Bayesian analysis of energy balance data from growing cattle using parametric and non-parametric modelling

Abstract

Abstract. Linear and non-linear models have been extensively utilised for the estimation of net and metabolisable energy requirements and for the estimation of the efficiencies of utilising dietary energy for maintenance and tissue gain. In growing animals, biological principles imply that energy retention rate is non-linearly related to the energy intake level because successive increments in energy intake above maintenance result in diminishing returns for tissue energy accretion. Heat production in growing cattle has been traditionally described by logarithmic regression and exponential models. The objective of the present study was to develop Bayesian models of energy retention and heat production in growing cattle using parametric and non-parametric techniques. Parametric models were used to represent models traditionally employed to describe energy use in growing steers and heifers whereas the non-parametric approach was introduced to describe energy utilisation while accounting for non-linearities without specifying a particular functional form. The Bayesian framework was used to incorporate prior knowledge of bioenergetics on tissue retention and heat production and to estimate net and metabolisable energy requirements (NE M and ME M , respectively), and the partial efficiencies of utilising dietary metabolisable energy for maintenance (k m ) and tissue energy gain (k g ). The database used for the study consisted of 719 records of indirect calorimetry on steers and non-pregnant, non-lactating heifers. The NE M was substantially larger in energy retention models (ranged from 0.40 to 0.50 MJ/kg BW 0.75 .day) than were NE M estimates from heat-production models (ranged from 0.29 to 0.49 MJ/kg BW 0.75 .day). Similarly, k m was also larger in energy retention models than in heat production models. These differences are explained by the nature of y-intercepts (NE M ) in these two models. Energy retention models estimate fasting catabolism as the y-intercept, while heat production models estimate fasting heat production. Conversely, ME M was virtually identical in all models and approximately equal to 0.53 MJ/kg BW 0.75 .day in this database.

Energetic efficiency and the first law: the California net energy system revisited

“…A k m > 1.00 means something is gotten for nothing and is necessarily prohibited by the first law. Estimates of k m reported by Baldwin (1995) and Moraes et al (2014) are similar to HE from bond breakage, such as glycogen → glucose, and may only partially represent metabolic processes associated with maintenance. Old and Garrett (1987) described the relationship between RE and MEI as a quadratic function; estimates of ME m were 0.0953 Mcal ME/ BW 0.750 × d −1 (Hereford steers) and 0.100 Mcal ME/BW 0.750 × d −1 (Charolais steers).…”

“…For cattle consuming ME such that RE < 0, sources of energy contributing to the total energy economy of the animal are not exclusively ME; for RE > 0 there is a blend of metabolic processes. Baldwin (1995) described k m as ~0.90; Moraes et al, (2014), in a Bayesian framework, used an informed prior, k m = 0.94, similar to that described by Baldwin (1995) and reported a CrI that included 1.0; Moraes et al, (2014) also reported efficiencies greater than 1.0 (CrI = 0.76 to 1.13). Baldwin (1995) and Moraes et al (2014) estimates of k m differ greatly from the efficiency of ATP synthesis.…”

“…Baldwin (1995) described k m as ~0.90; Moraes et al, (2014), in a Bayesian framework, used an informed prior, k m = 0.94, similar to that described by Baldwin (1995) and reported a CrI that included 1.0; Moraes et al, (2014) also reported efficiencies greater than 1.0 (CrI = 0.76 to 1.13). Baldwin (1995) and Moraes et al (2014) estimates of k m differ greatly from the efficiency of ATP synthesis. If work is performed by a system, the change in energy (ΔE) is equal to heat (q) minus work (w).…”

“…If work is performed by a system, the change in energy (ΔE) is equal to heat (q) minus work (w). In the system described by Moraes et al (2014), for k m not different from 1.0, q and w = 0; a state of equilibrium exists. Efficiencies greater than 1.0 are inconsistent with the first law of thermodynamics, which states that you can't get something for nothing.…”

A glimpse of the future in animal nutrition science. 2. Current and future solutions

“…In their analysis, the inclusion of the molecular breeding value of ribeye area increased by 13% the precision to predict body weight at 28% empty body fat. Despite the development of new concepts for nutrition modeling, revisions of relationships established a long time ago are still needed for three reasons: collection of new data and incorporation with old data (Ellis et al, 2014;Galyean and Tedeschi, 2014); data used to develop past relationships were deemed deficient and/or were based on assumptions that do not hold anymore (Galyean et al, 2016); or more advanced mathematical and/or statistical analyses have been proposed (Moraes et al, 2014a;Moraes et al, 2014b).…”