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Method of Analysis of the Sample Matching of Diagnostic Ranges of Mineral Nutrients in Soil and Cacao Leaves
Communications In Soil Science and Plant Analysis
Abstract
Nutritional diagnostic ranges (NDRs) for soil mineral nutrients (SMNs) and leaf mineral nutrients (LMNs) were obtained from the response of the relative dry biomass of cacao beans (rDBCB) and the relative dry biomass of cacao pod husk (rDBCH). Using an exploratory approach, the sample matching levels of the NDRs were determined to discriminate the results of the soil and leaf nutritional diagnostics. These objectives have been achieved from two methodological processes: a new approach to the boundary line technique where the two-dimensional graph is divided into class intervals based on the predictor variables to then establish the NDR from second degree polynomial regressions, and the development of a classification system for soil and leaf samples by NDR to later verify the corresponding matching levels. This new graphical analysis approach has also allowed us to observe how the SMNs and LMNs present different diagnostic profiles for the prediction of rDBCB and rDBCH responses. The leaf nitrogen (N), potassium (K), magnesium (Mg), and manganese (Mn) concentrations showed an NDR matching level above 80% as predictors of rDBCB and rDBCH responses. Leaf calcium (Ca) concentration showed a level between 60% and 80%. Soil phosphorus (P) concentration showed more than 80% of the sample matching level classified by NDR, followed by the concentrations of K, Ca, and zinc (Zn) in the soil that showed a level of coincidence between 60% and 80%. The lack of uniformity in the genetic potential of cacao production and management has produced differences between predictions.
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Aim of study: The interpretation of results of leaf analysis can be performed by nutritional balance methods, such as Kenworthy method (KW) and diagnostic levels of contents, whose achievements for cacao constitute the main objective of this work.
Area of study: Bahia, Brazil.
Material and methods: The database covered cacao trees in two cultivation systems: agroforestry systems and full sun. The reference populations were composed of plots with relative yield higher than the average plus half a standard deviation of each of these cultivation systems, in addition to a combined population of both systems.
Main results: The norms of the KW method were compared by the t test, for mean, with 72% concordance; and F, for variance, 82% concordant. The diagnoses made based on specific norms per cultivation system and the general norm agreed on average of 91%. Potential response curves were obtained as a function of the Balanced Indices of Kenworthy (BIK) for each nutrient, by the boundary-line method, in addition to sufficiency ranges for BIK and for leaf contents for cacao.
Research highlights: It is concluded that the general KW norms associated with the original Kenworthy ranges or the specific ranges for cacao are efficient in the nutritional diagnosis of cacao.
In view of its high economic value, cacao (Theobroma cacao L.) scientists are seeking technological innovations that increases production and improve quality of cacao beans. The objective of this study was to characterize the mineral (N, K, P, Ca, Mg, Si, Fe, Mn, Zn, Cu, Cd, Ba) composition of cacao beans of clone PH-16 grown in different soil types (Argisols, Cambisols and Latosols) and cropping systems (Cacao Cabruca, Cacao x Erythrina and Cacao x Rubber). With the exception of nitrogen, K was the mineral element most accumulated by cacao beans of PH-16 clone. Potassium, Ca, P and Mg mineral content of dry cacao beans were positively correlated with each other and showed similarity in clusters of average contents in relationship to the different cropping sites. Silicon content in cacao beans is proportionately close to the content of macronutrients. Variations in the content of Mn, Fe, Zn, Cu, Cd and Ba in cacao beans were related to the cropping sites because these mineral elements did not show any significant correlations with each other. Barium contents observed in this study correspond to levels of other micronutrients. In four sites, Cd content was higher than the limit set by the European Union.
The aim of this study was to evaluate the variability, partition, and correlation of Fe, Mn, and Zn in the leaves and fruit components (pod husk,
pulp, tegument, and cotyledons) of cacao trees. These contents were also
correlated with chemical attributes of the soils in regions classified as
humid (H), humid to sub-humid (SH), and sub-humid to dry (SD) in the
South Bahia, Brazil. Soils samples were collected, along with leaves and
fruits from the PH16 clone of the cacao tree, for analysis of Fe, Mn, and
Zn. Descriptive statistics and Pearson’s correlation were applied, as well as
Shapiro Wilk’s normality test and Tukey’s test for comparison of the climate
regions. The accumulation order for Fe and Zn in the fruit components
was tegument > pod husk > leaf > cotyledons; and for Mn the order was
pod husk > leaf > tegument > cotyledons. The increase in hydric restriction,
from the most humid region to the driest, causes natural bioconcentration
of Fe, Mn, and Zn in the fruit components used to produce food (cotyledons and pulp). The Mn contents in the leaf can be used as indicators of
its accumulation in the cotyledon and cacao pulp.
The mineral nutrient ratios are parameters for evaluating the crop nutritional balance through foliar analysis. This study aimed to verify the correlations between the main mineral nutrient ratios in leaves and the cacao productivity of 48 cropping areas. The chemical analyses were carried out to determine foliar N, P, K, Ca, Mg, S, Fe, Zn, Cu and Mn nutrient concentrations. The Zn/Cu and the Ca/Mg ratios showed a positive nutritional relation with cacao productivity. The ratios with Cu as denominator – Mn/Cu, Ca/Cu, Mg/Cu, P/Cu, N/Cu and K/Cu – also showed a positive nutritional relation with cacao productivity. The P/Zn and N/Zn nutrient ratios showed a negative nutritional relation with the cacao productivity.
The understanding of the mineral nutritional status of the cacao (Theobroma cacao L.) is one of the main strategies needed to increase the productivity of cacao beans. The main objective of this work is to verify the linear relationships, bivariate and multivariate analysis between the foliar nutrient concentrations of 48 cropping areas and graphically identifying the consistency of this information. For this study, foliar samples collected from cacao cropping areas, with known productivity of dry cacao beans (kg ha−1 year⁻¹), were analyzed for N, P, K, Ca, Mg, S, Fe, Mn, Zn and Cu concentrations. The interpretation of the results by the exploratory analysis technique linked to the linear correlation analysis proved to be an essential tool to support nutritional diagnosis systems. The cropping areas with very high productivity equal to or higher than 1600 kg of dry cacao beans ha−1 year⁻¹ were positively correlated with the macronutrients K, Ca, and Mg, and the micronutrients Fe, Mn and Zn. The negative correlation of these same high productivity cropping areas with the concentrations of the N and P macronutrients and with the Cu micronutrient may be a phenomenon related to the high nutritional demand for these nutrients in the productive phase.
In cacao crop the understanding of the multiple relationships between bean and pod husk dry biomass and mineral nutrition in the soil-plant system is scarce. The main objective of this work is to verify the linear, bivariate and multivariate correlations between the mineral nutrient concentrations in the soil, leaves and beans of 53 cacao trees with known dry biomass of cacao beans and pod husk, and further graphically identifying the consistency of these information. For this study, soil samples, leaves and fruits (pod husk and beans) were collected from each cacao trees, for the analysis of nitrogen-N, phosphorous-P, potassium-K, calcium-Ca, magnesium-Mg, iron-Fe, manganese-Mn, zinc-Zn and cooper-Cu mineral nutrient concentrations. The interpretation of the results by the exploratory analysis technique linked to the linear correlation analysis proved to be an essential tool to support studies related to mineral nutrition in the soil-plant system. Foliar N concentration were directly related to the high and very high dry biomass classes of cacao beans. Levels of exchangeable Ca and Mg in the soil were inversely correlated with the dry biomass of cacao pod husk (DBCH), in contrast to results with the positive correlations of these nutrients in the leaves and cacao beans data sets. The foliar concentrations of Zn, Mn, Fe and Cu are shown to be more positively associated with DBCH than dry biomass classes of cacao beans. The concentrations of Fe, Mn and Cu in dry cacao beans show such similar pattern of association with dry biomass of pod husk and beans.
Nutrient sufficiency ranges are useful for diagnosing and correcting plant nutritional status in order to optimize yield and protect the environment. This study was conducted to determine nutrient sufficiency ranges for nitrogen (N), phosphorus (P), potassium (K), calcium (Ca), magnesium (Mg), iron (Fe), manganese (Mn), zinc (Zn), and copper (Cu) in mango trees grown in El-Salhiya, Egypt, through boundary-line approach (BLA) and compositional nutrient diagnosis (CND) technique. For this purpose, foliar samples from 310 mango trees were collected during two successive years from the study area and fruit yields were recorded. The nutrient sufficiency ranges generated by BLA were 0.744–1.430% for N, 0.074–0.142% for P, 0.543–1.045% for K, 1.366–2.653% for Ca, 0.155–0.305% for Mg, 389–1148 ppm for Fe, 23.1–60.5 ppm for Mn, 28.4–56.3 ppm for Zn, and 2.37–12.10 ppm for Cu. The CND-derived nutrient sufficiency ranges were 0.917–1.215% for N, 0.066–0.106% for P, 0.585–0.943% for K, 1.003–2.077% for Ca, 0.112–0.378% for Mg, 277.5–849.2 ppm for Fe, 27.9–82.4 ppm for Mn, 29.2–44.6 ppm for Zn, and 2.42–11.37 ppm for Cu. The optimum nutrient concentrations generated from BLA were in general comparable to those obtained using CND technique. Only Ca and Fe optimum concentrations showed poor match. Seven significant nutrient interactions were strongly evidenced through principal component analysis of the computed CND indexes. The positive interaction was P-K, while the negative interactions were P-Mg, K-Mg, Ca-Zn, P-Fe, K-Fe, and Zn-Cu.
Reliable fertilizer recommendations depend on the correctness of the crop production models fitted to the data, but generally the crop models are built empirically, neglecting important physiological aspects related with response to fertilizers, or they are based in laws of plant mineral nutrition seen by many authors as conflicting theories: the Liebig's Law of the Minimum and Mitscherlich's Law of Diminishing Returns. We developed a new approach to modelling the crop response to fertilizers that reconcile these laws. In this study, the Liebig's Law is applied at the cellular level to explain plant production and, as a result, crop models compatible with the Law of Diminishing Returns are derived. Some classical crop models appear here as special cases of our methodology, and a new interpretation for Mitscherlich's Law is also provided.
A new approach to the study of crop productivity has been developed in which the performance of the best in the sample examined is taken as a standard against which to judge the remainder, on the assumption that there are reasons other than chance which account for the inferior performance of part of the population.The line defining the best performance in the population lies at the edge of any body of data, hence the name 'Boundary Line', and occurs wherever a cause-and- effect relationship exists between two variables. When the best performance can be quantified, the overall deficiency in yield due to inferior performance can be assessed and the magnitude of the shortfall used in deciding if investigations to increase yield are justified. When it is allied to a knowledge of the components of yield, the position of the Boundary Line can be used to direct attention to phases of growth most likely to respond to better management.
Two commonly used forms for crop response to inputs are a smooth, differentiable production function and a linear response
and plateau (LRP) model. This paper reconciles these two views by showing that smooth functions can be derived by aggregating
the effects of heterogenous inputs on LRP functions. Data on corn growth are used to test two specific aggregations.
1—In a previous paper*, dealing with the importance of properties of sufficiency in the statistical theory of small samples, attention was mainly confined to the theory of estimation. In the present paper the structure of small sample tests, whether these are related to problems of estimation and fiducial distributions, or are of the nature of tests of goodness of fit, is considered further.
The selection of class intervals, which can strongly affect the visual impression given by a map, is currently a totally anarchic branch of cartography. While practising cartographers have barely accustomed themselves to the routine techniques of class selection, recent work has widened the choice available and extended the opportunity to produce a desired bias. Systems of class intervals, apart from those fixed exogenously or in arbitrary fashion, are classified into idiographic or serial types, the latter being recommended here. Scale transformations leading towards symmetrical frequency distributions are important and are required for proportional as well as graded symbolization. It is suggested that class intervals should not be optimized in relation to details of the statistical frequency distribution, but should be selected according to the overall shape of this distribution. For rectangular distributions, equal division of the range is appropriate: for dominantly unimodal distributions, intervals related to the standard deviation (on a scale which makes the distribution symmetrical): and for J-shaped distributions, geometric progressions to bases which are greater as skewness increases. Techniques are given for calibrating geometric progressions relative to the median, and for dealing with the special characteristics of percentages.
A new semi-theoretical thin layer model for modeling the air drying of cocoa beans with overnight tempering at ambient temperature was developed. The new model was a combination of the Page and two-term drying model. Results showed that the new model was found best described the drying process under the conditions tested (60, 70 and 80 °C). Effective diffusivities were found between 7.46 × 10−11 and 1.87 × 10−10 m2/s. The Arrhenius constant and activation energy were estimated at 8.43 × 10−4 m2/s and 44.92 KJ/mol, respectively. Analyses of pH and cut test for bean quality showed that beans dried at 60 °C had lower acidity and good flavour quality as compared to other drying treatments.
An algorithm to fit boundary lines, using cubic smoothing splines, was written and used to identify yield responses to changes in soil properties. This method involves fitting a curve that represents the maximum yield response to each predictor value, which represents the yield potential at each soil property value. Boundary-line yield responses to individual soil properties were found to differ from responses found by fitting curves through the data scatter. The effects of correlated variables appeared to be lessened using the boundary line approach. Multivariate boundary-line models, based on the Law of the Minimum, were found to be useful for the identification of site-specific causes of yield variation and yield potentials. The boundary line was found to be a useful complement to more traditional data analysis techniques.
The boundary line model was proposed to interpret biological data sets, where one variable is a biological response (e.g. crop yield) to an independent variable (e.g. available water content of the soil). The upper (or lower) boundary on a plot of the dependent variable (ordinate) against the independent variable (abscissa) represents the limiting response of the dependent variable to the independent variable value. Although the concept has been widely used, the methods proposed to define the boundary line have been subject to criticism. This is because of their ad hoc nature and lack of theoretical basis. In this article, we present a novel method for fitting the boundary line to a set of data. The method uses a censored probability distribution to interpret the data structure. The parameters of the distribution (and hence the boundary line parameters) are fitted using maximum likelihood and related confidence intervals deduced. The method is demonstrated using both simulated and real data sets.
During the past three decades a large body of research has investigated the problem of specifying class intervals for choropleth maps. This work, however, has focused almost exclusively on placing observations in quasi-continuous data distributions into ordinal bins along the number line. All enumeration units that fall into each bin are then assigned an areal symbol that is used to create the choropleth map. The geographical characteristics of the data are only indirectly considered by such approaches to classification. In this article, we design, implement, and evaluate a new approach to classification that places class-interval selection into a multicriteria framework. In this framework, we consider not only number–line relationships, but also the area covered by each class, the fragmentation of the resulting classifications, and the degree to which they are spatially autocorrelated. This task is accomplished through the use of a genetic algorithm that creates optimal classifications with respect to multiple criteria. These results can be evaluated and a selection of one or more classifications can be made based on the goals of the cartographer. An interactive software tool to support classification decisions is also designed and described.
The main intent of this paper is to introduce a new statistical procedure for testing a complete sample for normality. The test statistic is obtained by dividing the square of an appropriate linear combination of the sample order statistics by the usual symmetric estimate of variance. This ratio is both scale and origin invariant and hence the statistic is appropriate for a test of the composite hypothesis of normality. Testing for distributional assumptions in general and for normality in particular has been a major area of continuing statistical research-both theoretically and practically. A possible cause of such sustained interest is that many statistical procedures have been derived based on particular distributional assumptions-especially that of normality. Although in many cases the techniques are more robust than the assumptions underlying them, still a knowledge that the underlying assumption is incorrect may temper the use and application of the methods. Moreover, the study of a body of data with the stimulus of a distributional test may encourage consideration of, for example, normalizing transformations and the use of alternate methods such as distribution-free techniques, as well as detection of gross peculiarities such as outliers or errors. The test procedure developed in this paper is defined and some of its analytical properties described in ? 2. Operational information and tables useful in employing the test are detailed in ? 3 (which may be read independently of the rest of the paper). Some examples are given in ? 4. Section 5 consists of an extract from an empirical sampling study of the comparison of the effectiveness of various alternative tests. Discussion and concluding remarks are given in ?6. 2. THE W TEST FOR NORMALITY (COMPLETE SAMPLES) 2 1. Motivation and early work This study was initiated, in part, in an attempt to summarize formally certain indications of probability plots. In particular, could one condense departures from statistical linearity of probability plots into one or a few 'degrees of freedom' in the manner of the application of analysis of variance in regression analysis? In a probability plot, one can consider the regression of the ordered observations on the expected values of the order statistics from a standardized version of the hypothesized distribution-the plot tending to be linear if the hypothesis is true. Hence a possible method of testing the distributional assumptionis by means of an analysis of variance type procedure. Using generalized least squares (the ordered variates are correlated) linear and higher-order
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