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Principles of Building a Mathematical Model for the Influence of Mineral Fertilizers on Grain Yield
The intensiveness of agricultural systems is given by the sum of the production factors provided per time unit and area. In this sense, fertilizers represent one of the factors with high variability in the intensification process. In agricultural practice, in order to maintain high yields, the fertilizers that are commonly applied contain either one or more macro elements (NPK). In the unifactorial model proposed in the paper, which starts from a Mitscherlich-type model, the constants were determined and then the concordance was checked between the experimental data and the theoretical data on a wheat crop. Afterwards, the optimum of the benefit was studied. Subsequently, using a function which generalizes empirically to two variables, good concordance was also found between the theoretical and experimental data. The optimum benefit was determined by employing the least squares method in calculating the constants. By hypothesis, the bifactorial model takes into consideration all three nutritive elements: nitrogen, phosphorus and potassium, but considers them as two independent variables, namely x for nitrogen and y for the phosphorus-potassium complex in equal proportions.
The present paper proposes a bifactorial model obtained by a generalization of the unifactorial Mitscherlich model. After analysing the graphic representation of the experimental data and the theoretical curves, one can conclude that they present good concordance. Treatments with nitrogen fertilizers within the limits of 0 – 200 kg a.i. ha-1 determined different optimum and maximum values for each of the four fertilization variants with phosphorus and potassium (optimum value 97 kg ha-1 N on P0K0 with yield increase of 1224 kg ha-1; optimum 107 kg ha-1 N on P50K50, with an increase of 952 kg ha-1; 111 kg ha-1 N on P100K100 with an increase of 968 kg ha-1 and 103 kg ha-1 N on P150K150 with an increase of 1413 kg ha-1). From an economical point of view, we will maximize the benefit corresponding to production value in the hypothesis that only one fertilizer is applied, namely a complex fertilizer of the type N15P15K15. For the actual price values q = 0.2 € ∙ Kg−1, p = 0.6€ kg−1 the solution of the equation above is x = 221 kg ℎa−1. © 2015, University of Zagreb - Faculty of Agriculture. All rights reserved.
Cited By (since 1996):2, Export Date: 18 October 2014
Patterns and variations in concentration of carbon-based secondary compounds in plant tissues have been explained by means of different complementary and, in some cases, contradictory plant defence hypotheses for more than 20 years. These hypotheses are conceptual models which consider environmental impacts on plant internal demands. In the present study, a mathematical model is presented, which converts and integrates the concepts of the 'Growth-Differentiation Balance' hypothesis and the 'Protein Competition' model into a dynamic plant growth model, that was tested with concentration data of polyphenols in leaves of juvenile apple, beech and spruce trees. The modelling approach is part of the plant growth model PLATHO that considers simultaneously different environmental impacts on the most important physiological processes of plants.
The modelling approach for plant internal resource allocation is based on a priority scheme assuming that growth processes have priority over allocation to secondary compounds and that growth-related metabolism is more strongly affected by nitrogen deficiency than defence-related secondary metabolism.
It is shown that the model can reproduce the effect of nitrogen fertilization on allocation patterns in apple trees and the effects of elevated CO(2) and competition in juvenile beech and spruce trees. The analysis of model behaviour reveals that large fluctuations in plant internal availability of carbon and nitrogen are possible within a single vegetation period. Furthermore, the model displays a non-linear allocation behaviour to carbon-based secondary compounds.
The simulation results corroborate the underlying assumptions of the presented modelling approach for resource partitioning between growth-related primary metabolism and defence-related secondary metabolism. Thus, the dynamical modelling approach, which considers variable source and sink strengths of plant internal resources within different phenological growth stages, presents a successful translation of existing concepts into a dynamic mathematical model.
Background:
Modelling plant growth allows us to test hypotheses and carry out virtual experiments concerning plant growth processes that could otherwise take years in field conditions. The visualization of growth simulations allows us to see directly and vividly the outcome of a given model and provides us with an instructive tool useful for agronomists and foresters, as well as for teaching. Functional-structural (FS) plant growth models are nowadays particularly important for integrating biological processes with environmental conditions in 3-D virtual plants, and provide the basis for more advanced research in plant sciences.
Scope:
In this viewpoint paper, we ask the following questions. Are we modelling the correct processes that drive plant growth, and is growth driven mostly by sink or source activity? In current models, is the importance of soil resources (nutrients, water, temperature and their interaction with meristematic activity) considered adequately? Do classic models account for architectural adjustment as well as integrating the fundamental principles of development? Whilst answering these questions with the available data in the literature, we put forward the opinion that plant architecture and sink activity must be pushed to the centre of plant growth models. In natural conditions, sinks will more often drive growth than source activity, because sink activity is often controlled by finite soil resources or developmental constraints. PMA06: This viewpoint paper also serves as an introduction to this Special Issue devoted to plant growth modelling, which includes new research covering areas stretching from cell growth to biomechanics. All papers were presented at the Second International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications (PMA06), held in Beijing, China, from 13-17 November, 2006. Although a large number of papers are devoted to FS models of agricultural and forest crop species, physiological and genetic processes have recently been included and point the way to a new direction in plant modelling research.
Overview properties inherent in a wide class of biotech, medical and Web information systems with the discovery of basic modeling tools. The study of choice overall structure of mathematical models of these systems for in-depth study of their common properties is realised
In this paper the analysis of the existent intellectual educational systems is conducted, the method of modeling of effective studies is offered.
We admit that the mathematical relation between agricultural production f(x, y) and the two types of fertilizers x and y is given by function (1). The coefficients that appear are determined by using the least squares method by comparison with the experimental data. We took into consideration the following economic indicators: absolute benefit, relative benefit, profitableness and cost price. These are maximized or minimized, thus obtaining the optimal solutions by annulling the partial derivatives.
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