Compositional Nutrient Diagnosis for Plant Tissue Analysis

Provides an implementation of Compositional Nutrient Diagnosis (CND) for plant tissue tests. Computes scale invariant simplex filling values(Rd), row-centered log-ratios (CLR), iterative database partitioning via Cate-Nelson procedures, cubic polynomial regression of cumulative variance ratio functions to determine inflection point yield cutoffs, critical CND nutrient imbalance thresholds (r^2) using the chi-square distribution, diagnostic standardized indices (Ix) and automated Cate Nelson scatter partitioning. Includes linear, non-linear, cumulative variance, chi-square and quadrant plotting functions.Methodology and theoretical frameworks are grounded in Parent and Dafir (1992) and Khiari et al. (2001) .

cndplantanalysis

Overview

cndplantanalysis is an R package designed for Compositional Nutrient Diagnosis (CND) of plant tissue tests. CND translates constrained leaf nutrient concentrations into unconstrained, scale-invariant row-centered log ratios within a $d$-dimensional multinomial simplex ($S^d$).

The package provides an end-to-end, reproducible workflow for:

1. Transforming raw nutrient concentrations into row-centered log ratios ($V_X$) and filling values ($R_d$).
2. Conducting iterative database partitioning via the Cate–Nelson procedure.
3. Fitting cubic polynomial regression models to cumulative variance functions $F_i^C(V_X)$ to establish objective, non-arbitrary yield cutoffs at inflection points ($-b / 3a$).
4. Deriving theoretical critical nutrient imbalance thresholds ($r^2$) mapped from the cumulative chi-square distribution with $d + 1$ degrees of freedom.
5. Standardizing independent tissue samples against high-yield (hyp) reference norms to calculate individual nutrient indices ($I_X$) and the global nutrient imbalance index ($r^2$).
6. Performing automated empirical Cate–Nelson ANOVA grid search and generating publication-ready ggplot2 diagnostic plots.

Theoretical Grounding

The statistical and agronomic methodology implemented in cndplantanalysis is grounded in foundational CND literature:

• Parent, L. E., & Dafir, M. (1992). A theoretical concept of compositional nutrient diagnosis. Journal of the American Society for Horticultural Science, 117(2), 239–242. doi:10.21273/JASHS.117.2.239
• Khiari, L., Parent, L. E., & Tremblay, N. (2001). Selecting the high-yield subpopulation for diagnosing nutrient imbalance in crops. Agronomy Journal, 93(4), 802–808. doi:10.2134/agronj2001.934802x

Installation

You can install the development version of cndplantanalysis from CRAN:

install.packages("cndplantanalysis")

Core Functions

Quick-Start Workflow Example

This example demonstrates a complete step-by-step CND analysis using survey and validation data (e.g., sweet corn survey dataset from Khiari et al., 2001):

library(cndplantanalysis)
library(ggplot2)

# ==============================================================================
# Step 1: Prepare Survey Data & Calculate Simplex Values (Rd and G)
# ==============================================================================
# Sample dataset with Yield and nutrient concentrations (N, P)
survey_data <- data.frame(
  Sample = paste0("S", 1:40),
  Yield  = c(12.93, 10.32, 8.65, 8.34, 8.21, 8.14, 8.10, 8.09, 7.93, 7.93,
             6.94, 6.94, 6.72, 6.56, 5.76, 5.75, 5.60, 5.60, 5.51, 5.48,
             5.31, 5.31, 5.16, 5.16, 4.96, 4.92, 4.76, 4.76, 4.46, 4.46,
             3.97, 3.97, 3.94, 3.89, 2.78, 2.38, 1.99, 1.99, 1.19, 1.14),
  N      = c(3.52, 4.20, 3.82, 3.55, 4.36, 4.09, 3.79, 4.48, 4.48, 3.97,
             4.47, 3.29, 4.19, 4.26, 3.72, 4.47, 3.96, 3.51, 3.48, 3.89,
             4.17, 3.86, 4.70, 4.07, 4.38, 3.79, 4.00, 4.09, 3.97, 3.92,
             3.96, 5.05, 2.66, 3.89, 4.49, 4.54, 4.69, 4.42, 4.11, 3.03),
  P      = c(0.35, 0.37, 0.65, 0.42, 0.42, 0.39, 0.48, 0.43, 0.41, 0.36,
             0.33, 0.25, 0.35, 0.80, 0.32, 0.49, 0.34, 0.31, 0.30, 0.48,
             0.38, 0.38, 0.41, 0.38, 0.43, 0.33, 0.41, 0.33, 0.46, 0.44,
             0.43, 0.60, 0.44, 0.29, 0.47, 0.41, 0.39, 0.41, 0.35, 0.42)
)

simplex_res <- simplex_table(
  data = survey_data,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P")
)

# ==============================================================================
# Step 2: Compute Row-Centered Log Ratios (Vx)
# ==============================================================================
lc_res <- log_centered_table(
  simplex_data = simplex_res,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P")
)

# ==============================================================================
# Step 3: Iterative Partitioning & Cumulative Variance Ratios
# ==============================================================================
iter_res <- iteration_for_hyp(
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P"),
  digits = 2
)

# ==============================================================================
# Step 4: Fit Cubic Models & Extract CND Reference Norms
# ==============================================================================
cnd_out <- cut_off_table(
  iter_data = iter_res,
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P"),
  digits = 2
)

# View High-Yield CND Norms
print(cnd_out$norms_table)

# ==============================================================================
# Step 5: Diagnose New/Validation Specimens
# ==============================================================================
validation_data <- data.frame(
  Sample = c("V1", "V2", "V3", "V11"),
  Yield  = c(4.97, 8.34, 3.06, 5.25),
  N      = c(3.51, 3.76, 4.09, 2.81),
  P      = c(0.30, 0.38, 0.65, 0.28)
)

diag_results <- diagnose_specimen(
  new_data = validation_data,
  norms_table = cnd_out$norms_table,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P"),
  digits = 2
)

print(diag_results)

# ==============================================================================
# Step 6: Visualizations & Cate–Nelson Partitioning
# ==============================================================================
# A. Cumulative Variance Curve
p1 <- plot_cumulative_variance(iter_res, lc_res, nutrient = "all")

# B. Chi-Square Distribution Threshold
p2 <- plot_cnd_chisq(nutrient_cols = c("N", "P"), low_yield_pct = 67.5)

# C. Cate–Nelson Quadrant Scatter Plot
p3 <- plot_cate_nelson(diag_results, crit_r2 = 1.4, crit_yield = 6.40)

# D. Non-Linear Yield vs. r^2 Response
p4 <- plot_cnd_yield_nlr(
  data = diag_results,
  r2_col = "r2",
  yield_col = "Yield",
  critical_r2 = 1.4,
  plot_title = "Yield vs CND Nutrient Imbalance Index (r²)"
)

Authors

• Blesson B. Varghese
• Rohith A K
• Aliya Shirin K S
• Anjali S.
• Hilal Mohamed

License

This package is licensed under the GPL-3 License.