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A modified mitscherlich equation for rainfed crop production in semi-arid areas: 1. theory.

The classical Mitscherlich equation is based on Liebig's Law of the Minimum and describes the yield response of a crop to an increase in the main factor that is limiting growth. The maximum, or potential, yield is an important parameter in the Mitscherlich equation and is assumed to be constant, that is, not affected by other factors that limit actual yields under field conditions. The assumption that potential yield is a constant does not apply to rainfed agriculture in semi-arid regions because under such conditions potential yields vary with crop-available moisture. A theoretical framework for the application of the Mitscherlich equation to rainfed crop production is presented. Water-limited potential yield is assumed to be a linearly increasing function of available moisture. Similarly, the quantity of nutrients required by a crop to achieve water-limited potential yield is assumed to be a linearly increasing function of seasonal rainfall. Finally, nutrient availability is also thought to depend on available moisture. The general form of the modified Mitscherlich equation for response to nutrients is simplified, by expressing all moisture dependent parameters as functions of annual rainfall.

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

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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.

Keywords: Mitscherlich equation; feedstuff evaluation; fermentation kinetics; gas production technique; in vitro digestibility; substrate degradation.

Conflict of interest statement

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Observed (●) atypical gas production…

Observed (●) atypical gas production profiles and predicted curves resulting from fitting Equations…

Observed (●) typical gas production…

Observed (●) typical gas production profiles and predicted curves resulting from fitting Equations…

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Overview and application of the Mitscherlich equation and its extensions to estimate the soil nitrogen pool fraction associated with crop yield and nitrous oxide emission.

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Overview and application of the Mitscherlich equation and its extensions to estimate the soil nitrogen pool fraction associated with crop yield and nitrous oxide emission. / Dhanoa, Mewa Singh; Sanderson, Ruth ; Cardenas, Laura et al.

T1 - Overview and application of the Mitscherlich equation and its extensions to estimate the soil nitrogen pool fraction associated with crop yield and nitrous oxide emission.

AU - Dhanoa, Mewa Singh

AU - Sanderson, Ruth

AU - Cardenas, Laura

AU - Shepherd, Anita

AU - Chadwick, David

AU - Christopher D, Powell

AU - Jennifer L, Ellis

AU - Lopez, Secundino

AU - France, J

PY - 2022/5/6

Y1 - 2022/5/6

N2 - Background: Natural levels of soil nutrients are spatio-temporally variable and insufficient for agricultural purposes. Artificial fertilisers are applied to achieve higher crop growth rates and yield. Mitscherlich’s equation and Boule’s fertilizer units are described and illustrated in relation to crop yield then applied to estimate the nitrogen (N)-pool fraction in the soil that contributes to a component of greenhouse gas (GHG) emissions, specifically the nitrous oxide (N2O) flux.Methods: Mitscherlich (1909) proposed a diminishing returns model to extract information about soil N status for production responses. Mitscherlich’s equation was generalised by Baule (1918) and modified by Bray (1945) to account for soil nutrient contributions for multiple fertilisers. These models are examined in this study.Results: Their application results in the extraction of further information on soil nutrient variability and N2O emission across spatial locations.Conclusions: Mitscherlich’s equation and Boule’s fertilizer units are useful tools to study soil-fertiliser interaction and compare soil fertility and GHG emission.

AB - Background: Natural levels of soil nutrients are spatio-temporally variable and insufficient for agricultural purposes. Artificial fertilisers are applied to achieve higher crop growth rates and yield. Mitscherlich’s equation and Boule’s fertilizer units are described and illustrated in relation to crop yield then applied to estimate the nitrogen (N)-pool fraction in the soil that contributes to a component of greenhouse gas (GHG) emissions, specifically the nitrous oxide (N2O) flux.Methods: Mitscherlich (1909) proposed a diminishing returns model to extract information about soil N status for production responses. Mitscherlich’s equation was generalised by Baule (1918) and modified by Bray (1945) to account for soil nutrient contributions for multiple fertilisers. These models are examined in this study.Results: Their application results in the extraction of further information on soil nutrient variability and N2O emission across spatial locations.Conclusions: Mitscherlich’s equation and Boule’s fertilizer units are useful tools to study soil-fertiliser interaction and compare soil fertility and GHG emission.

KW - Nitrous oxide emission

KW - Soil nutrients

KW - Baule units

KW - Dickson formula

KW - Mitscherlich equation

KW - Nitrogen cycle

U2 - 10.1016/bs.agron.2022.03.005

DO - 10.1016/bs.agron.2022.03.005

M3 - Chapter

SN - 978-0-323-98957-2

T3 - Advances in Agronomy

BT - Advances in Agronomy

PB - Elsevier

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article discussing a topic in relation to mitscherlich equation

Proceedings of the British Society of Animal Science

Article contents

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

Published online by Cambridge University Press:  20 November 2017

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.

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A modified mitscherlich equation for rainfed crop production in semi-arid areas: 1. Theory

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Original Article

The classical Mitscherlich equation is based on Liebig's Law of the Minimum and describes the yield response of a crop to an increase in the main factor that is limiting growth. The maximum, or potential, yield is an important parameter in the Mitscherlich equation and is assumed to be constant, that is, not affected by other factors that limit actual yields under field conditions. The assumption that potential yield is a constant does not apply to rainfed agriculture in semi-arid regions because under such conditions potential yields vary with crop-available moisture. A theoretical framework for the application of the Mitscherlich equation to rainfed crop production is presented. Water-limited potential yield is assumed to be a linearly increasing function of available moisture. Similarly, the quantity of nutrients required by a crop to achieve water-limited potential yield is assumed to be a linearly increasing function of seasonal rainfall. Finally, nutrient availability is also thought to depend on available moisture. The general form of the modified Mitscherlich equation for response to nutrients is simplified, by expressing all moisture dependent parameters as functions of annual rainfall.

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Presenting data and distinguishing response curves

Plant and Soil volume  462 ,  pages 1–5 ( 2021 ) Cite this article

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When I first started doing research, about 65 years ago, every research institution had its own statistics department. It was the duty of the statisticians to make sure that every experiment was correctly designed, and analysed, as well as supervising the technical staff who tediously calculated sums of squares on the mechanical calculators in use at that time. While we may have teased the statisticians by calling their department the “Star Factory”, we nevertheless appreciated their wisdom and guidance. Thank heavens people no longer need to pound calculators. Such tedium has been taken over by computers. However, in many cases this has resulted in statisticians being seen as unnecessary, and perhaps the teaching of statistics has been neglected.

Similar considerations prompted Webster ( 2007 ) to write: “there has grown up a new generation of soil scientists who are as mystified by the analysis (of variance) as those of 30 years ago. Yet, whereas then the scientists did not do the analysis if they did not understand, now, with so much software around, they can do it at the press of a few buttons. They thereby obtain results, but their presentation of them and their discussions that follow suggest to me that in many instances they do not understand what they are doing.”

I illustrate some of the problems that arise using Table 1 . I have imagined an experiment in which responses to phosphorus are observed at two levels of lime for a very acidic soil. The soil is so acid (say pH CaCl2  < 4.5) that growth is limited by aluminium toxicity; the level of lime used raises pH CaCl2 to near 5.5, sufficient to alleviate aluminium toxicity but not sufficient to enter the region in which high pH decreases the rate of uptake (Barrow et al. 2020 ). This table does not come from any real manuscripts, but is an amalgam of Tables I have seen in many submitted manuscripts, and in quite a few published ones.

There are several problems with this kind of presentation. One is aesthetic; I find it ugly. It is also inefficient because, in practical terms, one can hardly see the results because of all the extra material. As Webster ( 2007 ) wrote: “The most important outcomes of almost all experiments are the means for the treatments… They should have pride of place in the results section of any paper or report”.

Now let us consider the alphabet soup that decorates such tables. The star factory of earlier times has become an alphabet factory. Methods for making multiple comparisons is a large and complicated subject and one about which many statisticians disagree. Several methods including those of Duncan ( 1955 ) and Tukey ( 1953 ) as quoted by Benjamini and Braun ( 2002 ) are based on the argument that as the number of treatments is increased, the number of possible comparisons is also increased and the possibility of detecting a false positive is increased. Therefore, the criterion for detecting differences should be more stringent. That would be sensible for an experiment intended to “pick a winner”. An example might be comparing different varieties of a crop for which there is no initial hypothesis and it might be reasonable to compare everything with everything else. However, for most experiments this is not the case; there is an initial hypothesis. Inclusion of an extra treatment, such as an extra level of phosphorus (P) in Table 1 , might be expected to improve the ability to test the hypothesis, rather than to decrease the sensitivity. Again, Webster ( 2007 ) has an appropriate comment: “One must ask why the inclusion of more treatments in an experiment should diminish the power of a test to detect true differences…: it does not make sense practically.”

There is another common problem which is also illustrated in Table 1 : the presence of “±” signs after each entry followed by a number. If the data are represented in figures there will similarly be an error bar of different lengths against each entry. There is a logical inconsistency in this custom. One of the most basic assumptions of an analysis of variance is equality or homogeneity of variances – the variance of data in groups should be the same. If this is not so, there are various transformations made to the data. If errors are indeed random, for some treatments the replicates will give very similar values, but for others the values will not be so close. It does not follow that treatments for which the replications give similar values are more accurately measured than others for which they don’t. If errors are indeed random this is what you should expect. Yet again, Webster ( 2007 ) has an appropriate comment: “in an experiment in which all the treatments are replicated equally the SE calculated as above is a single value applying to all means. You should quote it rather than SEs calculated separately from the data for the individual treatments or classes.”

Quite often, instead of being presented in tables, response data are represented by column graphs (Fig.  1 ). I do not understand why these are so popular. It seems to me that when the interval between each dataset is not constant, it is difficult to really get a picture of the results when they are presented this way. The effects of the treatments can be much more readily visualised when the data are presented as in Fig.  2 . Further, these days it is not difficult to fit non-linear curves to describe such data. This method of data presentation brings out the effects that are difficult to see when the other methods of presentation are used. At low pH, application of lime stimulates growth, but decreases the amount of P derived from the soil, as indicated by the dashed extrapolations to the horizontal axis.

figure 1

Illustrating the way the data of Table 1 is often presented – as column plots with the levels of P represented as symbols and the columns evenly spaced

figure 2

Dot plots of the data presented in Table 1 and Fig. 1 . The lines indicate the fit of a version of the Mitscherlich equation expressed as: y = m [1 – exp.(− c ( x  +  d )] where y is the yield, x is the P applied; and m, a, and d are parameters. The parameter m indicates the maximum yield to which the data trend; the parameter c indicates the slope of the response curve; and the parameter d indicates the P coming from the soil and seed; its magnitude is indicated by the extrapolations of the lines to the horizontal axis

With data such as these, why is there any need to compare individual means? Within each lime treatment, there is a highly significant regression. We can therefore assume that any change in the independent variable will produce a change in the dependent variable, the magnitude of which depends on the fitted relationship, and with a level of confidence that depends on the correlation coefficient. That leaves the question of distinguishing the response curves. In order to do this we set up the null hypothesis that they are not different and in that case a common curve adequately describes the results. We then compare the residual sums of squares for the improvement obtained by fitting separate curves. Table 2 shows that the null hypothesis can’t be sustained; the curves are different. However, with only five levels of applied P and with equations containing three terms, there are insufficient degrees of freedom to provide a sensitive test.

How one should choose treatments when planning to compare responses; is it better to have for each treatment, say, 10 individual points or five points that are the means for two observations? There are some general considerations. It is always better to explore the response over as wide a range of observations as possible and so the more levels the better. Further, there is no need to replicate observations when it is not intended to compare individual observations, but rather to compare response curves. In order to explore how to choose treatments more thoroughly, I wrote a small BASIC program (online resource 1 ).

The program first generates random errors in the observations with a normal distribution and specified standard deviation. Each group of 20 generated values was analysed in two different ways. In one of these ways, pairs of values were used to generate means and the resulting 10 observations were assumed to represent treatments as indicated in Fig.  3a . In the other way, individual values were used and the resulting 20 observations were assumed to represent treatments as indicated in Fig. 3b . The improvement produced by fitting separate curves rather than a common curve was then analysed as illustrated in Table 2 , and for the resulting pairs of values for the variance ratio, and the p value was calculated. In order to generate smooth frequency distribution curves, I used 5000 sets of randomly generated groups of 20 variables for each value of the standard distribution. The frequency distribution of the values for p was calculated using LibreOffice Calc and the curves plotted using Sigmaplot.

figure 3

Two ways treatments may be chosen when comparing two curves. In both cases, 20 observations are made; in part a, there are 10 means of 2 observations in part b, 20 individual points

Figure 4 shows that the p values are on average much lower when 20 individual values are analysed. This is mainly because there are more degrees of freedom against which to test significance. As the “experiment” becomes less precise – that is as the standard deviation of the error increases, both tests become less sensitive and the tails of the distribution may overlap. Nevertheless, on average, a more sensitive test is obtained when 20 individual values are used. Thus, in contrast to he generally accepted wisdom, you are more likely to distinguish curves if you devote your effort into more levels rather than more replications.

figure 4

Effect of the precision of an experiment as simulated by varying the values for the standard deviation (sd) of the distribution of errors. Values of p are for the significance of the difference between two response curves each of which is based on 10 observations. In one case there are 10 individual observations per curve; in the other, the 10 observations are 5 pairs of duplicates giving 5 means of two observations. . The vertical line indicates p  = 0.05

In summary: “In experiments with graded treatments do not make multiple comparisons of any kind; instead fit a response curve and analyse the data by regression” (Webster 2007 ). To which I would add, if you are not to compare means, it makes no sense to replicate observations. If you do so, you lose sensitivity.

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Barrow, N.J. Presenting data and distinguishing response curves. Plant Soil 462 , 1–5 (2021). https://doi.org/10.1007/s11104-021-04887-z

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Received : 06 January 2021

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Published : 27 February 2021

Issue Date : May 2021

DOI : https://doi.org/10.1007/s11104-021-04887-z

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Models based on the mitscherlich equation for describing typical and atypical gas production profiles obtained from in vitro digestibility studies using equine faecal inoculum.

article discussing a topic in relation to mitscherlich equation

Simple Summary

1. introduction, 2. materials and methods, 2.1. datasets, 2.1.1. experiment 1: inoculum from horses, 2.1.2. experiment 2: inoculum from ponies, 2.2. models fitted, 2.3. extent of degradation, 2.4. fitting and evaluation of models, 3.1. fitting behaviour, 3.2. parameter estimates and fitted gas production curves, 3.3. model evaluation, 3.4. extent of degradation, 4. discussion, 4.1. profile shapes and associated parameters, 4.2. extent of degradation, 5. conclusions, supplementary materials, author contributions, conflicts of interest.

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Powell, C.D.; Dhanoa, M.S.; Garber, A.; Murray, J.-A.M.D.; López, S.; Ellis, J.L.; France, J. Models Based on the Mitscherlich Equation for Describing Typical and Atypical Gas Production Profiles Obtained from In Vitro Digestibility Studies Using Equine Faecal Inoculum . Animals 2020 , 10 , 308. https://doi.org/10.3390/ani10020308

Powell CD, Dhanoa MS, Garber A, Murray J-AMD, López S, Ellis JL, France J. Models Based on the Mitscherlich Equation for Describing Typical and Atypical Gas Production Profiles Obtained from In Vitro Digestibility Studies Using Equine Faecal Inoculum . Animals . 2020; 10(2):308. https://doi.org/10.3390/ani10020308

Powell, Christopher D., Mewa S. Dhanoa, Anna Garber, Jo-Anne M. D. Murray, Secundino López, Jennifer L. Ellis, and James France. 2020. "Models Based on the Mitscherlich Equation for Describing Typical and Atypical Gas Production Profiles Obtained from In Vitro Digestibility Studies Using Equine Faecal Inoculum " Animals 10, no. 2: 308. https://doi.org/10.3390/ani10020308

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These chemistry research topics are ideal to consider when you want to write a good paper by searching for relevant information on the search engines.

Chemistry Research Paper Topics for Undergraduates

In terms of complexity, undergraduates topics are difficult than chemistry research topics for high school and college students. Nevertheless, undergraduates have many topics that they can find relevant and sufficient information to write about. Here are some of the best chemistry projects topics for undergraduates.

These chemistry paper topics are complex and students need several days to write solid papers about them.

Chemistry Research Topics for High School

There are many topics in chemistry high school learners can consider. Here are some of the best topics that high school students can choose for their research papers and essays.

These are cool chemistry topics that students can find information about online. Some students can even take a few hours to write essays on some of these topics.

The Best Topics in Current Chemistry

Perhaps, you want to write a paper or essay on a current topic. In that case, consider a topic in this category. This category comprises topics in medicinal, physical, and environmental chemistry. You can also find controversial chemistry topics in this category. Here are some of the best current topics in medicinal chemistry and other branches.

Chemical Engineering Topics for Research

Chemical engineering students are also required to write papers and essays. Here are some of the best topics to consider in this category.

This category has some of the best chemistry topics for presentation. What’s more, learners that want to learn while impressing their professors can consider them.

Great Physical Chemistry Topics

This category has some of the most interesting chemistry presentation topics. Nevertheless, physical chemistry is a difficult course for learners in different study levels. Here are some of the best topics to consider in this category.

Students that are pursuing physical chemistry topics can also find interesting chemistry topics for presentation in this category.

Biochemistry Topics

When looking for chemistry related topics, learners can consider ideas for their papers and essays in biochemistry. Here are some of the best chemistry topics for project in biochemistry.

These are some of the best chemistry project topics to consider in biochemistry. But, every learner should select a topic they are comfortable researching and writing about.

Whether a student needs chemistry IA topics or the best AP chemistry topics, they have many options to consider. Nevertheless, every learner should settle for an interesting chemistry topic to have an easy time researching and writing their paper or essay. Also, take a look at our ecology topics .

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IMAGES

  1. Mitscherlich Equation

    article discussing a topic in relation to mitscherlich equation

  2. Eilhard mitscherlich Isomorphism Inventor

    article discussing a topic in relation to mitscherlich equation

  3. Solved (see Figure 152 & A decibel level of 120 cll he

    article discussing a topic in relation to mitscherlich equation

  4. Mitscherlich's Law: A Supplement

    article discussing a topic in relation to mitscherlich equation

  5. Class 10th Math Ch-3 Pair of linear equation in two variables (Introduction) |FindYourValue

    article discussing a topic in relation to mitscherlich equation

  6. Potassium-Fixing Clay Minerals as Parameters that Define K Availability of K-Deficient Soils

    article discussing a topic in relation to mitscherlich equation

COMMENTS

  1. Overview and application of the Mitscherlich equation and its

    Baule's fertilizer units in relation to the fitted Mitscherlich-Baule response equation such that the first Baule unit increases the response to 50% of the asymptote and the second Baule unit moves it to a point half-way between the 50% and the asymptotic value, i.e., 75%, and so on.

  2. A modified mitscherlich equation for rainfed crop production in semi

    The Mitscherlich equation (1) can be modified to fit the Liebig model: (4) which gives upon integration: (5) where Yx has been replaced by Ye and EtL (kg dm kg'] nutrient) denotes the activity coefficient related the total-nutrient content (Nt) for the Liebig model and where it is further assumed that Yo= 0 ifNt=O.

  3. Overview and application of the Mitscherlich equation and its

    Mitscherlich's equation and Boule's fertilizer units are described and illustrated in relation to crop yield then applied to estimate the nitrogen (N)-pool fraction in the soil that...

  4. Models Based on the Mitscherlich Equation for Describing ...

    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.

  5. Overview and application of the Mitscherlich equation and its

    Mitscherlich's equation and Boule's fertilizer units are described and illustrated in relation to crop yield then applied to estimate the nitrogen (N)-pool fraction in the soil that contributes to a component of greenhouse gas (GHG) emissions, specifically the nitrous oxide (N2O) flux.

  6. PDF Models Based on the Mitscherlich Equation for Describing Typical and

    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.

  7. The Application of the Mitscherlich Equation for the ...

    The equation introduced by Mitscherlich has been generally used to express nutrient-yield relationships as follows: y = A (1—e -eb-ex) This paper reports an attempt to apply such a curve to soil nutrient-plant composition relationships, using the wheat plant. For this study soils deficient in phosphorus were selected in four different soil areas.

  8. Mitscherlich‐Bray Equation Used to Correlate Soil Phosphorus and Potato

    Abstract Very little is known about the response of potato (Solanum tuberosum L.) to P in northeast Florida where potato is a major winter crop. The purpose of this study was to correlate tuber yie...

  9. annotated.docx

    2 An Article Discussing A Topic In Relation To Mitcherlich Equation Or Mitchelich- Baule Equation: Annotated Bibliography K. Harmsen (2000). A modified Mitscherlich equation for rainfed crop production in semi-arid areas: 1. Theory.

  10. Mitscherlich's Law: Sum of two exponential Processes

    Mitscherlich first formulated the law in form of a differential equation: (1) where x is the quantity of fertilizer, y the crop-yield and (as usual in statistics) the hypothetical value of y; a is the maximum value of the yield (we exclude over-fertilization!) and b>0 is the most important exponential factor.

  11. Application of Mitscherlich-Bray Equation for Fertilizer Use on

    Field experiments were conducted at two locations in order to formulate phosphorus and potassium fertilizer recommendations of groundnut (Arachis hypogea) based on Mitscherlich-Bray equation.The treatments comprised four levels of phosphorus (0, 30, 60, and 90 kg phosphorus pentoxide (P 2 O 5) ha −1) and three levels of potassium (0, 30, and 60 kg potassium oxide (K 2 O) ha −1) in all ...

  12. PDF Conclusions 2009, 1st

    Mitscherlich first formulated the law in form of a differential equation: d yˆ/dx yˆ' b(a yˆ) (1) where x is the quantity of fertilizer, y the crop-yield and yˆ (as usual in statistics) the hypothetical value of y; a is the maximum value of the yield (we exclude over-fertilization!)

  13. The Mitscherlich equation: an alternative to linear models of methane

    Article contents Extract References The Mitscherlich equation: an alternative to linear models of methane emissions from cattle Published online by Cambridge University Press: 20 November 2017 J. A. N. Mills, E. Kebreab, L. A. Crompton and J. France Show author details J. A. N. Mills Affiliation:

  14. Solved: Mitscherlich's Equation An important agricultural proble

    In 1909 E. A. Mitscherlich proposed the following relation, which is known as Mitscherlich's equation: 8. Here b is the number of baules of nutrient applied, and Y is the percentage (as a decimal) of maximum yield produced. a. Verify that the formula predicts that 50% of maximum yield will be produced if 1 baule of nutrient is applied. b.

  15. A modified mitscherlich equation for rainfed crop production in semi

    The classical Mitscherlich equation is based on Liebig's Law of the Minimum and describes the yield response of a crop to an increase in the main factor that is limiting growth. The maximum, or potential, yield is an important parameter in the Mitscherlich equation and is assumed to be constant, that is, not affected by other factors that limit ...

  16. Baule-Mitscherlich Limiting Factor Equation

    Baule-Mitscherlich Limiting Factor Equation. Jacob Verduin Authors Info & Affiliations. 117, Issue 3041. p. 392. References. e Letters (0)

  17. Presenting data and distinguishing response curves

    Full size image. Fig. 2. Dot plots of the data presented in Table 1 and Fig. 1. The lines indicate the fit of a version of the Mitscherlich equation expressed as: y = m [1 - exp. (− c ( x + d )] where y is the yield, x is the P applied; and m, a, and d are parameters. The parameter m indicates the maximum yield to which the data trend; the ...

  18. PDF (1983) Teaching the Characteristics of Yield Response With the

    The Mitscherlich equation is a traditional and useful ex-pression of such a relationship. In this paper, some of the background and development of modified but gen-eral Mitscherlich equations with one or more independ-ent variables are presented. Interactive computer pro-grams in the BASIC and FORTRAN languages are de-scribed and listed.

  19. Animals

    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.

  20. PDF POSSIBLE RESEARCH TOPICS

    POSSIBLE RESEARCH TOPICS Your research paper, and the resulting thesis statement, must be an ARGUABLE issue. Be prepared to present the actual findings of your research convincingly even if you discover that your findings differ from your personal opinions. Remember, research is objective and not a "soap box" for personal views.

  21. 100+ Interesting Chemistry Research Paper Topics

    These concepts include stoichiometry, thermodynamics, nuclear chemistry, etc. Here is a list of general chemistry topics. Basics and behavior of atoms. Physical and chemical properties of matter. Chemical equations and formula. Reactions in chemistry. Energies associated with chemical reaction. Concept of nuclear chemistry.

  22. 100 Best Chemistry Topics For Your Academic Research

    Here are some of the best topics that high school students can choose for their research papers and essays. Analyze the effect of PH on planets. Explain the creation of pearls. Explain the growth of artificial diamonds. Explain how tea brewing can be optimized. Explain how heavy metals are detected in plants.

  23. Overview

    Select a topic. Choosing an interesting research topic is your first challenge. Here are some tips: Choose a topic that you are interested in! The research process is more relevant if you care about your topic. Narrow your topic to something manageable. If your topic is too broad, you will find too much information and not be able to focus.