Boundary Line Approach Research Articles

Boundary-Line Approach to Determine Standards of Nutrition for Mature Trees From Spatial Variation of Growth and Foliar Nutrient Concentrations in Natural Environments

Optimum nutritional standards for most tree species of eastern Canada are unknown. This can be attributed to the fact that controlled conditions typically required to develop such standards are impractical and prohibitive to obtain with mature trees. In this study, a boundary-line approach was developed for determining standards of optimum nutrition for forest trees based on natural variation in tree growth and nutritional status. The study site was located in the unmanaged forest of the Station de Biologie de l’Université de Montréal, 90 km north of Montreal in the Lower Laurentians in Quebec. As many as 87 dominant to codominant sugar maples were sampled (foliage, increment cores) and measured (live-crown ratio, dendrometer bands) over the 1995–2001 period. Leaves were analyzed for nitrogen (N), phosphorus (P), potassium (K), calcium (Ca), magnesium (Mg), and manganese (Mn), and radial growth was converted to basal-area growth for use with the boundary-line approach to determine standards of nutrition. An algorithm was developed to select boundary points to be used in quadratic models describing the relationships between leaf-nutrient concentration and basal-area growth. Eight, 10, and 20 intervals (points) and an index based on the live-crown ratio of the trees to correct for forest density were tested. The application of the boundary line on raw data without correction for outliers or live-crown ratio generally produced models that were significant. Correction of outliers and the use of 10 intervals generally improved the models. Critical and optimum leaf N, P, K, Ca, Mg, and Mn concentrations derived from the boundary-line approach were generally similar to published values. These results suggest that the approach is particularly well suited for the determination of critical and optimum nutrient concentrations and is less so for the determination of toxic concentrations.

Boundary-Line Approach to Determine Standards of Nutrition for Mature Trees From Spatial Variation of Growth and Foliar Nutrient Concentrations in Natural Environments

Abstract Optimum nutritional standards for most tree species of eastern Canada are unknown. This can be attributed to the fact that controlled conditions typically required to develop such standards are impractical and prohibitive to obtain with mature trees. In this study, a boundary-line approach was developed for determining standards of optimum nutrition for forest trees based on natural variation in tree growth and nutritional status. The study site was located in the unmanaged forest of the Station de Biologie de l’Université de Montréal, 90 km north of Montreal in the Lower Laurentians in Quebec. As many as 87 dominant to codominant sugar maples were sampled (foliage, increment cores) and measured (live-crown ratio, dendrometer bands) over the 1995–2001 period. Leaves were analyzed for nitrogen (N), phosphorus (P), potassium (K), calcium (Ca), magnesium (Mg), and manganese (Mn), and radial growth was converted to basal-area growth for use with the boundary-line approach to determine standards of nutrition. An algorithm was developed to select boundary points to be used in quadratic models describing the relationships between leaf-nutrient concentration and basal-area growth. Eight, 10, and 20 intervals (points) and an index based on the live-crown ratio of the trees to correct for forest density were tested. The application of the boundary line on raw data without correction for outliers or live-crown ratio generally produced models that were significant. Correction of outliers and the use of 10 intervals generally improved the models. Critical and optimum leaf N, P, K, Ca, Mg, and Mn concentrations derived from the boundary-line approach were generally similar to published values. These results suggest that the approach is particularly well suited for the determination of critical and optimum nutrient concentrations and is less so for the determination of toxic concentrations.

Using a boundary line approach to analyze N2O flux data from agricultural soils.

Predicting the N2O flux from soils is difficult because of the complex interplay of the various processes involved. In this study a boundary line approach was used to apply results from mechanistic experiments to N2O flux data resulting from measurements on field scale in southern Germany. Boundary lines were fitted to the rim of the data points in scattergrams depicting readily obtainable soil variables against the measured N2O flux. The boundary line approach is based on the hypothesis that this line depicts the functional dependency between the two variables. For determining these boundary lines a novel method was applied. The function best representing the relationship between the N2O flux and soil temperature had a maximum above 23 °C and the one between the N2O flux and the water filled pore space (WFPS, to represent water content) had a maximum at 72% WFPS. In the range of 0–20 mg N kg-1 the relationship between N2O flux and nitrate in the soil was best described by a linear function, whereas in the range of 0–35 mg N kg-1 a Michaelis–Menten function was more appropriate. The boundary lines specified in this study are in agreement with existing theoretical concepts as well as experimental results obtained under controlled and field conditions as reported in the literature. Therefore, the boundary line approach can be used to improve empirical models for predicting the N2O flux in the field.

Establishing critical values for soil and plant analysis by means of the boundary line development system (bolides)

Abstract Within the boundary line approach, optimal nutrient levels and optimal nutrient ranges are calculated. In order to ensure reproducibility, we propose the boundary line development system (BOLIDES) for the calculation of upper boundary lines. Data from the long‐term evaluation of the Local Resource Management concept being conducted at Vindum (Denmark) were analyzed by BOLIDES and quantitative results are discussed for plant available phosphate.

Prediction of Field Denitrification Rates: A Boundary-Line Approach

The high degree of spatial and temporal variability in denitrification and the complexity of the controls on the denitrification process make prediction of field denitrification rates difficult. We developed a denitrification model that requires only easily obtainable data to predict daily denitrification rates on Chernozemic soils. The model was developed using boundary-line analysis to establish relationships between soil properties and denitrification for some Saskatchewan soils. Predictions of denitrification are made from water-film thickness (grams of water per unit surface area), air porosity, organic C, NO−3, and maximum daily air temperature. The coefficient of determination (R2) for the relationship between predicted and measured denitrification rates was 0.47, with 50% of the predicted denitrification rates falling within the range of the replicates for the corresponding measured rates. When the model was tested using an independent data set, the correlation (R2) between predicted and actual denitrification rates was 0.50 indicating that the model can explain approximately one-half of the variability in denitrification for a range of soils. The model can be combined with a soil water budget to estimate daily denitrification rates from readily available soil and climatic data.

Soil and plant calibration for cucumbers grown in the mid‐Atlantic coastal plain

Abstract Few soil test and plant tissue calibration data exist for cucumbers (Cucumis sativus L.). Two years of a singly‐replicated cucumber fertility study were conducted to develop soil and plant data for calibration purposes employing the Boundary Line Approach. Fertility treatments consisting of 4 K levels (as KC1), 3 Mg levels (as MgCl2), 3 pH levels (as Calcitic limestone), and 4 N rates (as urea ammonium nitrate) were factorilly arranged and completely randomized to give 108 treatments in both 1987 and 1988. Analyses were performed upon leaf samples for N, P, K, Ca and Mg at early bloom and soil samples for Mehlich (M) 1‐ and 3‐ P, K, Ca and Mg, and pH. Cucumber yields were determined on early (two fruit pickings) and total (four fruit pickings) sampling periods. High‐yielding cucumbers were attained at soil K (Ml = 64 mg/kg) and Mg (Ml = 29 mg/kg) levels lower than currently recommended. No significant differences in correlation coefficients between either Mehlich (Ml, M3) extractant and cucumber ...

Utilization of the boundary line approach in the development of soil nutrient norms for soybean production

Abstract Boundary Unes, which previously have been employed for development of plant diagnostic norms for DRIS, were applied to soils for critical value Improvement. Soil test values and yields for soybeans (Glycine max L.) were collected for Alabama, Georgia, and South Carolina experiment station plots and farmers’ production fields. The sampling population was divided on the basis of surface soil texture and yield level in order to formulate soil critical value norms for both fine‐textured (clayey) and coarse‐textured (sandy) Ultisols in the southeastern United States. Boundary Une approach (BLA) norms for the fine‐ and coarse‐textured soils were similar to those norms employed by state‐operated soil testing laboratories for Piedmont and Coastal Plain soils, respectively. Two Coastal Plain soils having different surface soil textures, viz. clayey versus sandy, gave critical values by the BLA corresponding to the norms for fine‐ and coarse‐textured soils. Greater precision in the development of soil crit...

Use of Boundary Lines in Establishing Diagnostic Norms

AbstractWhether utilizing a critical value or a nutrient balance system such as the Diagnosis and Recommendation Integrated System (DRIS) for interpreting plant tissue composition, determination of accurate optima is of paramount importance. Two procedures for determining such optima, one using the mean of a high yielding population, the second establishing yield maxima at all nutrient values (henceforth termed the boundary line approach) were contrasted. Ear leaf nutrient composition and associated yield information were collected on over 8000 maize (Zea mays L.) samples from around the world. Values of N/DM, P/DM, K/DM (DM = dry matter), P/N, N/K, and K/P as well as the DRIS indices for N, P, and K were plotted against grain yields. Boundary lines confining the resultant scatters of points were then mathematically described. The boundary lines define yields that may occur under a given set of conditions and can be used to determine plant tissue optima, or as a yield specific alternative to the conventional critical value system. In addition, the maximum yield possible at any given compositional value may be predicted from boundary lines. A comparison of the optima determined via the boundary line approach and those estimated by the mean of the high yielding population revealed extremely small differences indicating that either method is acceptable for estimating these parameters.