Analysis of longitudinal data of beef cattle raised on pasture from northern Brazil using nonlinear models

Relationships between body- and udder-related type traits with somatic cell counts and potential use for an early selection method for water buffaloes (Bubalus bubalis)

Water buffalo milk is a reliable source of high-quality nutrients; however, the susceptibility of mastitis in buffaloes must be taken into consideration. An animal with somatic cell count (SCC) of greater than 250,000 cells/mL is reported to be likely to have mastitis which has serious adverse effects on animal health, reproduction, milk yield, and milk quality. Type traits (TTs) of water buffalo can affect SCC in animal milk to some extent, but few reports on the correlation between SCC and TTs are available. In this study, a total of 1908 records collected from 678 water buffaloes were investigated. The general linear model was used to identify factors associated with phenotypic variation of the somatic cell score (SCS) trait, including parity, lactation length, calving year, and calving season as fixed effects. Using PROC CORR analysis method, taking calving year and lactation length as covariates, the correlation co-efficient between TT and SCS was obtained. Our results showed that correlation co-efficients between the 45 TTs with SCS ranged from 0.003 to 0.443 (degree of correlation). The correlation between udder traits and SCS was greater than that between body structure traits and SCS. Among udder traits, distance between teats (including front and rear teat distance [r = 0.308], front teat distance [r = 0.211], and teat crossing distance [r = 0.412]) and teat circumference (r = 0.443) had the highest correlation with SCS, followed by the leg traits including rear leg height (r = -0.354) and hock bend angle (r = -0.170). Animal with high rear legs (>48 cm) and short teat crossing distance (<17 cm), and narrow teat circumference (<11 cm) exhibited low SCS. Using four nonlinear models (Von Bertalanffy, Brody, Logistic, and Gompertz), the optimal growth curves of the TTs highly correlated with the SCS (rear leg height and teat crossing distance) were fitted, and the correction co-efficients of these two TTs rear leg height and teat crossing distance of animal from young age (2 mo old) to first lactation (35 mo old) were attained for establishment of early selection method for water buffaloes with low SCS. This study provides theoretical support for early selection of low-SCS water buffaloes and lays a foundation for improving milk quality and promoting healthy development of water buffalo's dairy industry.

Fit and genetic parameters of the growth curve of Polled Nellore cattle

ABSTRACT This study was undertaken to compare different non-linear models for fitting growth curves of Polled Nellore animals as well as to estimate genetic parameters for the components of the growth curve. The study involved body weight-age data of 6,717 Polled Nellore cattle from birth to 650 days of age, which belonged to the Brazilian Association of Zebu Breeders (ABCZ), corresponding to the period from 1980 to 2011. Four non-linear models (Brody, Bertalanffy, Logistic, and Gompertz) were fitted and compared by the adjusted coefficient of determination (R2adj), mean absolute deviation of residuals (MAD), root mean square error (RMSE), Akaike information criterion (AIC), and Bayesian information criterion (BIC). To estimate the genetic parameters and genetic values of asymptotic weight (A), integration constant (B), and maturation rate (K), the Bayesian inference method was adopted. The Brody model showed the lowest values of MAD, RMSE, AIC, and BIC and the highest R2adj. Heritability estimates for parameters A, B, and K were 0.11, 0.16, and 0.30, respectively, whereas genetic correlations were 0.01 (A-B), -0.91 (A-K), and 0.24 (B-K). The Brody model provided the best fit. The K parameter shows enough genetic variability for selection in the herd. Heavier animals in adulthood tend to exhibit lower growth rates. Despite the low heritability estimate of parameter A, there were genetic gains, indicating that selection is being efficient on asymptotic weight.

Comparison on accuracy of different nonlinear models in predicting growth of Podolica bulls

Animal growth does not follow a linear pattern, being explained mathematically by functions that have parameters with biological meaning. These parameters are used to estimate the expected weight of animals at specific ages. Several nonlinear models have been used to describe growth. This study was carried out to estimate the parameters of logistic, Gompertz, Richards and von Bertalanffy growth curve models in a sample of Podolica young bulls to determine the goodness of fit. Animals were weighed every 3 months from birth to 810 days of age. The results indicate that all the growth models used were easily fitted to the observed data with Gompertz and logistic functions presenting less computational difficulty in terms of number of iterations to achieve convergence. Moreover, logistic and Richards equations provided the best overall fit being useful to describe the growth of Podolica bulls. Considering that the literature lacks information on growth curves in Podolica breed, the study of a mathematical model for growth describing the developmental pattern of a specific population within a peculiar environment is a useful tool to improve Podolica breed production.

Growth Pattern for Body Weight, Height at Withers and Body Length of Kalahari Red Goats

The objective of this research was to examine the growth pattern for body weight, body length and height at withers of Kalahari Red goats using non-linear models. The body size measurement data were collected from 227 Kalahari Red female goats and fit into Gompertz and Brody growth model. The results revealed that Gompertz growth model had the best goodness of fit to describe the growth of Kalahari Red goats for body weight, body length and height at withers as shown by higher coefficient of determination (97.9, 98.9 and 99.1, respectively). The correlation coefficients between A and k for body weight, body length and height at withers were negative in both models, implying that goats of larger mature size tended to have a slower growth rate in relation to their mature size. Height at withers-body weight has the highest correlation coefficient (0.96).

Growth pattern for body weight, hip height and body length of Brakmas cattle

The objective of this study was to determine the growth pattern for body weight, hip height and body length using non-linear model and the correlation between the parameters in Brakmas cows. Cross-sectional data of body weight, hip height and body length of 363 heads of Brakmas cows were collected to determine the growth pattern using Brody and Gompertz growth model. The results showed that Gompertz growth function had the best goodness of fit to describe the growth of Brakmas cattle for body weight, hip height and body length as shown by its high coefficient of determination (0.96, 0.99 and 0.99, respectively). Brody model estimated higher mature sizes compared to Gompertz model as the rate of maturing derived by Brody model are lower for the parameters as shown by negative correlation between mature size and maturing. Body length-body weight has the highest correlation coefficient (0.95) and hip height-body weight showed the lowest relationship (0.92).