Elsevier

Theriogenology

Volume 79, Issue 5, 15 March 2013, Pages 751-759
Theriogenology

Research article
Use of nonlinear models for describing scrotal circumference growth in Guzerat bulls raised under grazing conditions

https://doi.org/10.1016/j.theriogenology.2012.11.031Get rights and content

Abstract

The objective was to use various nonlinear models to describe scrotal circumference (SC) growth in Guzerat bulls on three farms in the state of Minas Gerais, Brazil. The nonlinear models were: Brody, Logistic, Gompertz, Richards, Von Bertalanffy, and Tanaka, where parameter A is the estimated testis size at maturity, B is the integration constant, k is a maturating index and, for the Richards and Tanaka models, m determines the inflection point. In Tanaka, A is an indefinite size of the testis, and B and k adjust the shape and inclination of the curve. A total of 7410 SC records were obtained every 3 months from 1034 bulls with ages varying between 2 and 69 months (<240 days of age = 159; 241–365 days = 451; 366–550 days = 1443; 551–730 days = 1705; and >731 days = 3652 SC measurements). Goodness of fit was evaluated by coefficients of determination (R2), error sum of squares, average prediction error (APE), and mean absolute deviation. The Richards model did not reach the convergence criterion. The R2 were similar for all models (0.68–0.69). The error sum of squares was lowest for the Tanaka model. All models fit the SC data poorly in the early and late periods. Logistic was the model which best estimated SC in the early phase (based on APE and mean absolute deviation). The Tanaka and Logistic models had the lowest APE between 300 and 1600 days of age. The Logistic model was chosen for analysis of the environmental influence on parameters A and k. Based on absolute growth rate, SC increased from 0.019 cm/d, peaking at 0.025 cm/d between 318 and 435 days of age. Farm, year, and season of birth significantly affected size of adult SC and SC growth rate. An increase in SC adult size (parameter A) was accompanied by decreased SC growth rate (parameter k). In conclusion, SC growth in Guzerat bulls was characterized by an accelerated growth phase, followed by decreased growth; this was best represented by the Logistic model. The inflection point occurred at approximately 376 days of age (mean SC of 17.9 cm). We inferred that early selection of testicular size might result in smaller testes at maturity.

Introduction

Scrotal circumference (SC) is frequently used in breeding programs, because of its easy measurement, high repeatability, and moderate to high heritability [1], [2], [3], [4]. In addition, SC is favorably associated with physical semen characteristics, age at puberty, sexual precocity, and weight gain [5], [6], [7], [8]. Furthermore, based on the genetic correlation between SC and reproductive characteristics in females, e.g., age at puberty, days to calving, and age at first calving, selection for SC had a positive influence on female reproductive performance [8], [9], [10], [11].

Zebu cattle are older at puberty and have delayed first calving (30–46 months) [12], [13]; these are attributed to genetic and environmental factors [14]. Bulls selected on the basis of larger SC and early puberty usually produce daughters reaching puberty at significantly earlier ages and greater percentages of heifers cycling early in the breeding season, even when used in crossbreeding [8], [10]. This is very important for cattle breeding in tropical countries, where delayed puberty and poor reproductive efficiency are major constraints limiting the cattle industry [15].

The SC at puberty is relatively constant among breeds and across bulls varying widely in age and weight at puberty; therefore, SC might be more useful than other characteristics for predicting age at puberty [1], [16], [17]. Scrotal circumference is more easily obtained than sperm production or behavioral measurements and should be useful in the selection of beef bulls for early sexual maturity [1].

Selection of bulls at the earliest possible age will not only improve reproduction, but also provide economic advantages by decreasing feeding and management costs and improve economic returns to producers [18]. However, Lunstra et al. [1] reported that male offspring of diverse heat-adapted sire breeds had lower postweaning testicular growth rates and were slower to reach puberty than offspring of European sire breeds. Therefore, there is a need for characterization of reproductive traits in bulls representing diverse beef breeds.

Furthermore, nutrition, breed, and environmental factors influence reproductive development and testicular size [19], [20]. Therefore, to achieve higher accuracy in assessing the reproductive capacity of bulls based on testicular measurements, comparisons should be made within the same age group, breed, bull stud, and year-season [21].

One way to describe testicular growth is using nonlinear regression models. The advantage of nonlinear models is that they can accommodate a large number of measurements in some parameters and, thus, permit appropriate biological interpretation. The benefit of these models in animal breeding is using these parameters to identify animals more suited for specific purposes [22]. Furthermore, a growth trait can be improved by using growth curves and their properties. In that regard, Kratochvílová, et al. [23] identified early and late maturing heifers during early phases of growth (6–9 months) using growth curve parameters of nonlinear models.

Given the growing interest in Zebu cattle because of their better adaptation than Bos taurus breeds to tropical conditions, and the need for producers to emphasize growth rate and early pubertal development in genetic improvement programs [17], the objective of this study was to evaluate six nonlinear models to describe SC development in Guzerat bulls and to evaluate environmental effects on growth curve parameters.

Section snippets

Bulls and scrotal circumference measurement

All procedures were approved by the ethics committee of Universidade Federal de Minas Gerais. This study was conducted on three farms located in Brasilândia de Minas (17°00′36″ South and 46°00′32″ West), Carlos Chagas (17°41′30″ South and 40°45′15″ West), and Unaí (16°21′43″ South and 46°54′09″ West), in the state of Minas Gerais, Brazil. The climate classification in this regions is Aw (tropical rainy climate, Köppen classification), with average temperature of 18° in the coldest month. The

Results

The Richards model did not reach the convergence criterion nor did it produce biologically interpretable parameters. For the Brody, Gompertz, Logistic, Von Bertalanffy, and Tanaka models, the values of the parameters estimated and standard error are shown (Table 2). Regarding parameter estimates, the Gompertz and Von Bertalanffy models had close values for SC at maturity (parameters A), and the Brody model estimated the highest value for A and the lowest value for the k parameter compared with

Discussion

The nonconvergence of the Richards model found in this study was also reported by others using this model to assess SC growth in sheep [25], goats [39], and cattle [26]. These results contrasted with those reported by Delgado et al. [40] and Jiménez-Severiano et al. [41] where the Richards model yielded good fit to the data for SC in Retinto bulls and Blackbelly ram lambs, respectively. Several authors warned about the difficulty of convergence of this model, because parameter m (the inflection

Acknowledgments

The authors thank Conselho Nacional de desenvolvimento Científico e Tecnológico (CNPq) for financial support, and Farm São Geraldo (Brasilândia), Farm Guzerá do Rosário (Carlos Chagas), and Farm Palestina (Unaí) for providing the opportunity and the facilities to collect data.

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