On the analysis of Canadian Holstein dairy cow lactation curves using standard growth functions
López, S. ; France, J. ; Odongo, N.E. ; McBride, R.A. ; Kebreab, E. ; Alzahal, O. ; McBride, B.W. ; Dijkstra, J. - \ 2015
Journal of Dairy Science 98 (2015)4. - ISSN 0022-0302 - p. 2701 - 2712.
milk-yield - extended lactations - mathematical-models - cattle - persistency - records - management - shapes
Six classical growth functions (monomolecular, Schumacher, Gompertz, logistic, Richards, and Morgan) were fitted to individual and average (by parity) cumulative milk production curves of Canadian Holstein dairy cows. The data analyzed consisted of approximately 91,000 daily milk yield records corresponding to 122 first, 99 second, and 92 third parity individual lactation curves. The functions were fitted using nonlinear regression procedures, and their performance was assessed using goodness-of-fit statistics (coefficient of determination, residual mean squares, Akaike information criterion, and the correlation and concordance coefficients between observed and adjusted milk yields at several days in milk). Overall, all the growth functions evaluated showed an acceptable fit to the cumulative milk production curves, with the Richards equation ranking first (smallest Akaike information criterion) followed by the Morgan equation. Differences among the functions in their goodness-of-fit were enlarged when fitted to average curves by parity, where the sigmoidal functions with a variable point of inflection (Richards and Morgan) outperformed the other 4 equations. All the functions provided satisfactory predictions of milk yield (calculated from the first derivative of the functions) at different lactation stages, from early to late lactation. The Richards and Morgan equations provided the most accurate estimates of peak yield and total milk production per 305-d lactation, whereas the least accurate estimates were obtained with the logistic equation. In conclusion, classical growth functions (especially sigmoidal functions with a variable point of inflection) proved to be feasible alternatives to fit cumulative milk production curves of dairy cows, resulting in suitable statistical performance and accurate estimates of lactation traits.
Analyzing metabolomics-based challenge tests
Vis, D.J. ; Westerhuis, J.A. ; Jacobs, D.M. ; Duynhoven, J.P.M. van; Wopereis, S. ; Ommen, B. van; Hendriks, M.M.W.B. ; Smilde, A.K. - \ 2015
Metabolomics 11 (2015)1. - ISSN 1573-3882 - p. 50 - 63.
glucose-tolerance test - insulin sensitivity - mathematical-models - component analysis - plasma metabolome - health - asca - reconstruction - phenotype - discovery
Challenge tests are used to assess the resilience of human beings to perturbations by analyzing responses to detect functional abnormalities. Well known examples are allergy tests and glucose tolerance tests. Increasingly, metabolomics analysis of blood or serum samples is used to analyze the biological response of the individual to these challenges. The information content of such metabolomics challenge test data involves both the disturbance and restoration of homeostasis on a metabolic level and is thus inherently different from the analysis of steady state data. It opens doors to study the variation of resilience between individuals beyond the classical biomarkers; preferably in terms of underlying biological processes. We review challenge tests in which metabolomics was used to analyze the biological response. Specifically, we describe strategies to perform statistical analyses on the responses and we will show some examples of these strategies applied to a postprandial challenge that was used to study a diet with anti-inflammatory properties. Finally we discuss open issues and give recommendation for further research.
Interpreting experimental data on egg production - applications of dynamic differential equations
France, J. ; Lopez, S. ; Kebreab, E. ; Dijkstra, J. - \ 2013
Poultry Science 92 (2013)9. - ISSN 0032-5791 - p. 2498 - 2508.
drosophila-melanogaster - gastrointestinal-tract - quantitative genetics - mathematical-models - phosphorus - calcium - absorption - fertility - algorithm
This contribution focuses on applying mathematical models based on systems of ordinary first-order differential equations to synthesize and interpret data from egg production experiments. Models based on linear systems of differential equations are contrasted with those based on nonlinear systems. Regression equations arising from analytical solutions to linear compartmental schemes are considered as candidate functions for describing egg production curves, together with aspects of parameter estimation. Extant candidate functions are reviewed, a role for growth functions such as the Gompertz equation suggested, and a function based on a simple new model outlined. Structurally, the new model comprises a single pool with an inflow and an outflow. Compartmental simulation models based on nonlinear systems of differential equations, and thus requiring numerical solution, are next discussed, and aspects of parameter estimation considered. This type of model is illustrated in relation to development and evaluation of a dynamic model of calcium and phosphorus flows in layers. The model consists of 8 state variables representing calcium and phosphorus pools in the crop, stomachs, plasma, and bone. The flow equations are described by Michaelis-Menten or mass action forms. Experiments that measure Ca and P uptake in layers fed different calcium concentrations during shell-forming days are used to evaluate the model. In addition to providing a useful management tool, such a simulation model also provides a means to evaluate feeding strategies aimed at reducing excretion of potential pollutants in poultry manure to the environment.
Evolution of blind beetles in isolated aquifers: a test of alternative modes of speciation
Leys, R. ; Nes, E.H. van; Watts, C.H. ; Cooper, S.J.B. ; Humphreys, W.F. ; Hogendoorn, K. - \ 2012
PLoS ONE 7 (2012)3. - ISSN 1932-6203 - 8 p.
subterranean diving beetles - mitochondrial-dna phylogeography - size-structured populations - sympatric speciation - western-australia - adaptive radiation - ecological speciation - mathematical-models - oceanic island - yilgarn region
Evidence is growing that not only allopatric but also sympatric speciation can be important in the evolution of species. Sympatric speciation has most convincingly been demonstrated in laboratory experiments with bacteria, but field-based evidence is limited to a few cases. The recently discovered plethora of subterranean diving beetle species in isolated aquifers in the arid interior of Australia offers a unique opportunity to evaluate alternative modes of speciation. This naturally replicated evolutionary experiment started 10-5 million years ago, when climate change forced the surface species to occupy geographically isolated subterranean aquifers. Using phylogenetic analysis, we determine the frequency of aquifers containing closely related sister species. By comparing observed frequencies with predictions from different statistical models, we show that it is very unlikely that the high number of sympatrically occurring sister species can be explained by a combination of allopatric evolution and repeated colonisations alone. Thus, diversification has occurred within the aquifers and likely involved sympatric, parapatric and/or microallopatric speciation
Some methodological and analytical considerations regarding application of the gas production technique
López, S. ; Dhanoa, M.S. ; Dijkstra, J. ; Bannink, A. ; Kebreab, E. ; France, J. - \ 2007
Animal Feed Science and Technology 135 (2007)1-2. - ISSN 0377-8401 - p. 139 - 156.
in-vitro digestibility - ruminant feeds - production profiles - chemical-composition - mathematical-models - degradation - extent - rumen - fermentation - kinetics
The in vitro gas production technique is used widely in animal nutrition for feed evaluation and to study the kinetics of microbial fermentation processes in the digestive tract. This technique is based on the assumption that gas produced in batch cultures inoculated with mixed microorganisms from ruminal or hindgut contents or faeces is directly related to the amount of substrate fermented. The technique relies on mathematical modelling to estimate the rate and extent of feed digestion from cumulative gas production profiles. Section 1 of this article deals with the application of gas laws to calculate the volume of gas produced from pressure measurements when batch cultures are incubated in gas-tight bottles. Calculation of the amount of a specific gas (methane) produced at a given incubation time from total gas production and composition is presented in Section 2. Then, the definition of specific rate of substrate degradation and that of gas production are considered. Next, a piecewise linear model based on the assumption that microbial growth and fermentation follows zero-order kinetics is derived and evaluated by comparison with other non-linear models with regard to goodness-of-fit of experimental data and estimation of rate and extent of degradation in the rumen of some feedstuffs. Finally, the possibility of using procedures to account for the inevitable cyclic trends in gas production profiles by data smoothing are discussed. All these considerations provide an insight into some of the mathematical and methodological aspects of the in vitro gas production technique and should contribute to facilitating the description and interpretation of experimental data.
Predicting the profile of nutrients available for absorption: from nutrient requirement to animal response and environmental impact
Dijkstra, J. ; Kebreab, E. ; Mills, J.A.N. ; Pellikaan, W.F. ; López, S. ; Bannink, A. ; France, J. - \ 2007
Animal 1 (2007)1. - ISSN 1751-7311 - p. 99 - 111.
lactating dairy-cows - microbial-growth - ruminal fermentation - mathematical-models - nitrogen fractions - continuous-culture - mechanistic model - net carbohydrate - passage kinetics - milk-production
Current feed evaluation systems for dairy cattle aim to match nutrient requirements with nutrient intake at pre-defined production levels. These systems were not developed to address, and are not suitable to predict, the responses to dietary changes in terms of production level and product composition, excretion of nutrients to the environment, and nutrition related disorders. The change from a requirement to a response system to meet the needs of various stakeholders requires prediction of the profile of absorbed nutrients and its subsequent utilisation for various purposes. This contribution examines the challenges to predicting the profile of nutrients available for absorption in dairy cattle and provides guidelines for further improved prediction with regard to animal production responses and environmental pollution. The profile of nutrients available for absorption comprises volatile fatty acids, long-chain fatty acids, amino acids and glucose. Thus the importance of processes in the reticulo-rumen is obvious. Much research into rumen fermentation is aimed at determination of substrate degradation rates. Quantitative knowledge on rates of passage of nutrients out of the rumen is rather limited compared with that on degradation rates, and thus should be an important theme in future research. Current systems largely ignore microbial metabolic variation, and extant mechanistic models of rumen fermentation give only limited attention to explicit representation of microbial metabolic activity. Recent molecular techniques indicate that knowledge on the presence and activity of various microbial species is far from complete. Such techniques may give a wealth of information, but to include such findings in systems predicting the nutrient profile requires close collaboration between molecular scientists and mathematical modellers on interpreting and evaluating quantitative data. Protozoal metabolism is of particular interest here given the paucity of quantitative data. Empirical models lack the biological basis necessary to evaluate mitigation strategies to reduce excretion of waste, including nitrogen, phosphorus and methane. Such models may have little predictive value when comparing various feeding strategies. Examples include the Intergovernmental Panel on Climate Change (IPCC) Tier II models to quantify methane emissions and current protein evaluation systems to evaluate low protein diets to reduce nitrogen losses to the environment. Nutrient based mechanistic models can address such issues. Since environmental issues generally attract more funding from governmental offices, further development of nutrient based models may well take place within an environmental framework
Rumen degradation characteristics of perennial ryegrass cultivars during the growing season
Tas, B.M. ; Taweel, H.Z. ; Smit, H.J. ; Elgersma, A. ; Dijkstra, J. ; Tamminga, S. - \ 2006
Animal Feed Science and Technology 131 (2006)1-2. - ISSN 0377-8401 - p. 102 - 119.
water-soluble carbohydrate - neutral detergent fiber - in-sacco degradation - grass lolium-perenne - dairy-cows - crude protein - intracellular constituents - chemical-composition - mathematical-models - animal nutrition
The objective of this experiment was to evaluate the effects of sward characteristics and chemical composition of eight diploid perennial ryegrass cultivars during the growing season on degradation characteristics in the rumen of dairy cows. As part of an indoor-feeding experiment with dairy cows, sward characteristics were measured, and samples of cultivars were collected on two consecutive days during seven periods throughout the summer. Cultivars did not differ (P>0.05) in sward characteristics. Two cultivars had higher concentrations of water-soluble carbohydrates (WSC, P25 g/kg DM) than among cultivars (
Development and validation of experimental protocols for use of cardinal models for prediction of microorganisms growth in food products
Pinon, A. ; Zwietering, M.H. ; Perrier, L. ; Membré, J.M. ; Leporq, B. ; Mettler, E. ; Thuault, D. ; Coroller, L. ; Stahl, V. ; Vialette, M. - \ 2004
Applied and Environmental Microbiology 70 (2004)2. - ISSN 0099-2240 - p. 1081 - 1087.
escherichia-coli o157-h7 - listeria-monocytogenes - sodium-chloride - water activity - brochothrix-thermosphacta - thermal inactivation - combined temperature - mathematical-models - storage-temperature - microbial-growth
An experimental protocol to validate secondary-model application to foods was suggested. Escherichia coli, Listeria monocytogenes, Bacillus cereus, Clostridium perfringens, and Salmonella were observed in various food categories, such as meat, dairy, egg, or seafood products. The secondary model validated in this study was based on the gamma concept, in which the environmental factors temperature, pH, and water activity (alpha(w)) were introduced as individual terms with microbe-dependent parameters, and the effect of foodstuffs on the growth rates of these species was described with a food- and microbe-dependent parameter. This food-oriented approach was carried out by challenge testing, generally at 15 and 10degreesC for L. monocytogenes, E. coli, B. cereus, and Salmonella and at 25 and 20degreesC for C. perfringens. About 222 kinetics in foods were generated. The results were compared to simulations generated by existing software, such as PMP. The bias factor was also calculated. The methodology to obtain a food-dependent parameter (fitting step) and therefore to compare results given by models with new independent data (validation step) is discussed in regard to its food safety application. The proposed methods were used within the French national program of predictive microbiology, Sym'Previus, to include challenge test results in the database and to obtain predictive models designed for microbial growth in food products.
Predictive modeling of migration from packaging materials into food products for regulatory purposes
Helmroth, I.E. ; Rijk, R. ; Dekker, M. ; Jongen, W.M.F. - \ 2002
Trends in Food Science and Technology 13 (2002)3. - ISSN 0924-2244 - p. 102 - 109.
polymer additive migration - worst-case migration - mathematical-models - free-volume - diffusion - polyethylene - polyolefins - temperature - partition - simulants
Migration of low-molecular weight compounds is one of the most important problems of packaging plastics and other plastics intended to come into contact with food products. Since migration experiments are time consuming and expensive, predictive modelling has been introduced as a promising alternative. The main objective of this article is to review current knowledge on migration modelling and highlight the consequences of using modelling for regulatory purposes.