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Multivariate lattice deformation: A spatially explicit framework for assessing crop rotation impacts on soil nutrient dynamics

Marco Mandap

Abstract

Crop rotation impacts on soil nutrients are typically assessed using field-averaged or single-nutrient analyses that ignore spatial heterogeneity and multivariate interactions. We propose a multivariate lattice model treating soil as a 4D tensor (space, time, and N, P, K channels). Crop rotations are represented as force vectors, with soil buffering capacity ("stiffness") varying spatially with texture. Lateral nutrient movement is introduced via kernel smoothing. Cumulative impact is quantified by Euclidean distance in N-P-K space, with significance assessed via Cramer-von Mises permutation tests. Simulating a three-year corn-soybean-wheat rotation on a 20 x 20 heterogeneous grid shows mean stress of 0.63 after one cycle, with maximum 0.91 in sandy areas. Phosphorus depletion (17.9%) exceeds nitrogen (10.8%), dominating stress in 19% of cells - obscured by single-nutrient analyses. Continuous corn increases mean stress by 41%. Cramer-von Mises tests detect significant deviation (p <= 0.002), and Moran's I (0.29-0.30) confirms spatial autocorrelation. Our framework identifies risk zones and guides site-specific management, bridging geostatistics with mechanistic crop models.

Multivariate lattice deformation: A spatially explicit framework for assessing crop rotation impacts on soil nutrient dynamics

Abstract

Crop rotation impacts on soil nutrients are typically assessed using field-averaged or single-nutrient analyses that ignore spatial heterogeneity and multivariate interactions. We propose a multivariate lattice model treating soil as a 4D tensor (space, time, and N, P, K channels). Crop rotations are represented as force vectors, with soil buffering capacity ("stiffness") varying spatially with texture. Lateral nutrient movement is introduced via kernel smoothing. Cumulative impact is quantified by Euclidean distance in N-P-K space, with significance assessed via Cramer-von Mises permutation tests. Simulating a three-year corn-soybean-wheat rotation on a 20 x 20 heterogeneous grid shows mean stress of 0.63 after one cycle, with maximum 0.91 in sandy areas. Phosphorus depletion (17.9%) exceeds nitrogen (10.8%), dominating stress in 19% of cells - obscured by single-nutrient analyses. Continuous corn increases mean stress by 41%. Cramer-von Mises tests detect significant deviation (p <= 0.002), and Moran's I (0.29-0.30) confirms spatial autocorrelation. Our framework identifies risk zones and guides site-specific management, bridging geostatistics with mechanistic crop models.
Paper Structure (69 sections, 16 equations, 2 figures, 4 tables)

This paper contains 69 sections, 16 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. The Challenge of Sustainable Nutrient Management
  3. Crop Rotation as a Sustainability Strategy
  4. The Multivariate Nature of Crop Nutrient Demand
  5. Spatial Heterogeneity: The Missing Dimension
  6. Buffering Capacity as Spatially Variable Resistance
  7. Modeling Approaches: Progress and Persistent Gaps
  8. Precision Agriculture: The Data Opportunity
  9. The Deformation Analogy: A Novel Conceptual Framework
  10. Research Objectives
  11. Contribution and Significance
  12. Methods
  13. Overview of the Modeling Framework
  14. Lattice State Representation
  15. State Variables
  16. ...and 54 more sections

Figures (2)

  • Figure 1: Comparison of multivariate stress patterns between (left) baseline corn-soybean-wheat rotation and (right) continuous corn after three years. Color scale represents deformation energy $D$, the Euclidean distance in N-P-K space from initial conditions. Warmer colors indicate greater stress. Note the intensification of stress in low-buffering regions (lower-left quadrant) under continuous corn.
  • Figure 2: Spatial distribution of deformation energy ($D$) across sensitivity scenarios. From left to right, top to bottom: Baseline (standard parameters), S1 (high smoothing, $\sigma = 3.0$), S2 (low stiffness contrast), S3 (high force magnitude, 1.5$\times$), and S4 (continuous corn). Color scale represents Euclidean distance in N-P-K space from initial conditions, with warmer colors indicating greater stress. Note the homogenization in S2 and the extreme hotspots in S3.