaluating the Brody, Gompertz, Logistic, Bertalanffy and Negative Exponential models in Turkish Norduz sheep; and Silva et al(24)in San Tabla 3. 0 (28.07)yβ 1 (0.47) y superior para β 2 (0.009).Lobo et al(30)en hembras de raza Santa Inés, encontraron valores superiores para β 0 (49.98)y β 2 (0.00425) e inferior para β 1 (0.6) a los del presente estudio.