A meta-analysis investigation based on literature data was conducted to estimate the effect size of nutritional and animal factors on phosphorus (P) excretion in feces and concentrations of P in milk. Two data sets were created for statistical analysis: One to derive prediction equations for P in feces (25 studies; 130 treatments) and another for P in milk (19 studies; 94 treatments). Prediction equations were derived using mixed model regression analysis with a random effect for study, and equations were evaluated based on values for Bayesian information criterion (BIC), root mean square prediction error (RMSPE), and concordance correlation coefficient (CCC) statistics. In terms of RMSPE and CCC values, fecal P excretion was best predicted by P intake, where P in feces (g/d)=-3.8(±3.45) + 0.64(±0.038) × P intake (g/d) (RMSPE: 18.3%, CCC: 0.869). However, significant effects of crude protein [g/kg of dry matter (DM)], neutral detergent fiber (g/kg of DM), and milk yield (kg/d) on fecal P excretion were also found. Despite a lack of improvement in terms of RMSPE and CCC values, these parameters may still explain part of the variation in fecal P excretion. For milk P, expressed as a fraction of P intake, the following equation had the highest CCC and the lowest RMSPE value: P in milk as a fraction of P intake (g/g)=0.42(±0.065) + 0.23(±0.018) × feed efficiency (i.e., fat- and protein-corrected milk yield/dry matter intake) - 0.11(±0.0199) × P in feed (g/kg of DM) (RMSPE: 19.7%; CCC: 0.761). Equations derived to predict fecal P as a fraction of P intake (g/g) or milk P content (g/kg) could not adequately explain the observed variation and did not perform well in terms of RMSPE and CCC values. Examination of the residuals showed that P balance was a seemingly confounding factor in some of the models. The results presented here can be used to estimate P in feces and milk based on commonly measured dietary and milk variables, but could also be used to guide development of mechanistic models on P metabolism in lactating dairy cattle. Factors to consider in future research and modeling efforts regarding efficiency of P use include the effects of dietary neutral detergent fiber, crude protein, starch, variation in P content of milk, and effects of P resorption from bone and body tissues during early lactation.

The purpose of this study was to evaluate prediction of methane emissions from finishing beef cattle using an extant mechanistic model with pH-independent or pH-dependent volatile fatty acid (VFA) stoichiometries, a recent stoichiometry adjustment for the use of monensin, and adaptation of the underlying model structure, to see if prediction improvements could be made for beef cattle. The database used for independent evaluation of methane predictions consisted of 74 animal means from six studies. For the "Bannink" stoichiometries, pH-dependence of stoichiometry improved the root mean square prediction error (RMSPE) statistic (38.8 to 36.6%) but the concordance correlation coefficient (CCC) statistic was reduced (0.509 to 0.469). Inclusion of monensin in the stoichiometry improved both pH-independent and pH-dependent predictions. For the "Murphy" stoichiometries, pH-dependence worsened the RMSPE (31.2 to 33.7%) as well as the CCC (0.611 to 0.465) statistic. Inclusion of monensin in the stoichiometry improved predictions with the pH-independent but not with the pH-dependent stoichiometry. Results indicate that although improvements have been made to the mechanistic model, further improvement in the representation of VFA stoichiometry, and likely the representation and prediction of pH and neutral detergent fiber digestibility, are required for more accurate prediction of methane emissions for finishing beef cattle. However, inclusion of an adjustment for monensin feeding generally lead to improved methane predictions.

We demonstrate, to our knowledge, the first bright circularly polarized high-harmonic beams in the soft X-ray region of the electromagnetic spectrum, and use them to implement X-ray magnetic circular dichroism measurements in a tabletop-scale setup. Using counterrotating circularly polarized laser fields at 1.3 and 0.79 μm, we generate circularly polarized harmonics with photon energies exceeding160 eV. The harmonic spectra emerge as a sequence of closely spaced pairs of left and right circularly polarized peaks, with energies determined by conservation of energy and spin angular momentum. We explain the single-atom and macroscopic physics by identifying the dominant electron quantum trajectories and optimal phasematching conditions. The first advanced phase-matched propagation simulations for circularly polarized harmonics reveal the influence of the finite phase-matching temporal window on the spectrum, as well as the unique polarization-shaped attosecond pulse train. Finally, we use, to our knowledge, the first tabletop X-ray magnetic circular dichroism measurements at the N4,5 absorption edges of Gd to validate the high degree of circularity, brightness, and stability of this light source. These results demonstrate the feasibility of manipulating the polarization, spectrum, and temporal shape of high harmonics in the soft X-ray region by manipulating the driving laser waveform.