The ontogenetic allometry of body morphology and chemical composition in dairy goat wethers

Abstract

We studied the ontogenetic growth of goat wethers (castrated male goats) of the Saanen and Swiss Alpine breeds based on a large range of intraspecific body mass (BM). The body parts and the chemical constituents of the empty body were described by the allometric function by using BM and the empty body mass (EBM) as the predictors for morphological traits and chemical composition, respectively. We fitted the allometric scaling function by applying the SAS NLMIXED procedure, but to evaluate assumptions regarding variances in morphological and compositional traits, we combined the scaling function with homoscedastic (MOD1), and the heteroscedastic exponential (MOD2) and power-of-the-mean (MOD3) variance functions. We also predicted the ontogenetic growth by using the traditional log-log transformation and back-transformed results into the arithmetic scale (MOD4). We obtained predictions from MOD4 in the arithmetic scale by a two-step process, and evaluated MOD1, MOD2 and MOD3 by a model selection framework, and compared MOD4 with MOD1, MOD2 and MOD3 based on goodness-of-fit measures. Based on information criteria for model selection, heterogeneous variance functions were more likely to describe 10 over 36 traits with a low level of model selection uncertainty. One trait was predicted by averaging the MOD1 and MOD2 variance functions; and nine traits were better described by averaging the MOD2 and MOD3 variance functions. The predictions for other 16 traits were averaged from MOD1, MOD2 and MOD3. However, MOD4 better described 11 traits according to the goodness-of-fit measures. Depending on the variable being analyzed, the body parts and the chemical amounts exhibited the three types of allometric behavior with respect to BM and EBM, that is, positive, negative and isometric ontogenetic growth. Reference BMs, that is, 20, 27, 35 and 45 kg, were used to compute the net protein and energy requirements based on the first derivative of the scaling function, and the results were presented in reference to the EBM and EBM0.75. Both the net protein and energy requirements scaled to EBM0.75 increased from 20 to 45 kg of BM.

The geometry of the lactation curve based on Wood's equation: a two-step prediction

“…In addition, the combined powers of equations 17 and 19 accounted for variations attributable to either scale and correlations among repeated measures (Tables 2 and 3). If not discounted, those variations can be understood as pseudorandom variations that otherwise would inflate the residual variation (Vieira et al, 2018). The nlme function of R accounts for all these issues and its main advantage is to integrate all information in a single variance-covariance matrix.…”

“…The AICc m and its derived measures constitute the I-T approach, which allows the comparison of the quality of fit of different models and, whenever necessary, establishes parameters for model averaging. If one takes the smallest AICc m value to choose a model over the others, does an incomplete procedure within the I-T framework (Burnham and Anderson, 2004;Vieira et al, 2018;. The smallest AICc m value indicates the lower information loss due to the fit of a given model among the feasible models evaluated.…”

“…However, if one assumes that a given model is the best solution and ignores the others, depending on the p m for the chosen model, its uncertainty can be large. This is why we assumed that a low uncertainty for a given model is 1 -p m < 0.10 ( Burnham and Anderson, 2004;Vieira et al, 2018).…”

“…The development of tools from theories of nonlinear mixed-effects models and generalized linear mixed-effects models (Pinheiro and Bates, 2000;Littell et al, 2006;Vonesh, 2012;Stroup, 2013) has provided instruments to describe several nonlinear phenomena in animal science (Zanton and Heinrichs, 2009;Strathe et al, 2010;Albertini et al, 2012;Araujo et al, 2015;Vieira et al, 2018Vieira et al, , 2020Rohem Júnior et al, 2020). The information-theoretic approach (I-T) provides the elements for evaluating the quality of fit of models by aiming at their predictive powers (Buckland et al, 1997;Sober, 2002;Burnham and Anderson, 2004;Burnham et al, 2011a).…”

Macromineral requirements for maintenance and growth in male and female hair sheep

“…The parameter σ refers to the standard deviation, and the term σ 2 refers to the random error variance; thus, Equation 7 represents the homogeneous variance with the assumption of homoscedasticity (25,26). In this case, the homogeneous (Equations 7 and 10), exponential (Equations 8, 11, 13, and 15), and Power-of-the-Means (Equations 9, 12, 14, and 16) variance functions were tested, as they are the most commonly used (27)(28)(29). An attempt to accommodate heteroscedasticity was performed with Equations 8 to 16.…”