Package {cndplantanalysis}

Empirical Cate Nelson Threshold Calculation via ANOVA Grid Search

Description

Evaluates candidate split points across bivariate diagnostic data (CND r^2 vs. Crop Yield) to automatically determine critical thresholds maximizing the ANOVA Sum of Squares Between groups (SS_{\text{between}}) (Nelson & Anderson, 1977; Khiari et al., 2001).

Usage

calc_cate_nelson_empirical(diag_data, yield_col = "Yield")

Arguments

Value

A named list containing:

Examples

{
data(plant_leaf_data)

simplex_res <- simplex_table(
  data = plant_leaf_data,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)

lc_res <- log_centered_table(
  simplex_data = simplex_res,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)
iter_res <- iteration_for_hyp(
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)
cnd_out <- cut_off_table(
  iter_data = iter_res,
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)

data(validation_data)
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","Ca","Mg","S")
)

auto_thresh <- calc_cate_nelson_empirical(diag_results, yield_col = "Yield")
print(auto_thresh)
}

Fit Cubic Models, Determine Yield Cutoff, and Extract CND High-Yield Norms

Description

Fits a cubic polynomial model F_i^C(V_X) = aY^3 + bY^2 + cY + d for each component, calculates the inflection point yield cutoff (-b / 3a), determines the maximum yield target, computes the low-yielding population percentage, and returns high-yield (hyp) and low-yield (lyp) CND norms (Khiari et al., 2001).

Usage

cut_off_table(iter_data, lc_data, yield_col, nutrient_cols, digits = 2)

Arguments

Details

Setting the second derivative of the cubic function to zero yields the inflection point:

\frac{\partial^2 F_i^C(V_X)}{\partial Y^2} = 6aY + 2b = 0 \implies Y_{\text{cutoff}} = -\frac{b}{3a}

The highest inflection point across all components is retained as the minimum yield target. The mean (V_X^*) and standard deviation (SD_X^*) of row-centered log ratios within the high-yield subpopulation (Y \ge Y_{\text{cutoff}}) form the baseline CND norms.

Value

A named list containing two data frames:

Examples

{

data(plant_leaf_data)

simplex_res <- simplex_table(
  data = plant_leaf_data,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)

lc_res <- log_centered_table(
  simplex_data = simplex_res,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)
iter_res <- iteration_for_hyp(
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)
cnd_out <- cut_off_table(
  iter_data = iter_res,
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)
print(cnd_out$cut_off_table)
print(cnd_out$ow_yield_percentage)
print(cnd_out$norms_table)
}

Diagnose Plant Tissue Specimens using CND Norms

Description

Standardizes new plant tissue samples against high-yield CND reference norms (V_X^* and SD_X^*), computing individual CND nutrient indices (I_X) and the global nutrient imbalance index (r^2).

Usage

diagnose_specimen(
  new_data,
  norms_table,
  sample_col,
  nutrient_cols,
  yield_col = NULL,
  digits = 2
)

Arguments

Details

Individual CND indices are calculated as standardized score deviations from high-yield norms:

I_X = \frac{V_X - V_X^*}{SD_X^*}

The global nutrient imbalance index (r^2) sums the squared indices across all d + 1 components:

r^2 = \sum_{i=1}^{d+1} I_{X_i}^2

Value

A data frame containing:

Examples

{
data(plant_leaf_data)
simplex_res <- simplex_table(
  data = plant_leaf_data,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)

lc_res <- log_centered_table(
  simplex_data = simplex_res,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)
iter_res <- iteration_for_hyp(
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)
cnd_out <- cut_off_table(
  iter_data = iter_res,
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)

data(validation_data)

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","Ca","Mg","S")
)
print(diag_results)
}

Iterative Partitioning and Variance Ratio Calculation for CND

Description

Iteratively partitions a yield-ordered dataset into two subpopulations (n_1 high-yielding and n_2 low-yielding specimens) across n - 3 steps, computing the variance ratio function f_i(V_X) and the cumulative variance ratio function F_i^C(V_X) for each component (Khiari et al., 2001).

Usage

iteration_for_hyp(lc_data, yield_col, nutrient_cols, digits = 2)

Arguments

Details

At each iteration i (from n_1 = 2 to n_1 = n - 2), the ratio function f_i(V_X) is evaluated as:

f_i(V_X) = \frac{\text{Var}(V_X \text{ of } n_2 \text{ low-yield observations})}{\text{Var}(V_X \text{ of } n_1 \text{ high-yield observations})}

The cumulative variance ratio function F_i^C(V_X) scales the accumulated variance ratios on a zero to hundred percentage scale:

F_i^C(V_X) = \frac{\sum_{j=1}^{i} f_j(V_X)}{\sum_{j=1}^{n-3} f_j(V_X)} \times 100

Value

A data frame containing:

Examples

{
data(plant_leaf_data)
simplex_res <- simplex_table(
  data = plant_leaf_data,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)

lc_res <- log_centered_table(
  simplex_data = simplex_res,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)
iter_res <- iteration_for_hyp(
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)
}

Generate Log-Centered Ratio Table for CND

Description

Computes row-centered log ratios (V_X) for all d + 1 components in the simplex S^d by taking the natural logarithm of each component proportion divided by the geometric mean G (Aitchison, 1986; Parent & Dafir, 1992; Khiari et al., 2001).

Usage

log_centered_table(simplex_data, sample_col, yield_col, nutrient_cols)

Arguments

Details

Row-centered log ratios transform constrained compositional tissue proportions into scale-invariant, unconstrained variables:

V_X = \ln\left(\frac{X}{G}\right)

for each nutrient X and the residual filling value R_d. A fundamental property of CND row-centered log ratios is that their sum across all d + 1 components equals zero:

\sum_{i=1}^{d+1} V_{X_i} = 0

Value

A data frame containing:

Examples

{
data(plant_leaf_data)
simplex_res <- simplex_table(
  data = plant_leaf_data,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)

lc_res <- log_centered_table(
  simplex_data = simplex_res,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)
}

Example Crop Dataset for CND

Description

A dataset containing leaf sample nutrient information for demonstrating CND methodology. All the nutrients used for analysis should in percentage (%).

Usage

plant_leaf_data

Format

An object of class data.frame with 100 rows and 7 columns.

Details

@format A data frame with 100 rows and 7 columns:

Sample

Unique identifier for each leaf sample

Yield

Yield corresponding to each sample

N

Nitrogen concentration (%)

P

Phosphorus concentration (%)

Ca

Calcium concentration (%)

Mg

Magnesium concentration (%)

S

Sulfur concentration (%)

@details This dataset is provided as an example for applying CND functions in the package. It includes macronutrients (N, P, Ca, Mg, S), Sample and yield columns.

@examples

Load the dataset

data(plant_leaf_data)

#Sorts dataset by yield, computes the residual filling value simplex_res <- simplex_table( data = plant_leaf_data, sample_col = "Sample", yield_col = "Yield", nutrient_cols = c("N", "P","Ca","Mg","S") ) print(simplex_res)

#Computes scale-invariant row-centered log ratios lc_res <- log_centered_table( simplex_data = simplex_res, sample_col = "Sample", yield_col = "Yield", nutrient_cols = c("N", "P","Ca","Mg","S") ) print(lc_res)

#Iteratively partitions the database iter_res <- iteration_for_hyp( lc_data = lc_res, yield_col = "Yield", nutrient_cols = c("N", "P","Ca","Mg","S"), digits = 2)

print(head(iter_res))

#Fits cubic models , calculates inflection point yield cutoffs and extracts high-yield norms. cnd_out <- cut_off_table( iter_data = iter_res, lc_data = lc_res, yield_col = "Yield", nutrient_cols = c("N", "P","Ca","Mg","S"), digits = 2)

print(cnd_out$cut_off_table) print(cnd_out$norms_table)

#Plots upper-tail cumulative chi-square distribution curve and marks theoretical critical threshold. plot_cnd_chisq(nutrient_cols = c("N", "P","Ca","Mg","S"), low_yield_pct = 78, max_r2 = 16)

#Generates a connected scatter plot cumulative function vs. Yield for an #individual nutrient or all nutrients simultaneously. p_cum <- plot_cumulative_variance(iter_res, lc_res, nutrient = "all") print(p_cum)

Cate Nelson Quadrant Scatter Plot for CND Imbalance Index vs. Yield

Description

Generates a publication-ready ggplot2 scatter diagram partitioning crop yield against the global CND nutrient imbalance index (r^2) using Cate Nelson ANOVA quadrant lines (Khiari et al., 2001). Automatically calculates critical split points if not provided.

Usage

plot_cate_nelson(
  diag_data,
  crit_r2 = NULL,
  crit_yield = NULL,
  yield_col = "Yield"
)

Arguments

Value

A ggplot object representing the Cate Nelson quadrant scatter diagram.

Examples

data(plant_leaf_data)

simplex_res <- simplex_table(
  data = plant_leaf_data,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)

lc_res <- log_centered_table(
  simplex_data = simplex_res,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)
iter_res <- iteration_for_hyp(
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)
cnd_out <- cut_off_table(
  iter_data = iter_res,
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)

data(validation_data)
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","Ca","Mg","S")
)

p_cn <- plot_cate_nelson(diag_results, crit_r2 = 1.4, crit_yield = 6.40)

Plot Cumulative Chi-Square Distribution Curve and Mark Theoretical Critical CND r^2

Description

Plots the theoretical upper-tail cumulative chi-square distribution curve for d + 1 degrees of freedom and marks the theoretical critical CND nutrient imbalance threshold (r^2) corresponding to the low-yield subpopulation percentage (Parent et al., 1994; Khiari et al., 2001).

Usage

plot_cnd_chisq(nutrient_cols, low_yield_pct, max_r2 = 16, digits = 2)

Arguments

Details

Because CND indices (I_X) are independent unit-normal variables, their sum of squares follows a chi-square distribution with d + 1 degrees of freedom:

r^2 = \sum_{i=1}^{d+1} I_{X_i}^2 \sim \chi^2(d + 1)

Mapping the proportion of low-yielding observations as an upper-tail cumulative probability yields the theoretical critical threshold r^2 = \text{qchisq}(p, df = d + 1, \text{lower.tail} = \text{FALSE}).

Value

Generates a plot and invisibly returns a list with df, low_yield_pct, and critical_r2.

Examples

plot_cnd_chisq(nutrient_cols = c("N", "P","Ca","Mg","S"), low_yield_pct = 78, max_r2 = 16)

Linear Regression Plot for Crop Yield vs. CND Imbalance Index (r^2)

Description

Fits a simple linear regression model relating crop yield to the global CND nutrient imbalance index (r^2) based on output from diagnose_specimen (Khiari et al., 2001).

Usage

plot_cnd_yield_linear(
  x = NULL,
  y = NULL,
  data = NULL,
  r2_col = "r2",
  yield_col = "Yield",
  critical_r2 = 1.4,
  x_label = "CND r^2",
  y_label = "Yield",
  plot_title = "Linear Yield Trend with CND Imbalance Index"
)

Arguments

Value

A list containing:

Examples

data(plant_leaf_data)
simplex_res <- simplex_table(
  data = plant_leaf_data,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)

lc_res <- log_centered_table(
  simplex_data = simplex_res,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)
iter_res <- iteration_for_hyp(
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)
cnd_out <- cut_off_table(
  iter_data = iter_res,
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)

data(validation_data)
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","Ca","Mg","S")
)

linear_result <- plot_cnd_yield_linear(
  data = diag_results,
  r2_col = "r2",
  yield_col = "Yield",
  critical_r2 = 1.4,
  y_label = "Yield",
  plot_title = "Linear Yield Trend with CND Imbalance Index"
)
linear_result$predicted_yield
summary(linear_result$model)
print(linear_result$plot)

Non-Linear Polynomial Regression Plot for Crop Yield vs. CND Imbalance Index

Description

Fits a non-linear polynomial regression model relating crop yield to the global CND nutrient imbalance index (r^2) based on output from diagnose_specimen or direct vector inputs. Predicts and visualizes the extrapolated yield at a specified critical r^2 threshold with arrow and point annotations.

Usage

plot_cnd_yield_nlr(
  x = NULL,
  y = NULL,
  data = NULL,
  r2_col = "r2",
  yield_col = "yield",
  critical_r2 = 9.65,
  x_label = "CND r^2",
  y_label = "Yield",
  plot_title = "Non-Linear Regression: Yield vs. Imbalance Index",
  poly_degree = 2
)

Arguments

Value

A list containing:

Examples

data(plant_leaf_data)
simplex_res <- simplex_table(
  data = plant_leaf_data,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)

lc_res <- log_centered_table(
  simplex_data = simplex_res,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)
iter_res <- iteration_for_hyp(
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)
cnd_out <- cut_off_table(
  iter_data = iter_res,
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"),
  digits = 2
)

data(validation_data)
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","Ca","Mg","S")
)
# Example using diagnose_specimen output data frame
nlr_result<- plot_cnd_yield_nlr(
  data = diag_results,
  r2_col = "r2",
  yield_col = "Yield",
  critical_r2 = 3.23,
  poly_degree = 2
)

nlr_result$predicted_yield
summary(nlr_result$model)
print(nlr_result$plot)

# Example using direct vector inputs
nlr_out2 <- plot_cnd_yield_nlr(
  x = diag_results$r2,
  y = diag_results$Yield,
  critical_r2 = 3.23
)

Connected Scatter Plot for Cumulative Variance Ratio Function Fi(Vx) vs. Yield

Description

Generates a connected scatter plot (line + points) using ggplot2 displaying the cumulative variance ratio function F_i^C(V_X) on the y-axis versus crop yield on the x-axis for selected nutrients or all nutrients simultaneously (Khiari et al., 2001).

Usage

plot_cumulative_variance(
  iter_data,
  lc_data,
  nutrient = "all",
  yield_col = "Yield"
)

Arguments

Value

A ggplot object representing the connected scatter plot.

Examples

data(plant_leaf_data)

simplex_res <- simplex_table(
  data = plant_leaf_data,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)

lc_res <- log_centered_table(
  simplex_data = simplex_res,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S")
)
iter_res <- iteration_for_hyp(
  lc_data = lc_res,
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"))

p_cum <- plot_cumulative_variance(iter_res, lc_res, nutrient = "all")

Generate Simplex Table for Compositional Nutrient Diagnosis (CND)

Description

Rearranges a plant tissue database by crop yield in descending order, calculates the scale-invariant filling value (R_d) for the d-dimensional simplex (S^d), and computes the geometric mean (G) across all d + 1 components (Parent & Dafir, 1992; Khiari et al., 2001).

Usage

simplex_table(data, sample_col, yield_col, nutrient_cols)

Arguments

Details

In Compositional Nutrient Diagnosis (CND), plant tissue composition forms a d-dimensional simplex (S^d) composed of d + 1 nutrient proportions including d nutrients and a residual filling value (R_d):

R_d = 100 - \sum_{i=1}^{d} \text{Nutrient}_i

The geometric mean (G) of all d + 1 components is computed as:

G = \left( \left( \prod_{i=1}^{d} \text{Nutrient}_i \right) \times R_d \right)^{\frac{1}{d + 1}}

Value

A data frame arranged in descending order of crop yield containing:

Examples

{
data(plant_leaf_data)
simplex_res <- simplex_table(
  data = plant_leaf_data,
  sample_col = "Sample",
  yield_col = "Yield",
  nutrient_cols = c("N", "P","Ca","Mg","S"))
}

Example Crop Dataset for CND norms validation

Description

A dataset containing leaf sample nutrient information for demonstrating CND norms validation methodology. All the nutrients used for analysis should in percentage (%).

Usage

validation_data

Format

An object of class data.frame with 20 rows and 7 columns.

Details

@format A data frame with 20 rows and 7 columns:

Sample

Unique identifier for each leaf sample

Yield

Yield corresponding to each sample

N

Nitrogen concentration (%)

P

Phosphorus concentration (%)

Ca

Calcium concentration (%)

Mg

Magnesium concentration (%)

S

Sulfur concentration (%)

@details This dataset is provided as an example dataset for standardizing its row-centered log ratio against the high-yield norms to obtain the CND index and to compute global nutrient imbalance index. The dataset includes following columns:Sample,Yield and macronutrients (N, P, Ca, Mg, S).

@examples

Load the dataset

data(validation_data)

#Standardizes new crop samples against norms to calculate individual CND nutrient indices and global imbalance index. 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","Ca","Mg","S")) print(diag_results)

#Evaluates candidate split pairs via ANOVA grid search to maximize between sum of squares for automated Cate–Nelson thresholding. auto_thresh <- calc_cate_nelson_empirical(diag_results, yield_col = "Yield") auto_thresh

#Generates a quadrant scatter plot (Yield vs. r^2) with automated or specified Cate–Nelson threshold lines. plot_cate_nelson(diag_results)

#If there are specified values then use function in following way p_cn <- plot_cate_nelson(diag_results, crit_r2 = 1.4, crit_yield = 6.40) print(p_cn)

#Fits a non-linear polynomial regression (ggplot2) relating crop yield to CND indices. regplot<- plot_cnd_yield_nlr( data = diag_results, r2_col = "r2", # Name of your r^2 column yield_col = "Yield", # Name of your yield column critical_r2 = 3.23, # Custom critical value y_label = "Yield", # Y-axis label plot_title = "Yield vs CND Imbalance Index") regplot

#Fits a linear regression model (ggplot2) relating crop yield to CND indices. plot <- plot_cnd_yield_linear( data = diag_results, r2_col = "r2", # Column name for r^2 yield_col = "Yield", # Column name for yield critical_r2 = 3.23, # Critical value y_label = "Yield vs CND Imbalane Index")