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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.4 Mayabeque Oct.-Dec. 2015




Genetic parameters of growth traits in Cuban Zebu through the multi-trait animal model and reaction norm model


Parámetros genéticos de rasgos de crecimiento en el Cebú Cubano mediante modelo animal bicarácter y de norma de reacción



Yusleiby Rodríguez,I Raquel Ponce de León,I Manuel Rodríguez,II

IInstituto de Ciencia Animal, Apartado Postal 24, San José de las Lajas, Mayabeque, Cuba.
IICentro de Investigaciones para el Mejoramiento Animal de la Ganadería Tropical.




A multi-trait animal model (15,904 data) and a reaction norm model (13,068 data) were studied, in order to estimate genetic parameters and environmental awareness of the weight at 18 months (P18) and (TDG) of Cuban Zebu during the performance test for future sires. The animals were born between 1981 and 2012 and were the offspring of 295 parents. Multi-trait animal model allowed to obtain the solutions of fixed effect of from the group of contemporaries, heritabilities and genetic tendencies of P18 and trial daily gain TDG. Later, a reaction norm model of sire type was considered, with the group of contemporaries (herd-year-three-month period of animal birth) as fix effect the effect of random regression of sire (cubic, square and linear Legendre polynomials) through an environmental gradient, expressed as solution of fix effect, so a total of 6 environmental classes were created. Estimated values of heritability, through the animal model, were 0.20 ± 0.02 and 0.28 ± 0.02 for TDG and P18, respectively, with a genetic correlation of 0.94 among them. Using the reaction norm model, the estimates varied from 0.13±0.04 to 0.43±0.08, and the highest corresponded to favorable environments or positive gradients. Correlation values, very close to 1, indicate the non-existence of genotype x environment interaction in most of the cases. However, there may be correlations lower than 0.8 in the most unfavorable environment, which indicates that sires selected in favorable environments may not have the same performance after passing to unfavorable environments.

Key words: Performance test, genetic correlation, environmental gradient.


Se estudiaron dos modelos, uno animal bicarácter (15904 datos) y otro de norma de reacción (13068datos) para estimar los parámetros genéticos y la sensibilidad ambiental de peso a los 18 meses (P18) y ganancia diaria en prueba (GPD) del Cebú Cubano d. Los animales nacieron entre 1981 y 2012 y eran hijos de 295 padres. El modelo animal bicaracter permitió obtener las soluciones del efecto fijo del grupo de contemporáneos, las heredabilidades y tendencias genéticas de P18 y GPD Posteriormente se consideró un modelo de norma de reacción de tipo semental, con el grupo de contemporáneos (rebaño-año-trimestre de nacimiento) como efecto fijo y el efecto de la regresión aleatoria del padre (Polinomio de Legendre lineal, cuadrático y cúbico) a través de un gradiente ambiental, expresado como la solución del efecto fijo, para lo que se crearon un total de seis clases ambientales. Los valores estimados de heredabilidad mediante el modelo animal fueron de 0.20 ± 0.02 y 0.28 ± 0.02 para GPD y P18 respectivamente, con una correlación genética entre ellos de 0.94. Mediante el modelo de norma de reacción, los estimados variaron de 0.13±0.04 a 0.43±0.08 y los mayores correspondieron al ambiente favorables o gradientes positivos. Los valores de correlación, muy cercanos a uno indican la no existencia de interacción genotipo x ambiente en la mayoría de los casos. Sin embargo, en el ambiente más desfavorable puede manifestarse correlaciones menores que 0.8, lo que indica que los sementales seleccionados en ambientes favorables, podrían no comportarse de la misma forma al pasar a ambientes desfavorables.

Palabras clave: Prueba de comportamiento, correlación genética, gradiente ambiental.




Nowadays, in Cuba, estimation of breeding value of sires is performed through a single-trait animal model that estimates the genetic value of all evaluated animals, and the bulls with the highest breeding value for liveweight at the end of the test are selected. However, the possible existence of genotype-environment interaction is not considered, despite the candidates to parents of the next generation should be evaluated and selected under conditions that may not be the same as those for exploiting their offspring. The emerging of models of random regression and reaction norm opened new possibilities for IGA evaluations. Thanks to artificial insemination, the performance of the offspring of the same bull may be compared under different environmental conditions (countries, geographic regions, even in an environmental gradient). During the last years, several studies have used random regression with linear Legendre polynomials to evaluate the possible environmental awareness, relating the variation of the norm inclination coefficient as an indicator of IGA importance (Corrêa et al. 2009 and Pegolo 2009).



This study used records of performance test for future sires from Cuban Zebu breed, born between 1981 and 2012, in five genetic enterprises: Camilo Cienfuegos (Pinar del Río), San Juan (Matanzas), San Lino (Cienfuegos), Abra Güinía (Villa Clara), Rescate de Sanguilí (Camagüey) and Manuel Fajardo (Granma).

The values of final weight were fitted to 18 months (P18) and the variable trial daily gain (TDG) was created as the difference between final and initial weight, divided into the days that lasted the test. Two groups of contemporaries were created using the information of herd, year and three-month period of animal birth.   

A multi-trait animal model was used for analyzing P18 and TDG, which considered the group of contemporaries as fix effect and the animal and error as random effects. This first file with data was composed by 15,904 observations with 580 groups of contemporaries and pedigree had a total of 40,594 observations and included 1,852 sires and 22,990 mothers.

From this first model, heritabilities and genetic correlation were obtained between both traits, as well as solutions (minimum square means for fix effect). This solution (in the case of TDG) was used for creating an environmental gradient (6 classes) for the reaction norm model, with values that varied from -330 to 390. In addition, the genetic tendencies of the two traits, analyzed in the animal model, were estimated, as the regression of the mean of breeding value of the population during the birth year. 

The reaction norm model (sire type) had a pedigree file with 295 sires, 187 paternal grandparents and 86 maternal grandparents. This model considered the random regression of sire in the environmental gradient or management group and was composed by 13.068 records and 548 groups of contemporaries. Groups with less than 5 individuals were removed, as well as those parents with less than 10 kids and not represented, at least, by 3 environmental classes.

The used general model was represented as follows:


 yijis the weight value of the j-th kid belonging to the i-th sire

GCij is the fix effect of the group of contemporaries belonging to the progeny of the i-th sire

αijØm (GAij) represents the random regression of the i-th
sire αij) in the environmental group

GAijand Øm represent the coefficient of Legendre polynomial of m order

Variants were tested in the order of Legendre polynomials (linear, square and cubic). The Wombat software (Meyer 2006) was used for calculating genetic parameters, as well as the matrix of (co) variances of random regression coefficients.



Table 1 shows the goodness of fit criteria of the used models, having the multi-trait model the best fit, which is caused by the highest number of observations used in it. Within the reaction norm, there are few differences but the best fit was obtained for the Legendre polynomial of third degree.

Heritability estimates (h2), according to the multi-trait model, were 0.20 ± 0.02 and 0.28 ± 0.02 for TDG and P18 respectively, with a genetic correlation of 0.9413 among them, which indicates that both characters are determined by the same group of genes. Therefore, it can be selected by any of them with similar results for the genetic progress of population.

Genetic tendencies for P18 (y = 0.404x+0.051, with R² = 0.903) and TDG (y = 0.404x + 0.051, with R² = 0.903) show a slight growth through the years for the studied traits, which indicates a low genetic progress for these traits, adding the increased generational intervals of current animal husbandry.

Using the norm reaction model, the highest h2 estimates were obtained in the favorable environmental extreme (figure 1). Points of minimum heritability were in the negative region of the environmental gradient (between -130 and -30), following the tendency of higher genetic variances in the positive environments. This result was obtained according to the literature for regression models with first degree polynomials (Fikse et al. 2003). However, it is different from that described by Pegolo  (2009) for Nellore cattle in Brazil, using a similar methodology. This author found that the way of calculating environmental descriptors influenced on the estimation of genetic parameters of the analyzed population, being the models with cubic polynomials able to identify heterogeneity details among the environments, mainly the unfavorable ones.

In a previous study, Rodríguez et al. (2014) analyzed a similar model for final weight in this same genotype and using, as gradient, the standard mean of gain in the corresponding groups of contemporaries, considering the gradient as 18 and 8 environmental classes. In this case, the authors obtained a different performance, where the lowest values of h2 were represented in the mean gradients.

Table 1 also shows that most of genetic correlations among the different environmental classes were positive and had values very close to 1. The possible explanation (Falconer and Mackay 1996) is that this trait may be partially controlled by the same group of genes in each environment, and, therefore, the genetic merit is similar for all the environmental subclasses. However, it is important to highlight that the most negative extreme (class 1), taking into account the error values, could show correlations lower than 0.8, which indicates that sires selected in favorable environments may not have a similar performance in these unfavorable environments (negative gradients).  

It is possible to carry out a process of selection by P18 or TDG in Cuban Zebu, regarding the values of obtained heritabilities, with a better fit for the multi-trait model, counting on a higher number of observations and without the restrictions of the reaction model.

This study did not show an environmental awareness among the mean and positive gradients. However, among the negative extremes and the rest, it should be considered with caution because it showed significant values.



Corrêa, M. B. B., Dionello, N. J. L. & Cardoso, F. F. 2009. “Caracterização da interação genótipo-ambiente e comparação entre modelos para ajuste do ganho pós-desmama de bovinos Devon via normas de reação”. Revista Brasileira de Zootecnia, 38 (8): 1468–1477.

Falconer, D. S. & Mackay, T. F. C. 1996. Introduction to Quantitative Genetics. Essex, England: Longman Group Ltd, 464 p.

Fikse, W. F., Rekaya, R. & Weigel, K. A. 2003. “Assessment of environmental descriptors for studying genotype by environment interaction”. Livestock production science, 82 (2): 223–231.

Meyer, K. 2006. “‘WOMBAT’ – Digging deep for quantitative genetic analyses by restricted maximum likelihood”. In: World Congress on genetic applied to Livestock Production, Belo Horizonte, p. 8.

Pegolo, N. T. 2009. Interação genótipo-ambiente e sensibilidade ambiental em bovinos de corte. Ph.D. Thesis, Departamento de Genética. Faculdade de Medicina de Ribeirão Preto. Universidade de São Paulo, Brasil.

Rodríguez, Y., Ponce de León, R., Tamassia, N. & Nunes, H. 2014. “Influences of environmental descriptor for detect genotype by environmental interaction in Cuban Zebu population”. In: Proceedings, 10th World Congress of Genetics Applied to Livestock Production, Canada.



Received: November 24, 2015
Accepted: January 10, 2016



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

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