Genetic and environmental variation in methane emissions of sheep at pasture

A total of 2,600 methane (CH4) and 1,847 CO2 measurements of sheep housed for 1 h in portable accumulation chambers (PAC) were recorded at 5 sites from the Australian Sheep CRC Information Nucleus, which was set up to test leading young industry sires for an extensive range of current and novel production traits. The final validated dataset had 2,455 methane records from 2,279 animals, which were the progeny of 187 sires and 1,653 dams with 7,690 animals in the pedigree file. The protocol involved rounding up animals from pasture into a holding paddock before the first measurement on each day and then measuring in groups of up to 16 sheep over the course of the day. Methane emissions declined linearly (with different slopes for each site) with time since the sheep were drafted into the holding area. After log transformation, estimated repeatability (rpt) and heritability (h(2)) of liveweight-adjusted CH4 emissions averaged 25% and 11.7%, respectively, for a single 1-h measurement. Sire × site interactions were small and nonsignificant. Correlations between EBV for methane emissions and Sheep Genetics Australia EBV for production traits were used as approximations to genetic correlations. Apart from small positive correlations with weaning and yearling weights (r = 0.21-0.25, P < 0.05), there were no significant relationships between production trait and methane EBV (calculated from a model adjusting for liveweight by fitting separate slopes for each site). To improve accuracy, future protocols should use the mean of 2 (rpt = 39%, h(2) = 18.6%) or 3 (rpt = 48%, h(2) = 23.2%) PAC measurements. Repeat tests under different pasture conditions and time of year should also be considered, as well as protocols measuring animals directly off pasture instead of rounding them up in the morning. Reducing the time in the PAC from 1 h to 40 min would have a relatively small effect on overall accuracy and partly offset the additional time needed for more tests per animal. Field testing in PAC has the potential to provide accurate comparisons of animal and site methane emissions, with potentially lower cost/increased accuracy compared to alternatives such as SF6 tracers or open path lasers. If similar results are obtained from tests with different protocols/seasonal conditions, use of PAC measurements in a multitrait selection index with production traits could potentially reduce methane emissions from Australian sheep for the same production level

Numerical Analysis of Re-Uniform Convergence for Boundary Layer Equations for a Flat Plate

In this article we consider grid approximations of a boundary value problem for boundary layer equations for a flat plate outside of a neighbourhood of its leading edge. The perturbation parameter &quot; = Re multiplying the highest derivative can take arbitrary values from the half-interval (0; 1]; here Re is the Reynolds number. We consider the case when the solution of this problem is self-similar. For this Prandtl problem by using piecewise uniform meshes, which are refined in the neighbourhood of a parabolic boundary layer, we construct a finite difference scheme that converges &quot;--uniformly. We present the technique for experimental substantiation of &quot;--uniform convergence of both the grid solution itself and its normalized difference derivatives, which are considered outside of a neighbourhood of the leading edge of the plate. We study also the applicability of fitted operator methods for the numerical approximation of the Prandtl problem. It is shown that the use of meshes condensing in the parabolic boundary layer region is necessary for achieving &quot;--uniform convergence

Numerical Analysis of Re-Uniform Convergence for Boundary Layer Equations for a Flat Plate

. In this article we consider grid approximations of a boundary value problem for boundary layer equations for a flat plate outside of a neighbourhood of its leading edge. The perturbation parameter &quot; = Re \Gamma1 multiplying the highest derivative can take arbitrary values from the half-interval (0; 1]; here Re is the Reynolds number. We consider the case when the solution of this problem is self-similar. For this Prandtl problem by using piecewise uniform meshes, which are refined in the neighbourhood of a parabolic boundary layer, we construct a finite difference scheme that converges &quot;--uniformly. We present the technique for experimental substantiation of &quot;--uniform convergence of both the grid solution itself and its normalized difference derivatives, which are considered outside of a neighbourhood of the leading edge of the plate. We study also the applicability of fitted operator methods for the numerical approximation of the Prandtl problem. It is shown that the use of meshe..

The epsilon-Uniform Convergence of the Discrete Derivatives for Singularly Perturbed Problems

. The derivatives of the solution of singularly perturbed differential equations become unbounded as the singular perturbation parameter &quot; tends to zero. Therefore to approximate such derivatives, it is required to scale the derivatives in such a way that they are of order one for all values of the perturbation parameter. In practice, derivatives are related to the flux or drag and, hence, it is desirable to have &quot;-- uniform approximations to the scaled derivatives. In this paper, singularly perturbed convection--diffusion problems are considered. The use of standard scaled discrete derivatives to approximate the scaled continuous derivatives of the solution of singularly perturbed problems is examined. Standard scaled discrete derivatives generated from exact numerical methods on a uniform mesh are shown to be not &quot;--uniformly convergent. On the other hand, standard scaled discrete derivatives computed from a numerical method based on an appropriately fitted piecewise--uniform mesh ..

A Technique for Computing Realistic Values of the Error Parameters for the Numerical Solutions of Singular Perturbation Problems

. In this paper we describe an experimental technique to determine approximate values of the error parameters associated with a parameter--uniform numerical method for solving singularly perturbed convection--diffusion problems. We employ the technique to compute realistic values of these parameters for the numerical solutions generated by a monotone parameter--uniform numerical method applied to an elliptic boundary value problem with different types of boundary layers such as regular, parabolic and corner layers. Such error parameters allow us effectively to evaluate actual error bounds for the numerical solutions and to determine the parameter-uniformity of new numerical methods and, therefore, their applicability in practice. 1 Introduction The numerical solution of a singularly perturbed problem and its actual maximum pointwise error depend on the singular perturbation parameter &quot; and the number N of mesh points in each coordinate direction of the discrete problem. A standard cri..