Prediction summaries and figures - didactic tutorial

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Last updated: 2026-04-08

Checks: 6 1

Knit directory: Integrating-nir-genomic-kernel/

This reproducible R Markdown analysis was created with workflowr (version 1.7.2). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.

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R Markdown file: uncommitted changes

The R Markdown file has unstaged changes. To know which version of the R Markdown file created these results, you’ll want to first commit it to the Git repo. If you’re still working on the analysis, you can ignore this warning. When you’re finished, you can run wflow_publish to commit the R Markdown file and build the HTML.

Environment: empty

Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

Seed: set.seed(20250829)

The command set.seed(20250829) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

Session information: recorded

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Cache: none

Nice! There were no cached chunks for this analysis, so you can be confident that you successfully produced the results during this run.

File paths: relative

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Repository version: 527ffca

Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility.

The results in this page were generated with repository version 527ffca. See the Past versions tab to see a history of the changes made to the R Markdown and HTML files.

Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated:

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---

Language / Idioma: English | Português

This file is the didactic version of the visualization stage. Its purpose is to take the raw prediction outputs produced in analysis_prediction_run_outputs.Rmd, reorganize them into interpretable summary tables, and then translate those summaries into compact comparisons and final figures.

At this point in the pipeline, the main analytical question is no longer how each model is specified, but how the fitted models behave under different prediction problems. For that reason, the visualization stage moves from model construction to model interpretation. It brings together performance summaries for CV1, CV2, CV0, and CV00, highlights contrasts between models with and without the weather kernel (W), and organizes the results into tables and figures that are easier to inspect than the raw prediction files themselves.

The current prediction workflow saves raw outputs in output/results/ using filenames that encode the validation scenario, trait, fitted model, repetition, and fold. For CV0 and CV00, the held-out environment label is also recorded in the filename and is later matched to Env through the filter Env == Env_leave. This naming structure is essential because it connects the execution stage to the interpretation stage.

Throughout this tutorial, the weather kernel (W) should be interpreted as a weather-derived source of similarity that complements, but does not replace, the categorical environment effect (E). The phenomic component (P) should also be interpreted carefully, because NIRS-based similarity can reflect strong environmental response in addition to potentially useful predictive signal.

What this script does

The workflow is organized around four practical tasks:

1. locate and read the prediction CSV files;
2. parse the filenames and recover trait, model, repetition, and leave-one-environment-out information;
3. summarize results for CV1, CV2, CV0, and CV00;
4. export clean tables and figures for the next manuscript-oriented stage.

To make interpretation easier, the models are ordered to help answer three practical questions:

1. does moving from linear to Gaussian or arc-cosine kernels improve predictive ability?
2. does adding the weather kernel (W) improve predictive ability?
3. does combining genomic and phenomic information improve predictive ability?

Inputs, outputs and next step

Inputs of this step - raw prediction outputs written by analysis_prediction_run_outputs.Rmd - light prediction metadata tables generated in the previous stage

Outputs of this step - final summary tables - model rankings - W-effect comparisons - kernel-family comparisons - final figures for downstream interpretation

Next step - the outputs generated here feed the manuscript-oriented summaries and the final interpretation of the project results.

1. Setup

The document begins by defining a consistent rendering style for code, tables, and figures. This helps the tutorial remain readable when it is inspected in HTML and keeps the visual presentation stable across the different outputs produced in this stage.

knitr::opts_chunk$set( echo = TRUE,
 warning = FALSE,
 message = FALSE,
 fig.width = 13,
 fig.height = 8,
  out.width = "100%" )

2. Load packages and locate project folders

The visualization stage depends on a small set of packages for data manipulation, figure construction, and table formatting. It also needs to locate the project folders correctly, because the summaries generated here must be written in stable output paths that can later be reused by the site and by manuscript-oriented materials.

This section standardizes the project root, locates the folders that contain the prediction outputs, and prepares the directories in which the final tables and figures will be written.

rm(list = ls())
options(scipen = 999)
packages_needed <- c( "dplyr",
 "tidyr",
 "readr",
 "tibble",
 "ggplot2",
 "ggthemes",
 "knitr",
 "kableExtra",
  "stringr" )
packages_missing <- packages_needed[!(packages_needed %in% installed.packages()[, "Package"])]
if (length(packages_missing) > 0) {
  stop(
    paste0(
      "The following packages are required for this module but are not installed: ",
      paste(packages_missing, collapse = ", "),
      ". Install them before rendering visualization.Rmd."
    )
  )
}
library(dplyr)
library(tidyr)
library(readr)
library(tibble)
library(ggplot2)
library(ggthemes)
library(knitr)
library(kableExtra)
library(stringr)
project_root <- getwd()
if (!dir.exists(file.path(project_root, "output")) && dir.exists(file.path(project_root, "..", "output"))) {
  project_root <- normalizePath(file.path(project_root, ".."))
}
if (!dir.exists(file.path(project_root, "output"))) {
  stop("Could not find the folder 'output/'.\nRun this script from the project root or from analysis/.")
}
results_dir <- file.path(project_root, "output", "results")
figures_dir <- file.path(project_root, "output", "figures")
tables_dir <- file.path(project_root, "output", "tables")
dir.create(figures_dir, recursive = TRUE, showWarnings = FALSE)
dir.create(tables_dir, recursive = TRUE, showWarnings = FALSE)

3. Model catalog used in the reduced pipeline

The visualization stage uses the same reduced catalog of 18 models adopted in the prediction workflow. Here that catalog is reorganized so that the summaries are easier to interpret in analytical terms. Instead of showing only model numbers, the table emphasizes the pathway being represented, the kernel family being used, and whether weather information is present.

This organization is important because the comparisons shown later in the document are not arbitrary. They are designed to help the reader understand where predictive gains come from and whether those gains are associated with weather information, kernel choice, or integration between genomic and phenomic sources.

model_catalog <- tibble( ModelNumber = c(1, 10, 3, 13, 5, 16, 2, 11, 4, 14, 6, 17, 7, 12, 8, 15, 9, 18),
 Model = paste0("Eta", c(1, 10, 3, 13, 5, 16, 2, 11, 4, 14, 6, 17, 7, 12, 8, 15, 9, 18)),
 Pathway = c( rep("Genomic pathway", 6), rep("Phenomic pathway", 6), rep("Combined G + P pathway", 6) ),
 KernelFamily = c( "Linear", "Linear", "Gaussian", "Gaussian", "Arc-cosine", "Arc-cosine", "Linear", "Linear", "Gaussian", "Gaussian", "Arc-cosine", "Arc-cosine", "Linear", "Linear", "Gaussian", "Gaussian", "Arc-cosine", "Arc-cosine" ),
 WeatherStatus = c( "Without W", "With W", "Without W", "With W", "Without W", "With W", "Without W", "With W", "Without W", "With W", "Without W", "With W", "Without W", "With W", "Without W", "With W", "Without W", "With W" ),
 Group = c( "Genomic baseline", "Weather single-source", "Genomic baseline", "Weather single-source", "Genomic baseline", "Weather single-source", "Phenomic baseline", "Weather single-source", "Phenomic baseline", "Weather single-source", "Phenomic baseline", "Weather single-source", "Combined baseline", "Weather combined", "Combined baseline", "Weather combined", "Combined baseline", "Weather combined" ),
 Description = c( "Genomic linear + E", "Genomic linear + W", "Genomic Gaussian + E", "Genomic Gaussian + W", "Genomic arc-cosine + E", "Genomic arc-cosine + W", "Phenomic linear + E", "Phenomic linear + W", "Phenomic Gaussian + E", "Phenomic Gaussian + W", "Phenomic arc-cosine + E", "Phenomic arc-cosine + W", "Combined linear + E", "Combined linear + W", "Combined Gaussian + E", "Combined Gaussian + W", "Combined arc-cosine + E", "Combined arc-cosine + W" ),
  ShortDescription = c( "G + E", "G + W", "GGK + E", "GGK + W", "GAK + E", "GAK + W", "P + E", "P + W", "PGK + E", "PGK + W", "PAK + E", "PAK + W", "G+P + E", "G+P + W", "GGK+PGK + E", "GGK+PGK + W", "GAK+PAK + E", "GAK+PAK + W" ) )
model_catalog

4. Comparison pairs used for W versus no-W contrasts

A central question in this project is whether adding the weather kernel (W) improves predictive ability. To answer that question fairly, the comparison must always be made between models that are structurally similar and differ only by the inclusion of weather information.

The comparison pairs defined below provide exactly that structure. They are later used to build tables that quantify how much predictive performance changes when W is introduced within the same pathway and kernel family.

comparison_pairs <- tibble( Comparison = c( "Genomic linear", "Genomic Gaussian", "Genomic arc-cosine", "Phenomic linear", "Phenomic Gaussian", "Phenomic arc-cosine", "Combined linear", "Combined Gaussian", "Combined arc-cosine" ),
 WithoutW = c("Eta1", "Eta3", "Eta5", "Eta2", "Eta4", "Eta6", "Eta7", "Eta8", "Eta9"),
  WithW = c("Eta10", "Eta13", "Eta16", "Eta11", "Eta14", "Eta17", "Eta12", "Eta15", "Eta18") )
comparison_pairs

5. Locate prediction files

The first operational step of the visualization stage is to locate the raw prediction files produced by the previous module. Under the current pipeline standard, these files are saved recursively inside output/results/, with an explicit directory hierarchy by validation scheme, trait, repetition, and fold.

At this stage, the script reads the results folder recursively, keeps only the prediction CSVs stored inside the structured CV1, CV2, CV0, and CV00 branches, and ignores other artifacts such as bglr_runs. This makes the downstream summaries compatible with the new Rep/Fold contract while preserving the distinction between genotype-based and leave-one-environment-out validation problems.

all_result_rel_paths <- list.files(
  results_dir,
  pattern = "\\.csv$",
  full.names = FALSE,
  recursive = TRUE
)

all_result_rel_paths <- gsub("\\\\", "/", all_result_rel_paths)

structured_idx <- grepl("^CV1/|^CV2/|^CV0/|^CV00/", all_result_rel_paths)
all_result_rel_paths <- all_result_rel_paths[structured_idx]
all_result_files <- file.path(results_dir, all_result_rel_paths)

cv12_idx <- grepl("^CV1/|^CV2/", all_result_rel_paths)
cvloo_idx <- grepl("^CV0/|^CV00/", all_result_rel_paths)

cv12_files <- all_result_files[cv12_idx]
cv12_rel_paths <- all_result_rel_paths[cv12_idx]

cvloo_files <- all_result_files[cvloo_idx]
cvloo_rel_paths <- all_result_rel_paths[cvloo_idx]

cat("Number of CV1/CV2 files:", length(cv12_files), "\n")

Number of CV1/CV2 files: 3600 

cat("Number of CV0/CV00 files:", length(cvloo_files), "\n")

Number of CV0/CV00 files: 14400 

if (length(cv12_files) == 0 && length(cvloo_files) == 0) {
  stop(
    "No prediction CSV files were found in output/results/. ",
    "Run analysis_prediction_run_outputs first."
  )
}

6. Read CV1 and CV2 files generated by the final prediction script

The CV1 and CV2 files contain the raw outputs needed to summarize prediction performance when the challenge is defined on the genotype axis. In the current workflow, repetition and fold are encoded both in the directory hierarchy and in the filename, so the script reconstructs those metadata explicitly before building the summaries.

This design is useful because it keeps the file system organized for quick inspection while still allowing the visualization stage to rebuild unified tables across repetitions and folds.

cv12_list <- vector("list", length(cv12_files))

for (i in seq_along(cv12_files)) {
  current_file <- cv12_files[i]
  current_rel_path <- cv12_rel_paths[i]
  path_parts <- strsplit(current_rel_path, "/")[[1]]

  if (length(path_parts) != 5) {
    stop(
      "Unexpected directory structure for CV1/CV2 file: ",
      current_rel_path,
      ". Expected pattern CV1/<trait>/repXX/foldXX/<file>.csv or ",
      "CV2/<trait>/repXX/foldXX/<file>.csv."
    )
  }

  current_cv <- path_parts[1]
  trait_from_path <- path_parts[2]
  rep_from_path <- as.numeric(gsub("^rep", "", path_parts[3]))
  fold_from_path <- as.numeric(gsub("^fold", "", path_parts[4]))

  file_name <- sub("\\.csv$", "", basename(current_file))
  file_parts <- strsplit(file_name, "_")[[1]]

  if (length(file_parts) != 5) {
    stop(
      "Unexpected filename for CV1/CV2 file: ",
      file_name,
      ". Expected pattern CV1_<trait>_Eta<model>_repXX_foldXX.csv or ",
      "CV2_<trait>_Eta<model>_repXX_foldXX.csv."
    )
  }

  current_trait <- file_parts[2]
  current_model_label <- file_parts[3]
  current_model_number <- as.numeric(gsub("^Eta", "", current_model_label))
  current_rep <- as.numeric(gsub("^rep", "", file_parts[4]))
  current_fold <- as.numeric(gsub("^fold", "", file_parts[5]))

  if (
    !identical(current_cv, file_parts[1]) ||
    !identical(trait_from_path, current_trait) ||
    !identical(rep_from_path, current_rep) ||
    !identical(fold_from_path, current_fold)
  ) {
    stop("Mismatch between path and filename metadata in: ", current_rel_path)
  }

  current_data <- readr::read_csv(current_file, show_col_types = FALSE)

  if (!("Env" %in% names(current_data)) || !("cor" %in% names(current_data))) {
    stop(
      "Unexpected column structure in file: ",
      file_name,
      ". The final prediction script should export columns including Env and cor."
    )
  }

  current_data <- current_data %>%
    mutate(
      RelativePath = current_rel_path,
      Fold = current_fold,
      CV = current_cv,
      Trait = current_trait,
      ModelNumber = current_model_number,
      Model = current_model_label,
      Rep = current_rep
    )

  cv12_list[[i]] <- current_data
}

cv12_raw <- bind_rows(cv12_list) %>%
  left_join(model_catalog, by = c("ModelNumber", "Model"))

if (!("Runtime_sec" %in% names(cv12_raw))) {
  cv12_raw$Runtime_sec <- NA_real_
}

readr::write_csv(cv12_raw, file.path(tables_dir, "prediction_cv1_cv2_raw.csv"))

7. Read CV0 and CV00 files generated by the final prediction script

The CV0 and CV00 files represent the most demanding prediction problems in the study because they involve a held-out environment. Under the current pipeline standard, the held-out environment is encoded both in the directory hierarchy and in the filename, so the script reconstructs that information explicitly before the leave-one-environment-out summaries are built.

This section reads those files, checks the consistency of the structured paths, and prepares the metadata needed to keep Env_leave explicit throughout the summaries.

cvloo_list <- vector("list", length(cvloo_files))

for (i in seq_along(cvloo_files)) {
  current_file <- cvloo_files[i]
  current_rel_path <- cvloo_rel_paths[i]
  path_parts <- strsplit(current_rel_path, "/")[[1]]

  if (length(path_parts) != 6) {
    stop(
      "Unexpected directory structure for CV0/CV00 file: ",
      current_rel_path,
      ". Expected pattern CV0/<Env_leave>/<trait>/repXX/foldXX/<file>.csv or ",
      "CV00/<Env_leave>/<trait>/repXX/foldXX/<file>.csv."
    )
  }

  current_cv <- path_parts[1]
  env_from_path <- path_parts[2]
  trait_from_path <- path_parts[3]
  rep_from_path <- as.numeric(gsub("^rep", "", path_parts[4]))
  fold_from_path <- as.numeric(gsub("^fold", "", path_parts[5]))

  file_name <- sub("\\.csv$", "", basename(current_file))
  file_parts <- strsplit(file_name, "_")[[1]]

  if (length(file_parts) < 6) {
    stop(
      "Unexpected filename for CV0/CV00 file: ",
      file_name,
      ". Expected pattern CV0_<trait>_<Env_leave>_Eta<model>_repXX_foldXX.csv or ",
      "CV00_<trait>_<Env_leave>_Eta<model>_repXX_foldXX.csv."
    )
  }

  current_trait <- file_parts[2]
  current_model_label <- file_parts[length(file_parts) - 2]
  current_model_number <- as.numeric(gsub("^Eta", "", current_model_label))
  current_rep <- as.numeric(gsub("^rep", "", file_parts[length(file_parts) - 1]))
  current_fold <- as.numeric(gsub("^fold", "", file_parts[length(file_parts)]))
  current_env_leave <- paste(file_parts[3:(length(file_parts) - 3)], collapse = "_")

  if (
    !identical(current_cv, file_parts[1]) ||
    !identical(env_from_path, current_env_leave) ||
    !identical(trait_from_path, current_trait) ||
    !identical(rep_from_path, current_rep) ||
    !identical(fold_from_path, current_fold)
  ) {
    stop("Mismatch between path and filename metadata in: ", current_rel_path)
  }

  current_data <- readr::read_csv(current_file, show_col_types = FALSE)

  if (!("Env" %in% names(current_data)) || !("cor" %in% names(current_data))) {
    stop(
      "Unexpected column structure in file: ",
      file_name,
      ". The final prediction script should export columns including Env and cor."
    )
  }

  current_data <- current_data %>%
    mutate(
      RelativePath = current_rel_path,
      Fold = current_fold,
      CV = current_cv,
      Trait = current_trait,
      Env_leave = current_env_leave,
      ModelNumber = current_model_number,
      Model = current_model_label,
      Rep = current_rep
    )

  cvloo_list[[i]] <- current_data
}

cvloo_raw <- bind_rows(cvloo_list) %>%
  left_join(model_catalog, by = c("ModelNumber", "Model"))

if (!("Runtime_sec" %in% names(cvloo_raw))) {
  cvloo_raw$Runtime_sec <- NA_real_
}

readr::write_csv(cvloo_raw, file.path(tables_dir, "prediction_cv0_cv00_raw.csv"))
readr::write_csv(model_catalog, file.path(tables_dir, "prediction_model_catalog.csv"))

8. Summarize CV1 and CV2

This stage builds the summaries for CV1 and CV2 in a stepwise way: first by environment and fold, then by environment within repetition, then by repetition, and finally by model-level means and standard deviations across repetitions.

Once the raw CV1 and CV2 files have been assembled, the next goal is to summarize them in a form that supports interpretation rather than file inspection. The summaries move from lower-level information to increasingly aggregated views, so that each model can be evaluated in terms of its typical predictive behavior across repetitions, folds, and environments.

This hierarchy is important because raw prediction files are too granular for interpretation. What matters at this stage is the stable performance pattern of each model under each validation scenario.

cv12_env_fold <- cv12_raw %>%
  group_by( ModelNumber,
   Model,
   Group,
   Pathway,
   KernelFamily,
   WeatherStatus,
   Description,
   ShortDescription,
   Trait,
   CV,
   Rep,
   Fold,
    Env ) %>%
  summarise( EnvCorrelation = mean(cor, na.rm = TRUE),
   ValidationCount = sum(!is.na(cor)),
   MeanRuntimeSec = mean(Runtime_sec, na.rm = TRUE),
    .groups = "drop" ) %>%
  mutate( EnvCorrelation = ifelse(is.nan(EnvCorrelation), NA_real_, EnvCorrelation),
    MeanRuntimeSec = ifelse(is.nan(MeanRuntimeSec), NA_real_, MeanRuntimeSec) ) %>%
  filter(!is.na(EnvCorrelation), ValidationCount > 0)
cv12_env_rep <- cv12_env_fold %>%
  group_by( ModelNumber,
   Model,
   Group,
   Pathway,
   KernelFamily,
   WeatherStatus,
   Description,
   ShortDescription,
   Trait,
   CV,
   Rep,
    Env ) %>%
  summarise( EnvCorrelation = weighted.mean(EnvCorrelation, w = ValidationCount, na.rm = TRUE),
   ValidationCount = sum(ValidationCount, na.rm = TRUE),
   MeanRuntimeSec = mean(MeanRuntimeSec, na.rm = TRUE),
    .groups = "drop" )
cv12_rep_summary <- cv12_env_rep %>%
  group_by( ModelNumber,
   Model,
   Group,
   Pathway,
   KernelFamily,
   WeatherStatus,
   Description,
   ShortDescription,
   Trait,
   CV,
    Rep ) %>%
  summarise( WeightedCorrelation = weighted.mean(EnvCorrelation, w = ValidationCount, na.rm = TRUE),
   MeanRuntimeSec = mean(MeanRuntimeSec, na.rm = TRUE),
    .groups = "drop" )
cv12_summary <- cv12_rep_summary %>%
  group_by( ModelNumber,
   Model,
   Group,
   Pathway,
   KernelFamily,
   WeatherStatus,
   Description,
   ShortDescription,
   Trait,
    CV ) %>%
  summarise( MeanCorrelation = mean(WeightedCorrelation, na.rm = TRUE),
   SDCorrelation = sd(WeightedCorrelation, na.rm = TRUE),
   NumberOfRepetitions = n(),
   MeanRuntimeSec = mean(MeanRuntimeSec, na.rm = TRUE),
    .groups = "drop" ) %>%
  mutate( SDCorrelation = ifelse(is.na(SDCorrelation), 0, SDCorrelation) )
readr::write_csv(cv12_env_fold, file.path(tables_dir, "prediction_cv1_cv2_by_rep_fold_env.csv"))
readr::write_csv(cv12_env_rep, file.path(tables_dir, "prediction_cv1_cv2_by_rep_env.csv"))
readr::write_csv(cv12_rep_summary, file.path(tables_dir, "prediction_cv1_cv2_by_rep.csv"))
readr::write_csv(cv12_summary, file.path(tables_dir, "prediction_cv1_cv2_summary.csv"))

9. Summarize CV0 and CV00

For leave-one-environment-out scenarios, the script first restricts the summaries to rows in which Env == Env_leave. This keeps only the held-out-environment component that is conceptually relevant for CV0 and CV00.

The summaries for CV0 and CV00 follow the same general logic as the CV1/CV2 summaries, but they keep the held-out environment explicit. This distinction is essential because predictive performance in leave-one-environment-out settings can vary strongly across environments.

By preserving Env_leave in the final tables, the script allows the reader to see not only which models perform well on average, but also whether that behavior is stable across the different environmental contexts.

cvloo_env_filtered <- cvloo_raw %>%
  filter(Env == Env_leave)
cvloo_env_fold <- cvloo_env_filtered %>%
  group_by( ModelNumber,
   Model,
   Group,
   Pathway,
   KernelFamily,
   WeatherStatus,
   Description,
   ShortDescription,
   Trait,
   CV,
   Env_leave,
   Rep,
   Fold,
    Env ) %>%
  summarise( LOEOCorrelation = mean(cor, na.rm = TRUE),
   ValidationCount = sum(!is.na(cor)),
   MeanRuntimeSec = mean(Runtime_sec, na.rm = TRUE),
    .groups = "drop" ) %>%
  mutate( LOEOCorrelation = ifelse(is.nan(LOEOCorrelation), NA_real_, LOEOCorrelation),
    MeanRuntimeSec = ifelse(is.nan(MeanRuntimeSec), NA_real_, MeanRuntimeSec) ) %>%
  filter(!is.na(LOEOCorrelation), ValidationCount > 0)
cvloo_rep_summary <- cvloo_env_fold %>%
  group_by( ModelNumber,
   Model,
   Group,
   Pathway,
   KernelFamily,
   WeatherStatus,
   Description,
   ShortDescription,
   Trait,
   CV,
   Env_leave,
    Rep ) %>%
  summarise( LOEOCorrelation = weighted.mean(LOEOCorrelation, w = ValidationCount, na.rm = TRUE),
   ValidationCount = sum(ValidationCount, na.rm = TRUE),
   MeanRuntimeSec = mean(MeanRuntimeSec, na.rm = TRUE),
    .groups = "drop" )
cvloo_summary <- cvloo_rep_summary %>%
  group_by( ModelNumber,
   Model,
   Group,
   Pathway,
   KernelFamily,
   WeatherStatus,
   Description,
   ShortDescription,
   Trait,
   CV,
    Env_leave ) %>%
  summarise( MeanCorrelation = mean(LOEOCorrelation, na.rm = TRUE),
   SDCorrelation = sd(LOEOCorrelation, na.rm = TRUE),
   NumberOfRuns = n(),
   MeanRuntimeSec = mean(MeanRuntimeSec, na.rm = TRUE),
    .groups = "drop" ) %>%
  mutate( SDCorrelation = ifelse(is.na(SDCorrelation), 0, SDCorrelation) )
readr::write_csv(cvloo_env_fold, file.path(tables_dir, "prediction_cv0_cv00_by_rep_fold_env.csv"))
readr::write_csv(cvloo_rep_summary, file.path(tables_dir, "prediction_cv0_cv00_by_run.csv"))
readr::write_csv(cvloo_summary, file.path(tables_dir, "prediction_cv0_cv00_summary.csv"))

10. Comparison tables

The summary tables describe model performance, but they do not yet answer the comparative questions that motivated the reduced pipeline. Those questions require derived contrasts, especially between models without and with W, and between different kernel families within the same pathway.

The tables built in this section reorganize the summaries into analytical comparisons that are easier to interpret and easier to carry into manuscript-oriented outputs.

cv12_w_effect <- comparison_pairs %>%
  left_join( cv12_summary %>% select(Trait, CV, Model, MeanCorrelation, SDCorrelation),
    by = c("WithoutW" = "Model") ) %>%
  rename( MeanWithoutW = MeanCorrelation, SDWithoutW = SDCorrelation ) %>%
  left_join( cv12_summary %>% select(Trait, CV, Model, MeanCorrelation, SDCorrelation),
    by = c("WithW" = "Model", "Trait", "CV") ) %>%
  rename( MeanWithW = MeanCorrelation, SDWithW = SDCorrelation ) %>%
  mutate( DeltaWithW = MeanWithW - MeanWithoutW ) %>%
  arrange(Trait, CV, Comparison)
cvloo_w_effect <- comparison_pairs %>%
  left_join( cvloo_summary %>% select(Trait, CV, Env_leave, Model, MeanCorrelation, SDCorrelation),
    by = c("WithoutW" = "Model") ) %>%
  rename( MeanWithoutW = MeanCorrelation, SDWithoutW = SDCorrelation ) %>%
  left_join( cvloo_summary %>% select(Trait, CV, Env_leave, Model, MeanCorrelation, SDCorrelation),
    by = c("WithW" = "Model", "Trait", "CV", "Env_leave") ) %>%
  rename( MeanWithW = MeanCorrelation, SDWithW = SDCorrelation ) %>%
  mutate( DeltaWithW = MeanWithW - MeanWithoutW ) %>%
  arrange(Trait, CV, Env_leave, Comparison)
cv12_kernel_family_compare <- cv12_summary %>%
  select(Trait, CV, Pathway, WeatherStatus, KernelFamily, MeanCorrelation) %>%
  pivot_wider(names_from = KernelFamily, values_from = MeanCorrelation) %>%
  mutate( Delta_Gaussian_vs_Linear = Gaussian - Linear,
   Delta_ArcCos_vs_Linear = `Arc-cosine` - Linear,
    Delta_ArcCos_vs_Gaussian = `Arc-cosine` - Gaussian ) %>%
  arrange(Trait, CV, Pathway, WeatherStatus)
cvloo_kernel_family_compare <- cvloo_summary %>%
  select(Trait, CV, Env_leave, Pathway, WeatherStatus, KernelFamily, MeanCorrelation) %>%
  pivot_wider(names_from = KernelFamily, values_from = MeanCorrelation) %>%
  mutate( Delta_Gaussian_vs_Linear = Gaussian - Linear,
   Delta_ArcCos_vs_Linear = `Arc-cosine` - Linear,
    Delta_ArcCos_vs_Gaussian = `Arc-cosine` - Gaussian ) %>%
  arrange(Trait, CV, Env_leave, Pathway, WeatherStatus)
readr::write_csv(cv12_w_effect, file.path(tables_dir, "prediction_cv1_cv2_w_effect_pairs.csv"))
readr::write_csv(cvloo_w_effect, file.path(tables_dir, "prediction_cv0_cv00_w_effect_pairs.csv"))
readr::write_csv(cv12_kernel_family_compare,
  file.path(tables_dir, "prediction_cv1_cv2_kernel_family_compare.csv"))
readr::write_csv(cvloo_kernel_family_compare,
  file.path(tables_dir, "prediction_cv0_cv00_kernel_family_compare.csv"))

11. Compact display tables

The full summaries are useful for traceability, but they are often too dense for quick inspection. For that reason, this stage also produces compact display tables that preserve the main analytical information while making the results easier to read in reports, supplementary material, or classroom discussion.

These reduced tables are especially useful when the reader wants to compare pathways, kernel families, or the relative position of the best-performing models without scanning the full outputs.

cv12_table_display <- cv12_summary %>%
  arrange(Trait, CV, Pathway, KernelFamily, WeatherStatus) %>%
  mutate( MeanCorrelation = round(MeanCorrelation, 3),
   SDCorrelation = round(SDCorrelation, 3),
    MeanRuntimeSec = round(MeanRuntimeSec, 2) ) %>%
  select( Trait,
   CV,
   Pathway,
   KernelFamily,
   WeatherStatus,
   ShortDescription,
   MeanCorrelation,
   SDCorrelation,
   NumberOfRepetitions,
    MeanRuntimeSec )
cvloo_table_display <- cvloo_summary %>%
  arrange(Trait, CV, Env_leave, Pathway, KernelFamily, WeatherStatus) %>%
  mutate( MeanCorrelation = round(MeanCorrelation, 3),
   SDCorrelation = round(SDCorrelation, 3),
    MeanRuntimeSec = round(MeanRuntimeSec, 2) ) %>%
  select( Trait,
   CV,
   Env_leave,
   Pathway,
   KernelFamily,
   WeatherStatus,
   ShortDescription,
   MeanCorrelation,
   SDCorrelation,
   NumberOfRuns,
    MeanRuntimeSec )
cv12_top3 <- cv12_summary %>%
  group_by(Trait, CV) %>%
  slice_max(order_by = MeanCorrelation, n = 3, with_ties = FALSE) %>%
  ungroup() %>%
  mutate( MeanCorrelation = round(MeanCorrelation, 3), SDCorrelation = round(SDCorrelation, 3) ) %>%
  select(Trait, CV, ShortDescription, MeanCorrelation, SDCorrelation)
cvloo_top3 <- cvloo_summary %>%
  group_by(Trait, CV, Env_leave) %>%
  slice_max(order_by = MeanCorrelation, n = 3, with_ties = FALSE) %>%
  ungroup() %>%
  mutate( MeanCorrelation = round(MeanCorrelation, 3), SDCorrelation = round(SDCorrelation, 3) ) %>%
  select(Trait, CV, Env_leave, ShortDescription, MeanCorrelation, SDCorrelation)
readr::write_csv(cv12_table_display, file.path(tables_dir, "prediction_cv1_cv2_display_table.csv"))
readr::write_csv(cvloo_table_display, file.path(tables_dir, "prediction_cv0_cv00_display_table.csv"))
readr::write_csv(cv12_top3, file.path(tables_dir, "prediction_cv1_cv2_top3.csv"))
readr::write_csv(cvloo_top3, file.path(tables_dir, "prediction_cv0_cv00_top3.csv"))

12. Top-3 tables

A compact ranking is often the easiest way to communicate the strongest results of a prediction study. The Top-3 tables below identify the best-performing models within each validation setting and help the reader quickly see which pathways dominate under each prediction problem.

The first table focuses on CV1 and CV2, where the challenge is defined around new or partially observed genotypes.

cv12_top3 %>%
  knitr::kable( caption = "Top 3 models for each trait and validation scheme in CV1 and CV2.",
    align = "llccc" ) %>%
  kableExtra::kable_styling( bootstrap_options = c("striped", "hover", "condensed", "responsive"),
   full_width = FALSE,
    position = "left" )

Top 3 models for each trait and validation scheme in CV1 and CV2.

Trait	CV	ShortDescription	MeanCorrelation	SDCorrelation
GY	CV1	GGK + W	0.727	0.012
GY	CV1	G + W	0.725	0.011
GY	CV1	GGK+PGK + W	0.723	0.011
GY	CV2	GGK+PGK + W	0.991	0.000
GY	CV2	GGK+PGK + E	0.989	0.000
GY	CV2	G + W	0.984	0.000
KW	CV1	P + E	0.762	0.010
KW	CV1	P + W	0.761	0.005
KW	CV1	G+P + E	0.728	0.015
KW	CV2	G+P + W	0.994	0.001
KW	CV2	GGK+PGK + W	0.994	0.000
KW	CV2	G+P + E	0.994	0.000

The second table focuses on CV0 and CV00, where performance is also conditioned by the held-out environment.

cvloo_top3 %>%
  knitr::kable( caption = "Top 3 models for each trait, validation scheme, and held-out environment in CV0 and CV00.",
    align = "lllccc" ) %>%
  kableExtra::kable_styling( bootstrap_options = c("striped", "hover", "condensed", "responsive"),
   full_width = FALSE,
    position = "left" )

Top 3 models for each trait, validation scheme, and held-out environment in CV0 and CV00.

Trait	CV	Env_leave	ShortDescription	MeanCorrelation	SDCorrelation
GY	CV0	CS11_WS	GAK + E	0.926	0.000
GY	CV0	CS11_WS	GAK + W	0.924	0.003
GY	CV0	CS11_WS	GGK + E	0.923	0.000
GY	CV0	CS11_WW	GGK + W	0.896	0.000
GY	CV0	CS11_WW	G + W	0.896	0.000
GY	CV0	CS11_WW	GGK + E	0.894	0.001
GY	CV0	CS12_WS	GGK + E	0.896	0.001
GY	CV0	CS12_WS	G + E	0.894	0.001
GY	CV0	CS12_WS	GGK + W	0.893	0.001
GY	CV0	CS12_WW	G + W	0.909	0.000
GY	CV0	CS12_WW	GGK + W	0.907	0.000
GY	CV0	CS12_WW	G + E	0.904	0.001
GY	CV00	CS11_WS	GAK + W	0.735	0.014
GY	CV00	CS11_WS	GAK + E	0.732	0.013
GY	CV00	CS11_WS	G + W	0.720	0.016
GY	CV00	CS11_WW	G + E	0.741	0.010
GY	CV00	CS11_WW	GGK + W	0.740	0.013
GY	CV00	CS11_WW	G + W	0.738	0.012
GY	CV00	CS12_WS	GGK + W	0.734	0.007
GY	CV00	CS12_WS	G + W	0.733	0.007
GY	CV00	CS12_WS	GGK + E	0.730	0.011
GY	CV00	CS12_WW	GGK+PGK + W	0.714	0.013
GY	CV00	CS12_WW	GGK + W	0.713	0.009
GY	CV00	CS12_WW	G + W	0.710	0.008
KW	CV0	CS11_WS	GAK + E	0.961	0.000
KW	CV0	CS11_WS	GGK + E	0.960	0.000
KW	CV0	CS11_WS	G + E	0.960	0.000
KW	CV0	CS11_WW	G + W	0.889	0.000
KW	CV0	CS11_WW	GGK+PGK + W	0.888	0.001
KW	CV0	CS11_WW	GGK + W	0.887	0.001
KW	CV0	CS12_WS	GGK + W	0.899	0.001
KW	CV0	CS12_WS	GGK + E	0.898	0.001
KW	CV0	CS12_WS	G + W	0.897	0.001
KW	CV0	CS12_WW	GGK + W	0.949	0.000
KW	CV0	CS12_WW	GGK+PGK + W	0.948	0.000
KW	CV0	CS12_WW	G + W	0.948	0.000
KW	CV00	CS11_WS	P + E	0.662	0.074
KW	CV00	CS11_WS	G+P + E	0.654	0.036
KW	CV00	CS11_WS	P + W	0.624	0.068
KW	CV00	CS11_WW	P + E	0.656	0.054
KW	CV00	CS11_WW	GGK + W	0.567	0.023
KW	CV00	CS11_WW	GGK+PGK + E	0.566	0.021
KW	CV00	CS12_WS	GGK+PGK + E	0.619	0.013
KW	CV00	CS12_WS	GGK + E	0.616	0.017
KW	CV00	CS12_WS	G + W	0.613	0.009
KW	CV00	CS12_WW	P + E	0.640	0.061
KW	CV00	CS12_WW	G+P + E	0.636	0.041
KW	CV00	CS12_WW	GGK+PGK + E	0.617	0.010

13. W-effect tables

These tables isolate one of the main scientific questions of the project: whether adding weather information improves prediction. Because the comparisons are defined through carefully matched model pairs, the resulting contrasts are easier to interpret than raw model-by-model inspection.

The first table presents the effect of adding W under CV1 and CV2.

cv12_w_effect %>%
  mutate( MeanWithoutW = round(MeanWithoutW, 3),
   MeanWithW = round(MeanWithW, 3),
    DeltaWithW = round(DeltaWithW, 3) ) %>%
  knitr::kable( caption = "Pairwise comparison of models without and with the weather kernel (W) in CV1 and CV2.",
    align = "lllccccc" ) %>%
  kableExtra::kable_styling( bootstrap_options = c("striped", "hover", "condensed", "responsive"),
   full_width = FALSE,
    position = "left" ) %>%
  kableExtra::scroll_box(width = "100%", height = "320px")

Pairwise comparison of models without and with the weather kernel (W) in CV1 and CV2.

Comparison	WithoutW	WithW	Trait	CV	MeanWithoutW	SDWithoutW	MeanWithW	SDWithW	DeltaWithW
Combined Gaussian	Eta8	Eta15	GY	CV1	0.717	0.0117158	0.723	0.0112130	0.006
Combined arc-cosine	Eta9	Eta18	GY	CV1	0.703	0.0100091	0.706	0.0087728	0.003
Combined linear	Eta7	Eta12	GY	CV1	0.713	0.0134212	0.719	0.0124435	0.006
Genomic Gaussian	Eta3	Eta13	GY	CV1	0.719	0.0106337	0.727	0.0120687	0.008
Genomic arc-cosine	Eta5	Eta16	GY	CV1	0.711	0.0065960	0.714	0.0083470	0.002
Genomic linear	Eta1	Eta10	GY	CV1	0.719	0.0128201	0.725	0.0109925	0.005
Phenomic Gaussian	Eta4	Eta14	GY	CV1	0.134	0.0274657	0.147	0.0191283	0.013
Phenomic arc-cosine	Eta6	Eta17	GY	CV1	0.178	0.0296188	0.177	0.0380569	-0.001
Phenomic linear	Eta2	Eta11	GY	CV1	0.645	0.0121966	0.637	0.0196734	-0.008
Combined Gaussian	Eta8	Eta15	GY	CV2	0.989	0.0001216	0.991	0.0000983	0.002
Combined arc-cosine	Eta9	Eta18	GY	CV2	0.966	0.0004052	0.970	0.0005673	0.004
Combined linear	Eta7	Eta12	GY	CV2	0.980	0.0002151	0.982	0.0001190	0.002
Genomic Gaussian	Eta3	Eta13	GY	CV2	0.973	0.0001704	0.974	0.0001302	0.001
Genomic arc-cosine	Eta5	Eta16	GY	CV2	0.964	0.0005435	0.968	0.0003975	0.004
Genomic linear	Eta1	Eta10	GY	CV2	0.982	0.0001184	0.984	0.0001054	0.002
Phenomic Gaussian	Eta4	Eta14	GY	CV2	0.945	0.0015159	0.949	0.0012284	0.004
Phenomic arc-cosine	Eta6	Eta17	GY	CV2	0.695	0.0090873	0.692	0.0137389	-0.003
Phenomic linear	Eta2	Eta11	GY	CV2	0.967	0.0067725	0.933	0.0773312	-0.034
Combined Gaussian	Eta8	Eta15	KW	CV1	0.603	0.0099057	0.595	0.0156243	-0.008
Combined arc-cosine	Eta9	Eta18	KW	CV1	0.555	0.0239686	0.548	0.0173955	-0.007
Combined linear	Eta7	Eta12	KW	CV1	0.728	0.0145741	0.708	0.0150303	-0.019
Genomic Gaussian	Eta3	Eta13	KW	CV1	0.602	0.0147757	0.595	0.0149952	-0.006
Genomic arc-cosine	Eta5	Eta16	KW	CV1	0.555	0.0199137	0.555	0.0168190	0.000
Genomic linear	Eta1	Eta10	KW	CV1	0.585	0.0151765	0.594	0.0179071	0.009
Phenomic Gaussian	Eta4	Eta14	KW	CV1	0.218	0.0160546	0.203	0.0203866	-0.015
Phenomic arc-cosine	Eta6	Eta17	KW	CV1	0.271	0.0271355	0.243	0.0285264	-0.028
Phenomic linear	Eta2	Eta11	KW	CV1	0.762	0.0099625	0.761	0.0053242	0.000
Combined Gaussian	Eta8	Eta15	KW	CV2	0.993	0.0000316	0.994	0.0000388	0.001
Combined arc-cosine	Eta9	Eta18	KW	CV2	0.977	0.0002182	0.978	0.0008926	0.001
Combined linear	Eta7	Eta12	KW	CV2	0.994	0.0002515	0.994	0.0005010	0.000
Genomic Gaussian	Eta3	Eta13	KW	CV2	0.982	0.0001168	0.983	0.0001170	0.001
Genomic arc-cosine	Eta5	Eta16	KW	CV2	0.974	0.0001071	0.975	0.0003408	0.001
Genomic linear	Eta1	Eta10	KW	CV2	0.989	0.0000573	0.990	0.0000506	0.001
Phenomic Gaussian	Eta4	Eta14	KW	CV2	0.955	0.0008444	0.958	0.0010135	0.003
Phenomic arc-cosine	Eta6	Eta17	KW	CV2	0.772	0.0028779	0.771	0.0079429	-0.001
Phenomic linear	Eta2	Eta11	KW	CV2	0.989	0.0011764	0.986	0.0042936	-0.003

The second table presents the same type of contrast under CV0 and CV00, where generalization to new environments becomes part of the prediction problem.

cvloo_w_effect %>%
  mutate( MeanWithoutW = round(MeanWithoutW, 3),
   MeanWithW = round(MeanWithW, 3),
    DeltaWithW = round(DeltaWithW, 3) ) %>%
  knitr::kable( caption = "Pairwise comparison of models without and with the weather kernel (W) in CV0 and CV00.",
    align = "llllccccc" ) %>%
  kableExtra::kable_styling( bootstrap_options = c("striped", "hover", "condensed", "responsive"),
   full_width = FALSE,
    position = "left" ) %>%
  kableExtra::scroll_box(width = "100%", height = "320px")

Pairwise comparison of models without and with the weather kernel (W) in CV0 and CV00.

Comparison	WithoutW	WithW	Trait	CV	Env_leave	MeanWithoutW	SDWithoutW	MeanWithW	SDWithW	DeltaWithW
Combined Gaussian	Eta8	Eta15	GY	CV0	CS11_WS	0.922	0.0006408	0.921	0.0005517	-0.001
Combined arc-cosine	Eta9	Eta18	GY	CV0	CS11_WS	0.915	0.0064663	0.906	0.0159762	-0.008
Combined linear	Eta7	Eta12	GY	CV0	CS11_WS	0.884	0.0160582	0.878	0.0198771	-0.006
Genomic Gaussian	Eta3	Eta13	GY	CV0	CS11_WS	0.923	0.0004691	0.922	0.0003833	0.000
Genomic arc-cosine	Eta5	Eta16	GY	CV0	CS11_WS	0.926	0.0002212	0.924	0.0031137	-0.001
Genomic linear	Eta1	Eta10	GY	CV0	CS11_WS	0.921	0.0005552	0.916	0.0004999	-0.005
Phenomic Gaussian	Eta4	Eta14	GY	CV0	CS11_WS	0.460	0.0046790	0.434	0.0085978	-0.026
Phenomic arc-cosine	Eta6	Eta17	GY	CV0	CS11_WS	0.421	0.0327846	0.398	0.0327840	-0.022
Phenomic linear	Eta2	Eta11	GY	CV0	CS11_WS	0.740	0.0417897	0.600	0.0937367	-0.140
Combined Gaussian	Eta8	Eta15	GY	CV0	CS11_WW	0.889	0.0007587	0.891	0.0012022	0.002
Combined arc-cosine	Eta9	Eta18	GY	CV0	CS11_WW	0.848	0.0282177	0.850	0.0307368	0.003
Combined linear	Eta7	Eta12	GY	CV0	CS11_WW	0.822	0.0652425	0.778	0.0747105	-0.043
Genomic Gaussian	Eta3	Eta13	GY	CV0	CS11_WW	0.894	0.0005965	0.896	0.0004316	0.002
Genomic arc-cosine	Eta5	Eta16	GY	CV0	CS11_WW	0.885	0.0005851	0.886	0.0031297	0.000
Genomic linear	Eta1	Eta10	GY	CV0	CS11_WW	0.893	0.0005283	0.896	0.0004761	0.002
Phenomic Gaussian	Eta4	Eta14	GY	CV0	CS11_WW	0.323	0.0079081	0.318	0.0074471	-0.005
Phenomic arc-cosine	Eta6	Eta17	GY	CV0	CS11_WW	0.310	0.0198619	0.275	0.0443295	-0.034
Phenomic linear	Eta2	Eta11	GY	CV0	CS11_WW	0.615	0.1492622	0.578	0.1292014	-0.038
Combined Gaussian	Eta8	Eta15	GY	CV0	CS12_WS	0.889	0.0008715	0.884	0.0007198	-0.005
Combined arc-cosine	Eta9	Eta18	GY	CV0	CS12_WS	0.861	0.0164014	0.855	0.0214819	-0.006
Combined linear	Eta7	Eta12	GY	CV0	CS12_WS	0.794	0.0574106	0.765	0.0375478	-0.029
Genomic Gaussian	Eta3	Eta13	GY	CV0	CS12_WS	0.896	0.0007279	0.893	0.0011026	-0.003
Genomic arc-cosine	Eta5	Eta16	GY	CV0	CS12_WS	0.884	0.0006309	0.883	0.0006255	0.000
Genomic linear	Eta1	Eta10	GY	CV0	CS12_WS	0.894	0.0011375	0.885	0.0006739	-0.010
Phenomic Gaussian	Eta4	Eta14	GY	CV0	CS12_WS	0.342	0.0078015	0.323	0.0078257	-0.020
Phenomic arc-cosine	Eta6	Eta17	GY	CV0	CS12_WS	0.273	0.0322555	0.257	0.0491397	-0.016
Phenomic linear	Eta2	Eta11	GY	CV0	CS12_WS	0.634	0.0757856	0.454	0.1025718	-0.180
Combined Gaussian	Eta8	Eta15	GY	CV0	CS12_WW	0.902	0.0005695	0.904	0.0004415	0.002
Combined arc-cosine	Eta9	Eta18	GY	CV0	CS12_WW	0.892	0.0095946	0.894	0.0083430	0.003
Combined linear	Eta7	Eta12	GY	CV0	CS12_WW	0.881	0.0134864	0.887	0.0098103	0.006
Genomic Gaussian	Eta3	Eta13	GY	CV0	CS12_WW	0.904	0.0004100	0.907	0.0004159	0.004
Genomic arc-cosine	Eta5	Eta16	GY	CV0	CS12_WW	0.902	0.0004584	0.904	0.0005408	0.002
Genomic linear	Eta1	Eta10	GY	CV0	CS12_WW	0.904	0.0005270	0.909	0.0004207	0.005
Phenomic Gaussian	Eta4	Eta14	GY	CV0	CS12_WW	0.359	0.0074689	0.350	0.0064624	-0.009
Phenomic arc-cosine	Eta6	Eta17	GY	CV0	CS12_WW	0.347	0.0265095	0.332	0.0285925	-0.015
Phenomic linear	Eta2	Eta11	GY	CV0	CS12_WW	0.592	0.1219799	0.512	0.1222827	-0.081
Combined Gaussian	Eta8	Eta15	GY	CV00	CS11_WS	0.719	0.0156232	0.716	0.0232356	-0.003
Combined arc-cosine	Eta9	Eta18	GY	CV00	CS11_WS	0.702	0.0164750	0.715	0.0144928	0.014
Combined linear	Eta7	Eta12	GY	CV00	CS11_WS	0.666	0.0336890	0.677	0.0357095	0.011
Genomic Gaussian	Eta3	Eta13	GY	CV00	CS11_WS	0.717	0.0210367	0.716	0.0249825	-0.002
Genomic arc-cosine	Eta5	Eta16	GY	CV00	CS11_WS	0.732	0.0133004	0.735	0.0139247	0.003
Genomic linear	Eta1	Eta10	GY	CV00	CS11_WS	0.710	0.0164292	0.720	0.0158158	0.011
Phenomic Gaussian	Eta4	Eta14	GY	CV00	CS11_WS	0.192	0.0265772	0.207	0.0534662	0.014
Phenomic arc-cosine	Eta6	Eta17	GY	CV00	CS11_WS	0.176	0.0470906	0.160	0.0463932	-0.017
Phenomic linear	Eta2	Eta11	GY	CV00	CS11_WS	0.547	0.0547123	0.468	0.0727954	-0.079
Combined Gaussian	Eta8	Eta15	GY	CV00	CS11_WW	0.734	0.0147333	0.734	0.0146172	0.000
Combined arc-cosine	Eta9	Eta18	GY	CV00	CS11_WW	0.648	0.0420356	0.643	0.0355772	-0.005
Combined linear	Eta7	Eta12	GY	CV00	CS11_WW	0.664	0.0551344	0.597	0.0889922	-0.067
Genomic Gaussian	Eta3	Eta13	GY	CV00	CS11_WW	0.738	0.0106728	0.740	0.0125027	0.003
Genomic arc-cosine	Eta5	Eta16	GY	CV00	CS11_WW	0.724	0.0092225	0.725	0.0099241	0.000
Genomic linear	Eta1	Eta10	GY	CV00	CS11_WW	0.741	0.0102739	0.738	0.0121891	-0.002
Phenomic Gaussian	Eta4	Eta14	GY	CV00	CS11_WW	0.167	0.0334714	0.192	0.0319594	0.025
Phenomic arc-cosine	Eta6	Eta17	GY	CV00	CS11_WW	0.128	0.0454014	0.126	0.0436496	-0.002
Phenomic linear	Eta2	Eta11	GY	CV00	CS11_WW	0.444	0.1253345	0.453	0.1196363	0.009
Combined Gaussian	Eta8	Eta15	GY	CV00	CS12_WS	0.722	0.0106525	0.727	0.0110813	0.005
Combined arc-cosine	Eta9	Eta18	GY	CV00	CS12_WS	0.624	0.0366770	0.620	0.0290091	-0.004
Combined linear	Eta7	Eta12	GY	CV00	CS12_WS	0.617	0.0577406	0.598	0.0459783	-0.019
Genomic Gaussian	Eta3	Eta13	GY	CV00	CS12_WS	0.730	0.0105024	0.734	0.0068753	0.004
Genomic arc-cosine	Eta5	Eta16	GY	CV00	CS12_WS	0.693	0.0081952	0.690	0.0113171	-0.003
Genomic linear	Eta1	Eta10	GY	CV00	CS12_WS	0.725	0.0120592	0.733	0.0073064	0.008
Phenomic Gaussian	Eta4	Eta14	GY	CV00	CS12_WS	0.132	0.0265251	0.129	0.0316274	-0.003
Phenomic arc-cosine	Eta6	Eta17	GY	CV00	CS12_WS	0.086	0.0531555	0.101	0.0517042	0.015
Phenomic linear	Eta2	Eta11	GY	CV00	CS12_WS	0.517	0.0691137	0.369	0.1174927	-0.148
Combined Gaussian	Eta8	Eta15	GY	CV00	CS12_WW	0.706	0.0153052	0.714	0.0127669	0.008
Combined arc-cosine	Eta9	Eta18	GY	CV00	CS12_WW	0.656	0.0155661	0.656	0.0259759	0.000
Combined linear	Eta7	Eta12	GY	CV00	CS12_WW	0.674	0.0268594	0.672	0.0388784	-0.001
Genomic Gaussian	Eta3	Eta13	GY	CV00	CS12_WW	0.701	0.0098703	0.713	0.0086880	0.012
Genomic arc-cosine	Eta5	Eta16	GY	CV00	CS12_WW	0.691	0.0100686	0.682	0.0124059	-0.008
Genomic linear	Eta1	Eta10	GY	CV00	CS12_WW	0.696	0.0179032	0.710	0.0075409	0.013
Phenomic Gaussian	Eta4	Eta14	GY	CV00	CS12_WW	0.119	0.0317911	0.114	0.0242938	-0.005
Phenomic arc-cosine	Eta6	Eta17	GY	CV00	CS12_WW	0.098	0.0427283	0.096	0.0740510	-0.002
Phenomic linear	Eta2	Eta11	GY	CV00	CS12_WW	0.410	0.1100689	0.386	0.0734259	-0.024
Combined Gaussian	Eta8	Eta15	KW	CV0	CS11_WS	0.959	0.0004251	0.955	0.0004242	-0.004
Combined arc-cosine	Eta9	Eta18	KW	CV0	CS11_WS	0.952	0.0060164	0.934	0.0117906	-0.018
Combined linear	Eta7	Eta12	KW	CV0	CS11_WS	0.928	0.0303599	0.904	0.0373431	-0.025
Genomic Gaussian	Eta3	Eta13	KW	CV0	CS11_WS	0.960	0.0001845	0.953	0.0003107	-0.008
Genomic arc-cosine	Eta5	Eta16	KW	CV0	CS11_WS	0.961	0.0001712	0.955	0.0059577	-0.006
Genomic linear	Eta1	Eta10	KW	CV0	CS11_WS	0.960	0.0003318	0.945	0.0003220	-0.015
Phenomic Gaussian	Eta4	Eta14	KW	CV0	CS11_WS	0.488	0.0064600	0.459	0.0053104	-0.029
Phenomic arc-cosine	Eta6	Eta17	KW	CV0	CS11_WS	0.514	0.0207448	0.529	0.0219561	0.015
Phenomic linear	Eta2	Eta11	KW	CV0	CS11_WS	0.800	0.0569121	0.708	0.0720481	-0.093
Combined Gaussian	Eta8	Eta15	KW	CV0	CS11_WW	0.886	0.0008546	0.888	0.0008502	0.002
Combined arc-cosine	Eta9	Eta18	KW	CV0	CS11_WW	0.855	0.0194615	0.850	0.0175722	-0.005
Combined linear	Eta7	Eta12	KW	CV0	CS11_WW	0.829	0.0365791	0.780	0.0736196	-0.048
Genomic Gaussian	Eta3	Eta13	KW	CV0	CS11_WW	0.885	0.0011692	0.887	0.0010117	0.002
Genomic arc-cosine	Eta5	Eta16	KW	CV0	CS11_WW	0.874	0.0006841	0.873	0.0064145	-0.002
Genomic linear	Eta1	Eta10	KW	CV0	CS11_WW	0.885	0.0011861	0.889	0.0003511	0.004
Phenomic Gaussian	Eta4	Eta14	KW	CV0	CS11_WW	0.331	0.0051097	0.327	0.0063766	-0.004
Phenomic arc-cosine	Eta6	Eta17	KW	CV0	CS11_WW	0.399	0.0311944	0.429	0.0314922	0.029
Phenomic linear	Eta2	Eta11	KW	CV0	CS11_WW	0.787	0.0671637	0.591	0.1578071	-0.196
Combined Gaussian	Eta8	Eta15	KW	CV0	CS12_WS	0.894	0.0011841	0.894	0.0009434	0.001
Combined arc-cosine	Eta9	Eta18	KW	CV0	CS12_WS	0.860	0.0250670	0.880	0.0136477	0.020
Combined linear	Eta7	Eta12	KW	CV0	CS12_WS	0.797	0.0640268	0.816	0.0478818	0.018
Genomic Gaussian	Eta3	Eta13	KW	CV0	CS12_WS	0.898	0.0011057	0.899	0.0005593	0.001
Genomic arc-cosine	Eta5	Eta16	KW	CV0	CS12_WS	0.888	0.0005409	0.889	0.0010068	0.001
Genomic linear	Eta1	Eta10	KW	CV0	CS12_WS	0.896	0.0008220	0.897	0.0010396	0.001
Phenomic Gaussian	Eta4	Eta14	KW	CV0	CS12_WS	0.410	0.0043472	0.400	0.0055684	-0.010
Phenomic arc-cosine	Eta6	Eta17	KW	CV0	CS12_WS	0.385	0.0316524	0.407	0.0309957	0.022
Phenomic linear	Eta2	Eta11	KW	CV0	CS12_WS	0.735	0.0917405	0.638	0.1303465	-0.097
Combined Gaussian	Eta8	Eta15	KW	CV0	CS12_WW	0.947	0.0004264	0.948	0.0003331	0.001
Combined arc-cosine	Eta9	Eta18	KW	CV0	CS12_WW	0.938	0.0061385	0.935	0.0105933	-0.003
Combined linear	Eta7	Eta12	KW	CV0	CS12_WW	0.922	0.0305936	0.928	0.0256338	0.006
Genomic Gaussian	Eta3	Eta13	KW	CV0	CS12_WW	0.947	0.0002290	0.949	0.0002453	0.002
Genomic arc-cosine	Eta5	Eta16	KW	CV0	CS12_WW	0.947	0.0002183	0.946	0.0021284	-0.001
Genomic linear	Eta1	Eta10	KW	CV0	CS12_WW	0.947	0.0002957	0.948	0.0003126	0.002
Phenomic Gaussian	Eta4	Eta14	KW	CV0	CS12_WW	0.431	0.0074450	0.429	0.0085145	-0.003
Phenomic arc-cosine	Eta6	Eta17	KW	CV0	CS12_WW	0.514	0.0186631	0.504	0.0290988	-0.010
Phenomic linear	Eta2	Eta11	KW	CV0	CS12_WW	0.824	0.0658355	0.746	0.0805916	-0.078
Combined Gaussian	Eta8	Eta15	KW	CV00	CS11_WS	0.586	0.0209643	0.566	0.0260974	-0.020
Combined arc-cosine	Eta9	Eta18	KW	CV00	CS11_WS	0.508	0.0472672	0.484	0.0409598	-0.025
Combined linear	Eta7	Eta12	KW	CV00	CS11_WS	0.654	0.0360532	0.608	0.0548281	-0.045
Genomic Gaussian	Eta3	Eta13	KW	CV00	CS11_WS	0.578	0.0220801	0.573	0.0223042	-0.005
Genomic arc-cosine	Eta5	Eta16	KW	CV00	CS11_WS	0.544	0.0268564	0.548	0.0163422	0.004
Genomic linear	Eta1	Eta10	KW	CV00	CS11_WS	0.565	0.0200134	0.562	0.0174611	-0.003
Phenomic Gaussian	Eta4	Eta14	KW	CV00	CS11_WS	0.218	0.0243076	0.202	0.0472486	-0.016
Phenomic arc-cosine	Eta6	Eta17	KW	CV00	CS11_WS	0.256	0.0252293	0.249	0.0365030	-0.007
Phenomic linear	Eta2	Eta11	KW	CV00	CS11_WS	0.662	0.0743260	0.624	0.0680554	-0.038
Combined Gaussian	Eta8	Eta15	KW	CV00	CS11_WW	0.566	0.0212727	0.562	0.0166412	-0.004
Combined arc-cosine	Eta9	Eta18	KW	CV00	CS11_WW	0.460	0.0504655	0.451	0.0487862	-0.009
Combined linear	Eta7	Eta12	KW	CV00	CS11_WW	0.544	0.0496768	0.488	0.0776466	-0.056
Genomic Gaussian	Eta3	Eta13	KW	CV00	CS11_WW	0.565	0.0197142	0.567	0.0234297	0.002
Genomic arc-cosine	Eta5	Eta16	KW	CV00	CS11_WW	0.525	0.0245290	0.511	0.0208822	-0.014
Genomic linear	Eta1	Eta10	KW	CV00	CS11_WW	0.563	0.0179097	0.565	0.0130631	0.002
Phenomic Gaussian	Eta4	Eta14	KW	CV00	CS11_WW	0.160	0.0141550	0.153	0.0236371	-0.007
Phenomic arc-cosine	Eta6	Eta17	KW	CV00	CS11_WW	0.222	0.0454472	0.172	0.0459169	-0.050
Phenomic linear	Eta2	Eta11	KW	CV00	CS11_WW	0.656	0.0537020	0.541	0.1089787	-0.115
Combined Gaussian	Eta8	Eta15	KW	CV00	CS12_WS	0.619	0.0125596	0.607	0.0129271	-0.012
Combined arc-cosine	Eta9	Eta18	KW	CV00	CS12_WS	0.511	0.0392188	0.550	0.0346599	0.039
Combined linear	Eta7	Eta12	KW	CV00	CS12_WS	0.553	0.0799328	0.552	0.0729139	-0.001
Genomic Gaussian	Eta3	Eta13	KW	CV00	CS12_WS	0.616	0.0174929	0.611	0.0169350	-0.005
Genomic arc-cosine	Eta5	Eta16	KW	CV00	CS12_WS	0.560	0.0085485	0.569	0.0098365	0.009
Genomic linear	Eta1	Eta10	KW	CV00	CS12_WS	0.602	0.0156413	0.613	0.0088231	0.011
Phenomic Gaussian	Eta4	Eta14	KW	CV00	CS12_WS	0.209	0.0273382	0.212	0.0227339	0.003
Phenomic arc-cosine	Eta6	Eta17	KW	CV00	CS12_WS	0.180	0.0753962	0.189	0.0409106	0.009
Phenomic linear	Eta2	Eta11	KW	CV00	CS12_WS	0.600	0.0894934	0.538	0.0973559	-0.062
Combined Gaussian	Eta8	Eta15	KW	CV00	CS12_WW	0.617	0.0102124	0.615	0.0248406	-0.002
Combined arc-cosine	Eta9	Eta18	KW	CV00	CS12_WW	0.576	0.0306078	0.554	0.0430405	-0.022
Combined linear	Eta7	Eta12	KW	CV00	CS12_WW	0.636	0.0411822	0.614	0.0398958	-0.022
Genomic Gaussian	Eta3	Eta13	KW	CV00	CS12_WW	0.600	0.0272165	0.609	0.0237787	0.009
Genomic arc-cosine	Eta5	Eta16	KW	CV00	CS12_WW	0.591	0.0295687	0.585	0.0195874	-0.006
Genomic linear	Eta1	Eta10	KW	CV00	CS12_WW	0.601	0.0150357	0.603	0.0329311	0.001
Phenomic Gaussian	Eta4	Eta14	KW	CV00	CS12_WW	0.197	0.0414129	0.198	0.0328087	0.002
Phenomic arc-cosine	Eta6	Eta17	KW	CV00	CS12_WW	0.239	0.0433968	0.256	0.0392577	0.017
Phenomic linear	Eta2	Eta11	KW	CV00	CS12_WW	0.640	0.0608590	0.602	0.0751970	-0.038

14. Kernel-family comparison tables

Kernel choice is another central analytical decision in this project. Rather than treating the linear, Gaussian, and arc-cosine formulations as isolated models, this section compares them within each pathway so that the effect of kernel family can be interpreted directly.

The first table reports these comparisons for CV1 and CV2.

cv12_kernel_family_compare %>%
  mutate( Linear = round(Linear, 3),
   Gaussian = round(Gaussian, 3),
   `Arc-cosine` = round(`Arc-cosine`, 3),
   Delta_Gaussian_vs_Linear = round(Delta_Gaussian_vs_Linear, 3),
   Delta_ArcCos_vs_Linear = round(Delta_ArcCos_vs_Linear, 3),
    Delta_ArcCos_vs_Gaussian = round(Delta_ArcCos_vs_Gaussian, 3) ) %>%
  knitr::kable( caption = "Comparison of kernel families within each analytical pathway in CV1 and CV2.",
    align = "llllcccccc" ) %>%
  kableExtra::kable_styling( bootstrap_options = c("striped", "hover", "condensed", "responsive"),
   full_width = FALSE,
    position = "left" ) %>%
  kableExtra::scroll_box(width = "100%", height = "320px")

Comparison of kernel families within each analytical pathway in CV1 and CV2.

Trait	CV	Pathway	WeatherStatus	Linear	Gaussian	Arc-cosine	Delta_Gaussian_vs_Linear	Delta_ArcCos_vs_Linear	Delta_ArcCos_vs_Gaussian
GY	CV1	Combined G + P pathway	With W	0.719	0.723	0.706	0.004	-0.013	-0.017
GY	CV1	Combined G + P pathway	Without W	0.713	0.717	0.703	0.004	-0.010	-0.014
GY	CV1	Genomic pathway	With W	0.725	0.727	0.714	0.003	-0.011	-0.014
GY	CV1	Genomic pathway	Without W	0.719	0.719	0.711	0.000	-0.008	-0.008
GY	CV1	Phenomic pathway	With W	0.637	0.147	0.177	-0.490	-0.460	0.030
GY	CV1	Phenomic pathway	Without W	0.645	0.134	0.178	-0.510	-0.467	0.043
GY	CV2	Combined G + P pathway	With W	0.982	0.991	0.970	0.008	-0.012	-0.021
GY	CV2	Combined G + P pathway	Without W	0.980	0.989	0.966	0.008	-0.014	-0.023
GY	CV2	Genomic pathway	With W	0.984	0.974	0.968	-0.010	-0.016	-0.006
GY	CV2	Genomic pathway	Without W	0.982	0.973	0.964	-0.009	-0.019	-0.009
GY	CV2	Phenomic pathway	With W	0.933	0.949	0.692	0.016	-0.241	-0.257
GY	CV2	Phenomic pathway	Without W	0.967	0.945	0.695	-0.022	-0.272	-0.249
KW	CV1	Combined G + P pathway	With W	0.708	0.595	0.548	-0.113	-0.160	-0.047
KW	CV1	Combined G + P pathway	Without W	0.728	0.603	0.555	-0.124	-0.173	-0.048
KW	CV1	Genomic pathway	With W	0.594	0.595	0.555	0.002	-0.038	-0.040
KW	CV1	Genomic pathway	Without W	0.585	0.602	0.555	0.017	-0.030	-0.047
KW	CV1	Phenomic pathway	With W	0.761	0.203	0.243	-0.558	-0.519	0.040
KW	CV1	Phenomic pathway	Without W	0.762	0.218	0.271	-0.544	-0.491	0.054
KW	CV2	Combined G + P pathway	With W	0.994	0.994	0.978	0.000	-0.016	-0.016
KW	CV2	Combined G + P pathway	Without W	0.994	0.993	0.977	-0.001	-0.017	-0.016
KW	CV2	Genomic pathway	With W	0.990	0.983	0.975	-0.007	-0.015	-0.008
KW	CV2	Genomic pathway	Without W	0.989	0.982	0.974	-0.007	-0.015	-0.008
KW	CV2	Phenomic pathway	With W	0.986	0.958	0.771	-0.028	-0.215	-0.187
KW	CV2	Phenomic pathway	Without W	0.989	0.955	0.772	-0.034	-0.217	-0.183

The second table reports the same comparisons for CV0 and CV00, where the results must be read together with the held-out environment structure.

cvloo_kernel_family_compare %>%
  mutate( Linear = round(Linear, 3),
   Gaussian = round(Gaussian, 3),
   `Arc-cosine` = round(`Arc-cosine`, 3),
   Delta_Gaussian_vs_Linear = round(Delta_Gaussian_vs_Linear, 3),
   Delta_ArcCos_vs_Linear = round(Delta_ArcCos_vs_Linear, 3),
    Delta_ArcCos_vs_Gaussian = round(Delta_ArcCos_vs_Gaussian, 3) ) %>%
  knitr::kable( caption = "Comparison of kernel families within each analytical pathway in CV0 and CV00.",
    align = "lllllcccccc" ) %>%
  kableExtra::kable_styling( bootstrap_options = c("striped", "hover", "condensed", "responsive"),
   full_width = FALSE,
    position = "left" ) %>%
  kableExtra::scroll_box(width = "100%", height = "320px")

Comparison of kernel families within each analytical pathway in CV0 and CV00.

Trait	CV	Env_leave	Pathway	WeatherStatus	Linear	Gaussian	Arc-cosine	Delta_Gaussian_vs_Linear	Delta_ArcCos_vs_Linear	Delta_ArcCos_vs_Gaussian
GY	CV0	CS11_WS	Combined G + P pathway	With W	0.878	0.921	0.906	0.042	0.028	-0.014
GY	CV0	CS11_WS	Combined G + P pathway	Without W	0.884	0.922	0.915	0.037	0.030	-0.007
GY	CV0	CS11_WS	Genomic pathway	With W	0.916	0.922	0.924	0.006	0.008	0.002
GY	CV0	CS11_WS	Genomic pathway	Without W	0.921	0.923	0.926	0.001	0.004	0.003
GY	CV0	CS11_WS	Phenomic pathway	With W	0.600	0.434	0.398	-0.166	-0.201	-0.036
GY	CV0	CS11_WS	Phenomic pathway	Without W	0.740	0.460	0.421	-0.280	-0.319	-0.039
GY	CV0	CS11_WW	Combined G + P pathway	With W	0.778	0.891	0.850	0.113	0.072	-0.041
GY	CV0	CS11_WW	Combined G + P pathway	Without W	0.822	0.889	0.848	0.067	0.026	-0.041
GY	CV0	CS11_WW	Genomic pathway	With W	0.896	0.896	0.886	0.000	-0.010	-0.010
GY	CV0	CS11_WW	Genomic pathway	Without W	0.893	0.894	0.885	0.001	-0.008	-0.009
GY	CV0	CS11_WW	Phenomic pathway	With W	0.578	0.318	0.275	-0.259	-0.302	-0.043
GY	CV0	CS11_WW	Phenomic pathway	Without W	0.615	0.323	0.310	-0.292	-0.305	-0.013
GY	CV0	CS12_WS	Combined G + P pathway	With W	0.765	0.884	0.855	0.119	0.090	-0.029
GY	CV0	CS12_WS	Combined G + P pathway	Without W	0.794	0.889	0.861	0.095	0.067	-0.028
GY	CV0	CS12_WS	Genomic pathway	With W	0.885	0.893	0.883	0.008	-0.001	-0.009
GY	CV0	CS12_WS	Genomic pathway	Without W	0.894	0.896	0.884	0.002	-0.011	-0.012
GY	CV0	CS12_WS	Phenomic pathway	With W	0.454	0.323	0.257	-0.131	-0.196	-0.065
GY	CV0	CS12_WS	Phenomic pathway	Without W	0.634	0.342	0.273	-0.292	-0.361	-0.069
GY	CV0	CS12_WW	Combined G + P pathway	With W	0.887	0.904	0.894	0.017	0.007	-0.009
GY	CV0	CS12_WW	Combined G + P pathway	Without W	0.881	0.902	0.892	0.021	0.011	-0.010
GY	CV0	CS12_WW	Genomic pathway	With W	0.909	0.907	0.904	-0.002	-0.005	-0.003
GY	CV0	CS12_WW	Genomic pathway	Without W	0.904	0.904	0.902	-0.001	-0.002	-0.001
GY	CV0	CS12_WW	Phenomic pathway	With W	0.512	0.350	0.332	-0.161	-0.180	-0.018
GY	CV0	CS12_WW	Phenomic pathway	Without W	0.592	0.359	0.347	-0.234	-0.246	-0.012
GY	CV00	CS11_WS	Combined G + P pathway	With W	0.677	0.716	0.715	0.039	0.038	-0.001
GY	CV00	CS11_WS	Combined G + P pathway	Without W	0.666	0.719	0.702	0.053	0.036	-0.017
GY	CV00	CS11_WS	Genomic pathway	With W	0.720	0.716	0.735	-0.005	0.015	0.019
GY	CV00	CS11_WS	Genomic pathway	Without W	0.710	0.717	0.732	0.007	0.023	0.015
GY	CV00	CS11_WS	Phenomic pathway	With W	0.468	0.207	0.160	-0.261	-0.308	-0.047
GY	CV00	CS11_WS	Phenomic pathway	Without W	0.547	0.192	0.176	-0.355	-0.371	-0.016
GY	CV00	CS11_WW	Combined G + P pathway	With W	0.597	0.734	0.643	0.137	0.046	-0.091
GY	CV00	CS11_WW	Combined G + P pathway	Without W	0.664	0.734	0.648	0.070	-0.016	-0.086
GY	CV00	CS11_WW	Genomic pathway	With W	0.738	0.740	0.725	0.002	-0.014	-0.016
GY	CV00	CS11_WW	Genomic pathway	Without W	0.741	0.738	0.724	-0.003	-0.016	-0.013
GY	CV00	CS11_WW	Phenomic pathway	With W	0.453	0.192	0.126	-0.261	-0.327	-0.066
GY	CV00	CS11_WW	Phenomic pathway	Without W	0.444	0.167	0.128	-0.277	-0.316	-0.039
GY	CV00	CS12_WS	Combined G + P pathway	With W	0.598	0.727	0.620	0.129	0.022	-0.107
GY	CV00	CS12_WS	Combined G + P pathway	Without W	0.617	0.722	0.624	0.105	0.007	-0.098
GY	CV00	CS12_WS	Genomic pathway	With W	0.733	0.734	0.690	0.001	-0.044	-0.044
GY	CV00	CS12_WS	Genomic pathway	Without W	0.725	0.730	0.693	0.005	-0.033	-0.037
GY	CV00	CS12_WS	Phenomic pathway	With W	0.369	0.129	0.101	-0.240	-0.268	-0.028
GY	CV00	CS12_WS	Phenomic pathway	Without W	0.517	0.132	0.086	-0.385	-0.431	-0.046
GY	CV00	CS12_WW	Combined G + P pathway	With W	0.672	0.714	0.656	0.042	-0.016	-0.058
GY	CV00	CS12_WW	Combined G + P pathway	Without W	0.674	0.706	0.656	0.032	-0.018	-0.050
GY	CV00	CS12_WW	Genomic pathway	With W	0.710	0.713	0.682	0.003	-0.027	-0.031
GY	CV00	CS12_WW	Genomic pathway	Without W	0.696	0.701	0.691	0.005	-0.006	-0.011
GY	CV00	CS12_WW	Phenomic pathway	With W	0.386	0.114	0.096	-0.272	-0.290	-0.018
GY	CV00	CS12_WW	Phenomic pathway	Without W	0.410	0.119	0.098	-0.291	-0.312	-0.021
KW	CV0	CS11_WS	Combined G + P pathway	With W	0.904	0.955	0.934	0.051	0.030	-0.021
KW	CV0	CS11_WS	Combined G + P pathway	Without W	0.928	0.959	0.952	0.031	0.024	-0.007
KW	CV0	CS11_WS	Genomic pathway	With W	0.945	0.953	0.955	0.008	0.010	0.002
KW	CV0	CS11_WS	Genomic pathway	Without W	0.960	0.960	0.961	0.000	0.001	0.001
KW	CV0	CS11_WS	Phenomic pathway	With W	0.708	0.459	0.529	-0.249	-0.179	0.070
KW	CV0	CS11_WS	Phenomic pathway	Without W	0.800	0.488	0.514	-0.312	-0.287	0.025
KW	CV0	CS11_WW	Combined G + P pathway	With W	0.780	0.888	0.850	0.108	0.070	-0.038
KW	CV0	CS11_WW	Combined G + P pathway	Without W	0.829	0.886	0.855	0.057	0.026	-0.031
KW	CV0	CS11_WW	Genomic pathway	With W	0.889	0.887	0.873	-0.002	-0.016	-0.015
KW	CV0	CS11_WW	Genomic pathway	Without W	0.885	0.885	0.874	0.000	-0.011	-0.011
KW	CV0	CS11_WW	Phenomic pathway	With W	0.591	0.327	0.429	-0.263	-0.162	0.101
KW	CV0	CS11_WW	Phenomic pathway	Without W	0.787	0.331	0.399	-0.455	-0.387	0.068
KW	CV0	CS12_WS	Combined G + P pathway	With W	0.816	0.894	0.880	0.079	0.064	-0.015
KW	CV0	CS12_WS	Combined G + P pathway	Without W	0.797	0.894	0.860	0.097	0.062	-0.034
KW	CV0	CS12_WS	Genomic pathway	With W	0.897	0.899	0.889	0.002	-0.009	-0.011
KW	CV0	CS12_WS	Genomic pathway	Without W	0.896	0.898	0.888	0.002	-0.008	-0.010
KW	CV0	CS12_WS	Phenomic pathway	With W	0.638	0.400	0.407	-0.238	-0.231	0.007
KW	CV0	CS12_WS	Phenomic pathway	Without W	0.735	0.410	0.385	-0.325	-0.350	-0.025
KW	CV0	CS12_WW	Combined G + P pathway	With W	0.928	0.948	0.935	0.020	0.007	-0.013
KW	CV0	CS12_WW	Combined G + P pathway	Without W	0.922	0.947	0.938	0.025	0.015	-0.010
KW	CV0	CS12_WW	Genomic pathway	With W	0.948	0.949	0.946	0.001	-0.002	-0.003
KW	CV0	CS12_WW	Genomic pathway	Without W	0.947	0.947	0.947	0.001	0.000	0.000
KW	CV0	CS12_WW	Phenomic pathway	With W	0.746	0.429	0.504	-0.318	-0.242	0.076
KW	CV0	CS12_WW	Phenomic pathway	Without W	0.824	0.431	0.514	-0.393	-0.310	0.083
KW	CV00	CS11_WS	Combined G + P pathway	With W	0.608	0.566	0.484	-0.042	-0.125	-0.083
KW	CV00	CS11_WS	Combined G + P pathway	Without W	0.654	0.586	0.508	-0.068	-0.145	-0.078
KW	CV00	CS11_WS	Genomic pathway	With W	0.562	0.573	0.548	0.010	-0.015	-0.025
KW	CV00	CS11_WS	Genomic pathway	Without W	0.565	0.578	0.544	0.012	-0.021	-0.034
KW	CV00	CS11_WS	Phenomic pathway	With W	0.624	0.202	0.249	-0.422	-0.375	0.047
KW	CV00	CS11_WS	Phenomic pathway	Without W	0.662	0.218	0.256	-0.444	-0.407	0.038
KW	CV00	CS11_WW	Combined G + P pathway	With W	0.488	0.562	0.451	0.073	-0.037	-0.111
KW	CV00	CS11_WW	Combined G + P pathway	Without W	0.544	0.566	0.460	0.021	-0.085	-0.106
KW	CV00	CS11_WW	Genomic pathway	With W	0.565	0.567	0.511	0.002	-0.054	-0.056
KW	CV00	CS11_WW	Genomic pathway	Without W	0.563	0.565	0.525	0.001	-0.039	-0.040
KW	CV00	CS11_WW	Phenomic pathway	With W	0.541	0.153	0.172	-0.388	-0.369	0.019
KW	CV00	CS11_WW	Phenomic pathway	Without W	0.656	0.160	0.222	-0.496	-0.434	0.062
KW	CV00	CS12_WS	Combined G + P pathway	With W	0.552	0.607	0.550	0.055	-0.002	-0.057
KW	CV00	CS12_WS	Combined G + P pathway	Without W	0.553	0.619	0.511	0.066	-0.042	-0.108
KW	CV00	CS12_WS	Genomic pathway	With W	0.613	0.611	0.569	-0.001	-0.044	-0.043
KW	CV00	CS12_WS	Genomic pathway	Without W	0.602	0.616	0.560	0.014	-0.042	-0.056
KW	CV00	CS12_WS	Phenomic pathway	With W	0.538	0.212	0.189	-0.327	-0.349	-0.022
KW	CV00	CS12_WS	Phenomic pathway	Without W	0.600	0.209	0.180	-0.391	-0.420	-0.029
KW	CV00	CS12_WW	Combined G + P pathway	With W	0.614	0.615	0.554	0.001	-0.061	-0.061
KW	CV00	CS12_WW	Combined G + P pathway	Without W	0.636	0.617	0.576	-0.019	-0.060	-0.041
KW	CV00	CS12_WW	Genomic pathway	With W	0.603	0.609	0.585	0.006	-0.018	-0.024
KW	CV00	CS12_WW	Genomic pathway	Without W	0.601	0.600	0.591	-0.001	-0.010	-0.009
KW	CV00	CS12_WW	Phenomic pathway	With W	0.602	0.198	0.256	-0.404	-0.346	0.057
KW	CV00	CS12_WW	Phenomic pathway	Without W	0.640	0.197	0.239	-0.443	-0.401	0.042

15. Figures

The figures produced in this stage are visual summaries of the final model catalog. Their role is to condense the numerical tables into patterns that can be recognized quickly, especially when the reader wants to compare pathways, kernel families, and the presence or absence of W.

The first figure summarizes predictive ability under CV1 and CV2, combining mean predictive correlations with uncertainty bars across models.

cv12_plot_data <- cv12_summary %>%
  mutate( ShortDescription = factor(ShortDescription, levels = model_catalog$ShortDescription) )
lower_limit_cv12 <- min(cv12_plot_data$MeanCorrelation - cv12_plot_data$SDCorrelation, na.rm = TRUE)
upper_limit_cv12 <- max(cv12_plot_data$MeanCorrelation + cv12_plot_data$SDCorrelation, na.rm = TRUE)
p_cv12 <- ggplot(cv12_plot_data, aes(x = ShortDescription, y = MeanCorrelation, fill = Group)) +
  geom_col(width = 0.75, color = "grey30") +
  geom_errorbar( aes( ymin = MeanCorrelation - SDCorrelation, ymax = MeanCorrelation + SDCorrelation ),
   width = 0.20,
    linewidth = 0.35 ) +
  facet_grid(Trait ~ CV) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "grey40") +
  coord_cartesian(ylim = c(lower_limit_cv12 - 0.03, upper_limit_cv12 + 0.03)) +
  scale_x_discrete(name = "Model description") +
  scale_y_continuous(name = "Predictive correlation") +
  ggthemes::scale_fill_gdocs(name = "Comparison group") +
  theme_bw() +
  theme( plot.title = element_text(face = "bold", size = 12, hjust = 0.5),
   strip.text = element_text(face = "bold", size = 10),
   axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1, size = 7),
   axis.text.y = element_text(size = 9),
   axis.title = element_text(size = 10),
   legend.position = "top",
   legend.title = element_text(size = 9),
    legend.text = element_text(size = 8) ) +
  labs(title = "Predictive ability under CV1 and CV2")
p_cv12

Past versions of figure-cv12-1.png

Version	Author	Date
6ce48a3	WevertonGomesCosta	2026-04-08
6b32571	WevertonGomesCosta	2026-04-05
00ef3ef	WevertonGomesCosta	2026-04-01
fae2421	WevertonGomesCosta	2026-03-30
4e5af9a	WevertonGomesCosta	2026-03-27

ggsave(file.path(figures_dir, "prediction_cv1_cv2.tiff"),
 plot = p_cv12,
 width = 14,
 height = 8,
 dpi = 300,
  bg = "white")

The second figure summarizes predictive ability under CV0 and CV00, keeping the held-out environments explicit in the layout so that environmental differences remain visible.

cvloo_plot_data <- cvloo_summary %>%
  mutate( ShortDescription = factor(ShortDescription, levels = model_catalog$ShortDescription),
    Env_leave = factor(Env_leave, levels = c("CS11_WS", "CS11_WW", "CS12_WS", "CS12_WW")) )
lower_limit_cvloo <- min(cvloo_plot_data$MeanCorrelation - cvloo_plot_data$SDCorrelation, na.rm = TRUE)
upper_limit_cvloo <- max(cvloo_plot_data$MeanCorrelation + cvloo_plot_data$SDCorrelation, na.rm = TRUE)
p_cvloo <- ggplot(cvloo_plot_data, aes(x = ShortDescription, y = MeanCorrelation, fill = Group)) +
  geom_col(width = 0.75, color = "grey30") +
  geom_errorbar( aes( ymin = MeanCorrelation - SDCorrelation, ymax = MeanCorrelation + SDCorrelation ),
   width = 0.20,
   linewidth = 0.35,
    na.rm = TRUE ) +
  facet_grid(Env_leave ~ Trait + CV) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "grey40") +
  coord_cartesian(ylim = c(lower_limit_cvloo - 0.03, upper_limit_cvloo + 0.03)) +
  scale_x_discrete(name = "Model description") +
  scale_y_continuous(name = "Predictive correlation") +
  ggthemes::scale_fill_gdocs(name = "Comparison group") +
  theme_bw() +
  theme( plot.title = element_text(face = "bold", size = 12, hjust = 0.5),
   strip.text = element_text(face = "bold", size = 9),
   axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1, size = 6),
   axis.text.y = element_text(size = 8),
   axis.title = element_text(size = 10),
   legend.position = "top",
   legend.title = element_text(size = 9),
    legend.text = element_text(size = 8) ) +
  labs(title = "Predictive ability under CV0 and CV00")
p_cvloo

Past versions of figure-cvloo-1.png

Version	Author	Date
6ce48a3	WevertonGomesCosta	2026-04-08
6b32571	WevertonGomesCosta	2026-04-05
00ef3ef	WevertonGomesCosta	2026-04-01
fae2421	WevertonGomesCosta	2026-03-30
4e5af9a	WevertonGomesCosta	2026-03-27

ggsave(file.path(figures_dir, "prediction_cv0_cv00.tiff"),
 plot = p_cvloo,
 width = 16,
 height = 12,
 dpi = 300,
  bg = "white")

16. Final notes

This tutorialized version is aligned with the current prediction workflow based on analysis_prediction_run_outputs.Rmd. It expects files in which:

• repetition and fold are encoded in both the directory hierarchy and the filename;
• CV0 and CV00 carry the held-out environment label in both the directory hierarchy and the filename;
• prediction CSV files are read recursively from output/results/;
• CV0 and CV00 still require the Env == Env_leave filter for the held-out-environment summaries.

After this stage, the pipeline is ready to move from technical summarization to manuscript-oriented interpretation. The tables written to output/tables/ are the main bridge between the computational workflow and the final discussion of results.

Stage navigation

Previous stage: Prediction — Part II
Next reference in the site: Home

Outside the site menu, the next analytical step is to use the outputs created here in manuscript-oriented summaries, interpretative tables, and pipeline review materials.

Session information

sessionInfo()

R version 4.5.1 (2025-06-13 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows 11 x64 (build 26200)

Matrix products: default
  LAPACK version 3.12.1

locale:
[1] LC_COLLATE=Portuguese_Brazil.utf8  LC_CTYPE=Portuguese_Brazil.utf8   
[3] LC_MONETARY=Portuguese_Brazil.utf8 LC_NUMERIC=C                      
[5] LC_TIME=Portuguese_Brazil.utf8    

time zone: America/Sao_Paulo
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] stringr_1.6.0    kableExtra_1.4.0 knitr_1.50       ggthemes_5.2.0  
 [5] ggplot2_4.0.2    tibble_3.3.1     readr_2.2.0      tidyr_1.3.2     
 [9] dplyr_1.2.0      workflowr_1.7.2 

loaded via a namespace (and not attached):
 [1] gtable_0.3.6       xfun_0.54          bslib_0.9.0        processx_3.8.6    
 [5] callr_3.7.6        tzdb_0.5.0         vctrs_0.7.1        tools_4.5.1       
 [9] ps_1.9.1           generics_0.1.4     parallel_4.5.1     pkgconfig_2.0.3   
[13] RColorBrewer_1.1-3 S7_0.2.1           lifecycle_1.0.5    compiler_4.5.1    
[17] farver_2.1.2       git2r_0.36.2       textshaping_1.0.4  getPass_0.2-4     
[21] httpuv_1.6.16      htmltools_0.5.9    sass_0.4.10        yaml_2.3.12       
[25] later_1.4.4        pillar_1.11.1      crayon_1.5.3       jquerylib_0.1.4   
[29] whisker_0.4.1      cachem_1.1.0       tidyselect_1.2.1   digest_0.6.39     
[33] stringi_1.8.7      purrr_1.2.1        labeling_0.4.3     rprojroot_2.1.1   
[37] fastmap_1.2.0      grid_4.5.1         cli_3.6.5          magrittr_2.0.4    
[41] withr_3.0.2        scales_1.4.0       promises_1.5.0     bit64_4.6.0-1     
[45] rmarkdown_2.30     httr_1.4.7         bit_4.6.0          otel_0.2.0        
[49] ragg_1.5.0         hms_1.1.4          evaluate_1.0.5     viridisLite_0.4.2 
[53] rlang_1.1.7        Rcpp_1.1.1         glue_1.8.0         xml2_1.5.1        
[57] svglite_2.2.2      rstudioapi_0.17.1  vroom_1.7.0        jsonlite_2.0.0    
[61] R6_2.6.1           systemfonts_1.3.1  fs_1.6.6