An Illustrative Analysis of Atypical Gas Production Profiles Obtained from In Vitro Digestibility Studies Using Fecal Inoculum

Gas production profiles typically show a monotonically increasing monophasic pattern. However, atypical gas production profiles exist whereby at least two consecutive phases of gas production or additional extraneous features that distort the typical profile are present. Such profiles are more likely to occur with the use of a fecal inoculum and are much less well described. The presence of multiple phases or non-descript extraneous features makes it difficult to apply directly recommended modeling approaches such as standard response functions or classical growth functions. To overcome such difficulties, extensions of the Mitscherlich equation and a numerical modeling option also based on the Mitscherlich are explored. The numerical modeling option uses an estimate of relative rate obtained from the smoothed data profile and an estimate of maximum gas produced together with any lag time information drawn from the raw data to construct a simple Mitscherlich equation. In summary, this article illustrates the analysis of atypical gas production profiles obtained using a fecal inoculum and explores the methodology of numerical modeling to reconstruct equivalent typical growth-like trends.

Models Based on the Mitscherlich Equation for Describing Typical and Atypical Gas Production Profiles Obtained from In Vitro Digestibility Studies Using Equine Faecal Inoculum

Two models are proposed to describe atypical biphasic gas production profiles obtained from in vitro digestibility studies. The models are extensions of the standard Mitscherlich equation, comprising either two Mitscherlich terms or one Mitscherlich and one linear term. Two models that describe typical monophasic gas production curves, the standard Mitscherlich and the France model [a generalised Mitscherlich (root-t) equation], were assessed for comparison. Models were fitted to 25 gas production profiles resulting from incubating feedstuffs with faecal inocula from equines. Seventeen profiles displayed atypical biphasic patterns while the other eight displayed typical monophasic patterns. Models were evaluated using statistical measures of goodness-of-fit and by analysis of residuals. Good agreement was found between observed atypical profiles values and fitted values obtained with the two biphasic models, and both can revert to a simple Mitscherlich allowing them to describe typical monophasic profiles. The models contain kinetic fermentation parameters that can be used in conjunction with substrate degradability information and digesta passage rate to calculate extent of substrate degradation in the rumen or hindgut. Thus, models link the in vitro gas production technique to nutrient supply in the animal by providing information relating to digestion and nutritive value of feedstuffs.

Influence of silvicultural properties of sod-podzolic soils of the green zone of the Bryansk region settlements on the growth of pine species

Confinement of plants to typological landscapes groups is shown, predominant soil types and dominant forest are presented. In steady-state conditions by standard methods the basic physical and chemical properties of soil are defined. Mitscherlich equation defined average growth of model trees in the first 30 years of life on test plots. The estimation of connection of average growth to soil rates by stepwise regression method was made, which is used to determine the influence of soil conditions on the growth of pine species. Based on this analysis, a table was made to show demands of the studied pine species for physical and chemical parameters of the upper soil layer.

An attempt at describing the growth of live organisms by means of a difference-differential equation

An attempt is made to create a formal growth model based on a difference-differential equation. The solution of this type of equation is a function of a continuous variable and of a variable assuming natural values. By using the Laplace transformation in respect to time and then solving a specific linear difference equation, a final relation showing the dependence of the amount of dry matter on a natural number and time -- w_n(t), was obtained. This function can be, in a certain sense, a generalization of the known Gregory-Naidenov monomolecular function. For n=1 the function w_n(t) transforms into a relation similar to the Mitscherlich equation, for n>1, its graphs have a characteristic sigmoid shape. Numerical methods are necessary to work out specific forms of the function w_n(t).

Biosolids effectiveness to yield ryegrass based on their nitrogen content

Biosolids have been reported to increase yields and supply plant nutrients. However, complying with health and environmental standards is necessary before applying biosolids to land. Thus, sludge stabilization is required to make biosolids safe enough for their agricultural use. Side effects of stabilization processes on agronomic features of sewage sludge are not quite known, although their understanding is essential for biosolids management. Based on a model equivalent to the Mitscherlich equation, effects of the most common processes for sludge stabilization were evaluated (composting, liming, heat-drying and solar irradiation) in relation to the agronomic effectiveness of biosolids to yield Lolium perenne L. on two tropical soils, with NH4H2PO4 as a reference. Sewage stabilization processes have affected the ability of biosolids to promote plant growth. Their effectiveness was usually higher than fertilizer in a Spodosol and lower in an Oxisol. Solar-irradiated sludge presented the highest effectiveness among the biosolids and reached peak yields at the lowest application rate independent on soil type. Biosolids could efficiently substitute fertilizers and even yield more plant dry matter than the NH4H2PO4 reference, depending on the biosolid and soil type.

The Mitscherlich equation: an alternative to linear models of methane emissions from cattle

Previous attempts to apply statistical models, which correlate nutrient intake with methane production, have been of limited value where predictions are obtained for nutrient intakes and diet types outside those used in model construction. Dynamic mechanistic models have proved more suitable for extrapolation, but they remain computationally expensive and are not applied easily in practical situations. The first objective of this research focussed on employing conventional techniques to generate statistical models of methane production appropriate to UK dairy systems. The second objective was to evaluate these models and a model published previously using both UK and North American datasets. Thirdly, non-linear models were considered as alternatives to the conventional linear regressions. The UK calorimetry data used to construct the linear models were also used to develop the three non-linear alternatives that were all of modified Mitscherlich (monomolecular) form.