Mathematical modelling in animal nutrition: a centenary review

A centenary review presents an opportunity to ponder over the processes of concept development and give thought to future directions. The current review aims to ascertain the ontogeny of current concepts, underline the connection between ideas and people and pay tribute to those pioneers who have contributed significantly to modelling in animal nutrition. Firstly, the paper draws a brief portrait of the use of mathematics in agriculture and animal nutrition prior to 1925. Thereafter, attention turns towards the historical development of growth modelling, feed evaluation systems and animal response models. Introduction of the factorial and compartmental approaches into animal nutrition is noted along with the particular branches of mathematics encountered in various models. Furthermore, certain concepts, especially bioenergetics or the heat doctrine, are challenged and alternatives are reviewed. The current state of knowledge of animal nutrition modelling results mostly from the discernment and unceasing efforts of our predecessors rather than serendipitous discoveries. The current review may stimulate those who wish for greater understanding and appreciation

Evaluation of models to predict the stoichiometry of volatile fatty acid profiles in rumen fluid of lactating Holstein cows

Volatile fatty acids (VFA), produced in the rumen by microbial fermentation, are the main energy source for ruminants. The VFA profile, particularly the nonglucogenic (acetate, Ac; butyrate, Bu) to glucogenic (propionate, Pr) VFA ratio (NGR), is associated with effects on methane production, milk composition, and energy balance. The aim of this study was to evaluate extant rumen VFA stoichiometry models for their ability to predict in vivo VFA molar proportions. The models were evaluated using an independent data set consisting of 101 treatments from 24 peer-reviewed publications with lactating Holstein cows. All publications contained a full diet description, rumen pH, and rumen VFA molar proportions. Stoichiometric models were evaluated based on root mean squared prediction error (RMSPE) and concordance correlation coefficient (CCC) analysis. Of all models evaluated, the 1998 Friggens model had the lowest RMSPE for Ac and Bu (7.2 and 20.2% of observed mean, respectively). The 2006 Bannink model had the lowest RMSPE and highest CCC for Pr (14.4% and 0.70, respectively). The 2008 Bannink model had comparable predictive performance for Pr to that of the 2006 Bannink model but a larger error due to overall bias (26.2% of MSPE). The 1982 Murphy model provided the poorest prediction of Bu, with the highest RMSPE and lowest CCC (24.6% and 0.15, respectively). The 1988 Argyle and Baldwin model had the highest CCC for Ac with an intermediate RMSPE (0.47 and 8.0%, respectively). The 2006 Sveinbjörnsson model had the highest RMSPE (13.9 and 34.0%, respectively) and lowest CCC (0.31 and 0.40, respectively) for Ac and Pr. The NGR predictions had the lowest RMSPE and highest CCC in the 2 models of Bannink, whereas the lowest predictive performance was in the 2006 Sveinbjörnsson model. It appears that the type of VFA produced is not a simple linear relationship between substrate inputs and pH as currently represented. The analysis demonstrates that most rumen VFA stoichiometric approaches explain a large part of the variation in VFA molar proportions among diets, in particular for Ac, whereas predictive power for Pr and Bu differ largely among approaches. The move toward feed evaluation systems based on animal response might necessitate an improved representation of rumen fermentation, focused on improving our understanding of VFA proportions in diets that vary from the mean

Deep redshift topological lensing: strategies for the T^3 candidate

The 3-torus (T^3) FLRW model better fits the nearly zero large-scale auto-correlation of the WMAP CMB sky maps than the infinite flat model. The T^3 model's WMAP parameters imply approximately equal-redshift topological lensing at z \sim 6. We investigate observational strategies for rejecting the T^3 solution or providing candidate topologically lensed galaxy pairs. T^3 holonomies are applied to (i) existing z \sim 6 observations and (ii) simulated observations, creating multiply connected catalogues. Corresponding simply connected catalogues are generated. Each catalogue is analysed using a successive filter method and collecting matched quadruples. Quadruple statistics between the multiply and simply connected catalogues are compared. The expected rejection of the hypothesis, or detection of candidate topologically lensed galaxies, is possible at a significance of 5% for a pair of T^3 axis-centred northern and southern surveys if photometric redshift accuracy is \sigma(\zphot) < 0.01 for a pair of nearly complete 100 deg^2 surveys with a total of > 500 galaxies over 4.3 < z < 6.6, or for a pair of 196 deg^2 surveys with > 400 galaxies and \sigma(\zphot) < 0.02 over 4<z<7. Dropping the maximum time interval in a pair from \Delta t =1 Gyr/h to \Delta t =0.1 Gyr/h yields a requirement of \sigma(\zphot) < 0.005 or \sigma(\zphot) < 0.01, respectively. Millions of z \sim 6 galaxies will be observed over fields of these sizes during the coming decades, implying much stronger constraints. The question is not if the hypothesis will be rejected or confirmed, it is when.Comment: 13 pages, 9 figures, 5 tables, MNRAS, accepte

Modelling the lactation curve of dairy cows using the differentials of growth functions

Descriptions of entire lactations were investigated using six mathematical equations. comprising the differentials of four growth functions (logistic. Gompertz, Schumacher and Morgan) and two other equations (Wood and Dijkstra). The data contained monthly milk yield records from 70 first, 70 second and 75 third parity Iranian Holstein cows. Indicators of fit were model behavior, statistical evaluation and biologically meaningful parameter estimates and lactation features. Analysis of variance with equation, parity and their interaction as factors and with cows as replicates was performed to compare goodness of fit of the equations. The interaction of equation and parity was not significant for any statistics, which showed that there vas no tendency For one equation to fit a given parity better than other equations. Although model behaviour analysis showed better performance of growth functions than the Wood and Dijkstra equations in filling the individual lactation curves, statistical evaluation revealed that there was no significant difference between file goodness of fit of the different equations. Evaluation of lactation features showed that the Dijkstra equation was able to estimate the initial milk yield and peak yield more accurately than the other equations. Overall evaluation of the different equations demonstrated the potential of the differentials of simple empirical growth functions used in file Current study as equations for fitting monthly milk records of Holstein dairy cattle

A review of mathematical functions for the analysis of growth in poultry

Poultry industries face various decisions in the production cycle that affect the profitability of an operation. Predictions of growth when the birds are ready for sale are important factors that contribute to the economy of poultry operations. Mathematical functions called ‘growth functions’ have been used to relate body weight (W) to age or cumulative feed intake. These can also be used as response functions to predict daily energy and protein dietary requirements for maintenance and growth (France et al., 1989). When describing growth versus age in poultry, a fixed point of inflexion can be a limitation with equations such as the Gompertz and logistic. Inflexion points vary depending on age, sex, breed and type of animal, so equations such as the Richards and López are generally recommended. For describing retention rate against daily intake, which generally does not exhibit an inflexion point, the monomolecular would appear the function of choice

Diagnosis of Helicobacter pylori by carbon-13 urea breath test using a portable mass spectrometer

CONTEXT: In the non-invasive detection of markers of disease, mass spectrometry is able to detect small quantities of volatile markers in exhaled air. However, the problem of size, expense and immobility of conventional mass spectrometry equipment has restricted its use. Now, a smaller, less expensive, portable quadrupole mass spectrometer system has been developed. Helicobacter pylori has been implicated in the development of chronic gastritis, gastric and duodenal ulcers and gastric cancer. OBJECTIVES: To compare the results obtained from the presence of H. pylori by a carbon-13 urea test using a portable quadrupole mass spectrometer system with those from a fixed mass spectrometer in a hospital-based clinical trial. METHODS: Following ethical approval, 45 patients attending a gastroenterology clinic at the Royal Liverpool University Hospital exhaled a breath sample into a Tedlar gas sampling bag. They then drank an orange juice containing urea radiolabelled with carbon and 30 min later gave a second breath sample. The carbon-13 content of both samples was measured using both quadrupole mass spectrometer systems. If the post-drink level exceeded the pre-drink level by 3% or more, a positive diagnosis for the presence of H. pylori was made. RESULTS: The findings were compared to the results using conventional isotope ratio mass spectrometry using a laboratory-based magnetic sector instrument off-site. The results showed agreement in 39 of the 45 patients. CONCLUSIONS: This study suggests that a portable quadrupole mass spectrometer is a potential alternative to the conventional centralised testing equipment. Future development of the portable quadrupole mass spectrometer to reduce further its size and cost is indicated, together with further work to validate this new equipment and to enhance its use in mass spectrometry diagnosis of other medical conditions

Atmospheric nitrogen oxides (NO and NO2) at Dome C, East Antarctica, during the OPALE campaign

Mixing ratios of the atmospheric nitrogen oxides NO and NO2 were measured as part of the OPALE (Oxidant Production in Antarctic Lands & Export) campaign at Dome C, East Antarctica (75.1 degrees S, 123.3 degrees E, 3233 m), during December 2011 to January 2012. Profiles of NOx mixing ratios of the lower 100m of the atmosphere confirm that, in contrast to the South Pole, air chemistry at Dome C is strongly influenced by large diurnal cycles in solar irradiance and a sudden collapse of the atmospheric boundary layer in the early evening. Depth profiles of mixing ratios in firn air suggest that the upper snowpack at Dome C holds a significant reservoir of photolytically produced NO2 and is a sink of gas-phase ozone (O-3). First-time observations of bromine oxide (BrO) at Dome C show that mixing ratios of BrO near the ground are low, certainly less than 5 pptv, with higher levels in the free troposphere. Assuming steady state, observed mixing ratios of BrO and RO2 radicals are too low to explain the large NO2 : NO ratios found in ambient air, possibly indicating the existence of an unknown process contributing to the atmospheric chemistry of reactive nitrogen above the Antarctic Plateau. During 2011-2012, NOx mixing ratios and flux were larger than in 2009-2010, consistent with also larger surface O-3 mixing ratios resulting from increased net O-3 production. Large NOx mixing ratios at Dome C arise from a combination of continuous sunlight, shallow mixing height and significant NOx emissions by surface snow (F-NOx). During 23 December 2011-12 January 2012, median F-NOx was twice that during the same period in 20092010 due to significantly larger atmospheric turbulence and a slightly stronger snowpack source. A tripling of F-NOx in December 2011 was largely due to changes in snowpack source strength caused primarily by changes in NO3- concentrations in the snow skin layer, and only to a secondary order by decrease of total column O-3 and associated increase in NO3- photolysis rates. A source of uncertainty in model estimates of F-NOx is the quantum yield of NO3- photolysis in natural snow, which may change over time as the snow ages

High fidelity simulations of ion trajectories in miniature ion traps using the boundary-element method

In this paper we present numerical modeling results for endcap and linear ion traps, used for experiments at the National Physical Laboratory in the UK and Innsbruck University respectively. The secular frequencies for Strontium-88 and Calcium-40 ions were calculated from ion trajectories, simulated using boundary-element and finite-difference numerical methods. The results were compared against experimental measurements. Both numerical methods showed high accuracy with boundary-element method being more accurate. Such simulations can be useful tools for designing new traps and trap arrays. They can also be used for obtaining precise trapping parameters for desired ion control when no analytical approach is possible as well as for investigating the ion heating rates due to thermal electronic noise.Comment: 6 pages, 5 figures, changes made to the text according to the editor's and referee's comment