Genotype × Environment Analysis of inv4m Introgression Effects
Analysis of inv4m GxE Interactions
August 11, 2025
Overview
This analysis examines Genotype × Environment (GxE) interactions for the inv4m introgression across two environments:
- PSU2022: Pennsylvania environment (+P treatment, colder/northern)
- CLY2025: North Carolina environment (warmer/southern)
Research Questions: 1. Does inv4m show consistent effects across environments? 2. Which traits (PH, DTA, DTS) exhibit significant GxE interactions? 3. How does genetic background (donor) modify inv4m effects?
1. Load Libraries and Data
library(tidyverse)
library(rstatix)
library(ggpubr)
library(ggtext)
library(emmeans)
library(effectsize)
library(broom)
library(patchwork)
library(viridis)# Load spatially corrected datasets
psu2022 <- read.csv("PSU2022_spatially_corrected_phenotypes.csv", stringsAsFactors = FALSE)
cly2025 <- read.csv("CLY2025_spatially_corrected_phenotypes.csv", stringsAsFactors = FALSE)
# Check data structure
cat("PSU2022 dimensions:", dim(psu2022), "\n")## PSU2022 dimensions: 127 24cat("CLY2025 dimensions:", dim(cly2025), "\n")## CLY2025 dimensions: 64 17cat("PSU2022 genotypes:", unique(psu2022$genotype), "\n")## PSU2022 genotypes: Inv4m CTRL B73 NUEcat("CLY2025 genotypes:", unique(cly2025$genotype), "\n")## CLY2025 genotypes: INV4M CTRLcat("PSU2022 treatments:", unique(psu2022$Treatment), "\n")## PSU2022 treatments: -P +Pcat("CLY2025 donors:", unique(cly2025$donor), "\n")## CLY2025 donors: TMEX MI21# Define shared phenotypes
shared_phenotypes <- c("PH", "DTA", "DTS")2. Phase 1: Within-Environment Analysis
2.1 PSU2022 High-P Environment Analysis
# Filter PSU2022 to +P treatment and relevant genotypes
psu2022_highp <- psu2022 %>%
filter(Treatment == "+P", genotype %in% c("CTRL", "Inv4m")) %>%
select(plotId, genotype, repId, all_of(shared_phenotypes)) %>%
mutate(
genotype = factor(genotype, levels = c("CTRL", "Inv4m")),
environment = "PSU2022_HighP"
) %>%
filter(complete.cases(.))
cat("PSU2022 +P data - Genotype counts:\n")## PSU2022 +P data - Genotype counts:print(table(psu2022_highp$genotype))##
## CTRL Inv4m
## 16 16cat("Sample size per genotype:", nrow(psu2022_highp), "total plots\n")## Sample size per genotype: 32 total plots# Statistical analysis for PSU2022 +P
psu2022_results <- psu2022_highp %>%
pivot_longer(cols = all_of(shared_phenotypes),
names_to = "trait", values_to = "value") %>%
group_by(trait) %>%
t_test(value ~ genotype) %>%
adjust_pvalue(method = "fdr") %>%
add_significance("p.adj")
# Calculate effect sizes (Cohen's d)
psu2022_cohens_d <- psu2022_highp %>%
pivot_longer(cols = all_of(shared_phenotypes),
names_to = "trait", values_to = "value") %>%
group_by(trait) %>%
rstatix::cohens_d(value ~ genotype, ref.group = "Inv4m", ci = TRUE)
# Combine results
psu2022_summary <- psu2022_results %>%
left_join(psu2022_cohens_d %>% select(trait, effsize, magnitude), by = "trait")
print("PSU2022 High-P Results:")## [1] "PSU2022 High-P Results:"print(psu2022_summary)## # A tibble: 3 × 13
## trait .y. group1 group2 n1 n2 statistic df p p.adj
## <chr> <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <dbl>
## 1 DTA value CTRL Inv4m 16 16 3.56 28.9 0.00129 0.00129
## 2 DTS value CTRL Inv4m 16 16 4.83 29.1 0.0000408 0.000122
## 3 PH value CTRL Inv4m 16 16 -3.57 29.7 0.00123 0.00129
## # ℹ 3 more variables: p.adj.signif <chr>, effsize <dbl>, magnitude <ord>2.2 CLY2025 MI21 Donor Analysis
# Filter CLY2025 to MI21 donor and standardize genotype names
cly2025_mi21 <- cly2025 %>%
filter(donor == "MI21") %>%
select(plotId, genotype, repId, donor, all_of(shared_phenotypes)) %>%
mutate(
genotype = case_when(
genotype == "INV4M" ~ "Inv4m",
genotype == "CTRL" ~ "CTRL",
TRUE ~ genotype
),
genotype = factor(genotype, levels = c("CTRL", "Inv4m")),
environment = "CLY2025"
) %>%
filter(genotype %in% c("CTRL", "Inv4m")) %>%
filter(complete.cases(.))
cat("CLY2025 MI21 data - Genotype counts:\n")## CLY2025 MI21 data - Genotype counts:print(table(cly2025_mi21$genotype))##
## CTRL Inv4m
## 16 16cat("Sample size per genotype:", nrow(cly2025_mi21), "total plots\n")## Sample size per genotype: 32 total plots# Statistical analysis for CLY2025 MI21
cly2025_results <- cly2025_mi21 %>%
pivot_longer(cols = all_of(shared_phenotypes),
names_to = "trait", values_to = "value") %>%
group_by(trait) %>%
t_test(value ~ genotype) %>%
adjust_pvalue(method = "fdr") %>%
add_significance("p.adj")
# Calculate effect sizes
cly2025_cohens_d <- cly2025_mi21 %>%
pivot_longer(cols = all_of(shared_phenotypes),
names_to = "trait", values_to = "value") %>%
group_by(trait) %>%
rstatix::cohens_d(value ~ genotype, ref.group = "Inv4m", ci = TRUE)
# Combine results
cly2025_summary <- cly2025_results %>%
left_join(cly2025_cohens_d %>% select(trait, effsize, magnitude), by = "trait")
print("CLY2025 MI21 Results:")## [1] "CLY2025 MI21 Results:"print(cly2025_summary)## # A tibble: 3 × 13
## trait .y. group1 group2 n1 n2 statistic df p p.adj
## <chr> <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <dbl>
## 1 DTA value CTRL Inv4m 16 16 2.19 29.7 0.0362 0.0362
## 2 DTS value CTRL Inv4m 16 16 3.16 30.0 0.00357 0.00536
## 3 PH value CTRL Inv4m 16 16 3.62 29.7 0.00109 0.00327
## # ℹ 3 more variables: p.adj.signif <chr>, effsize <dbl>, magnitude <ord>3. Phase 2: Cross-Environment GxE Analysis
3.1 Data Integration for GxE Analysis
# Combine datasets for GxE analysis
gxe_data <- bind_rows(
psu2022_highp %>% select(plotId, genotype, environment, all_of(shared_phenotypes)),
cly2025_mi21 %>% select(plotId, genotype, environment, all_of(shared_phenotypes))
) %>%
mutate(
genotype = factor(genotype, levels = c("CTRL", "Inv4m")),
environment = factor(environment, levels = c("PSU2022_HighP", "CLY2025"))
) %>%
filter(complete.cases(.))
cat("Combined GxE dataset dimensions:", dim(gxe_data), "\n")## Combined GxE dataset dimensions: 64 6cat("Sample sizes by environment and genotype:\n")## Sample sizes by environment and genotype:print(table(gxe_data$environment, gxe_data$genotype))##
## CTRL Inv4m
## PSU2022_HighP 16 16
## CLY2025 16 163.2 GxE Statistical Analysis
# Two-way ANOVA for each trait
gxe_anova_results <- list()
gxe_emmeans_results <- list()
gxe_effect_sizes <- list()
for (trait in shared_phenotypes) {
cat("\n=== Analyzing", trait, "===\n")
# Prepare data for this trait
trait_data <- gxe_data %>%
select(plotId, genotype, environment, value = all_of(trait)) %>%
filter(!is.na(value))
# Two-way ANOVA: Genotype × Environment
anova_model <- aov(value ~ genotype * environment, data = trait_data)
anova_summary <- summary(anova_model)
# Effect sizes (eta-squared)
effect_sizes <- effectsize::eta_squared(anova_model)
# Store results
gxe_anova_results[[trait]] <- anova_summary
gxe_effect_sizes[[trait]] <- effect_sizes
# Print ANOVA results
cat("ANOVA Results for", trait, ":\n")
print(anova_summary)
cat("Effect Sizes:\n")
print(effect_sizes)
# Post-hoc analysis with emmeans
emmeans_result <- emmeans(anova_model, ~ genotype | environment)
emmeans_contrast <- pairs(emmeans_result)
gxe_emmeans_results[[trait]] <- list(
means = emmeans_result,
contrasts = emmeans_contrast
)
cat("Estimated Marginal Means:\n")
print(emmeans_result)
cat("Pairwise Comparisons:\n")
print(emmeans_contrast)
}##
## === Analyzing PH ===
## ANOVA Results for PH :
## Df Sum Sq Mean Sq F value Pr(>F)
## genotype 1 3 3 0.184 0.67
## environment 1 5949 5949 359.482 < 2e-16 ***
## genotype:environment 1 424 424 25.595 4.26e-06 ***
## Residuals 60 993 17
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Effect Sizes:
## # Effect Size for ANOVA (Type I)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------------
## genotype | 3.05e-03 | [0.00, 1.00]
## environment | 0.86 | [0.80, 1.00]
## genotype:environment | 0.30 | [0.15, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].Estimated Marginal Means:
## environment = PSU2022_HighP:
## genotype emmean SE df lower.CL upper.CL
## CTRL 163 1.02 60 161 165
## Inv4m 168 1.02 60 166 170
##
## environment = CLY2025:
## genotype emmean SE df lower.CL upper.CL
## CTRL 187 1.02 60 185 189
## Inv4m 183 1.02 60 180 185
##
## Confidence level used: 0.95
## Pairwise Comparisons:
## environment = PSU2022_HighP:
## contrast estimate SE df t.ratio p.value
## CTRL - Inv4m -5.58 1.44 60 -3.880 0.0003
##
## environment = CLY2025:
## contrast estimate SE df t.ratio p.value
## CTRL - Inv4m 4.71 1.44 60 3.274 0.0018
##
##
## === Analyzing DTA ===
## ANOVA Results for DTA :
## Df Sum Sq Mean Sq F value Pr(>F)
## genotype 1 14.27 14.27 17.408 9.87e-05 ***
## environment 1 297.16 297.16 362.607 < 2e-16 ***
## genotype:environment 1 3.86 3.86 4.712 0.0339 *
## Residuals 60 49.17 0.82
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Effect Sizes:
## # Effect Size for ANOVA (Type I)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------------
## genotype | 0.22 | [0.09, 1.00]
## environment | 0.86 | [0.80, 1.00]
## genotype:environment | 0.07 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].Estimated Marginal Means:
## environment = PSU2022_HighP:
## genotype emmean SE df lower.CL upper.CL
## CTRL 73.9 0.226 60 73.4 74.3
## Inv4m 72.5 0.226 60 72.0 72.9
##
## environment = CLY2025:
## genotype emmean SE df lower.CL upper.CL
## CTRL 77.7 0.226 60 77.3 78.2
## Inv4m 77.3 0.226 60 76.8 77.7
##
## Confidence level used: 0.95
## Pairwise Comparisons:
## environment = PSU2022_HighP:
## contrast estimate SE df t.ratio p.value
## CTRL - Inv4m 1.436 0.32 60 4.485 <.0001
##
## environment = CLY2025:
## contrast estimate SE df t.ratio p.value
## CTRL - Inv4m 0.453 0.32 60 1.415 0.1621
##
##
## === Analyzing DTS ===
## ANOVA Results for DTS :
## Df Sum Sq Mean Sq F value Pr(>F)
## genotype 1 17.55 17.55 32.976 3.29e-07 ***
## environment 1 176.92 176.92 332.481 < 2e-16 ***
## genotype:environment 1 1.66 1.66 3.115 0.0827 .
## Residuals 60 31.93 0.53
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Effect Sizes:
## # Effect Size for ANOVA (Type I)
##
## Parameter | Eta2 (partial) | 95% CI
## ----------------------------------------------------
## genotype | 0.35 | [0.20, 1.00]
## environment | 0.85 | [0.79, 1.00]
## genotype:environment | 0.05 | [0.00, 1.00]
##
## - One-sided CIs: upper bound fixed at [1.00].Estimated Marginal Means:
## environment = PSU2022_HighP:
## genotype emmean SE df lower.CL upper.CL
## CTRL 75.36 0.182 60 74.99 75.72
## Inv4m 73.99 0.182 60 73.62 74.35
##
## environment = CLY2025:
## genotype emmean SE df lower.CL upper.CL
## CTRL 78.36 0.182 60 77.99 78.72
## Inv4m 77.63 0.182 60 77.27 78.00
##
## Confidence level used: 0.95
## Pairwise Comparisons:
## environment = PSU2022_HighP:
## contrast estimate SE df t.ratio p.value
## CTRL - Inv4m 1.369 0.258 60 5.309 <.0001
##
## environment = CLY2025:
## contrast estimate SE df t.ratio p.value
## CTRL - Inv4m 0.725 0.258 60 2.813 0.00663.3 GxE Interaction Effects
# Extract interaction p-values and effect sizes
gxe_interaction_summary <- data.frame(
trait = shared_phenotypes,
interaction_p = numeric(length(shared_phenotypes)),
interaction_eta2 = numeric(length(shared_phenotypes)),
genotype_p = numeric(length(shared_phenotypes)),
environment_p = numeric(length(shared_phenotypes))
)
for (i in seq_along(shared_phenotypes)) {
trait <- shared_phenotypes[i]
# Extract p-values from ANOVA
anova_df <- as.data.frame(gxe_anova_results[[trait]][[1]])
gxe_interaction_summary$interaction_p[i] <- anova_df["genotype:environment", "Pr(>F)"]
gxe_interaction_summary$genotype_p[i] <- anova_df["genotype", "Pr(>F)"]
gxe_interaction_summary$environment_p[i] <- anova_df["environment", "Pr(>F)"]
# Extract eta-squared for interaction
interaction_row <- gxe_effect_sizes[[trait]] %>%
filter(Parameter == "genotype:environment")
gxe_interaction_summary$interaction_eta2[i] <-
if(nrow(interaction_row) > 0) interaction_row$Eta2[1] else NA
}
# Add significance indicators
gxe_interaction_summary <- gxe_interaction_summary %>%
mutate(
interaction_sig = case_when(
interaction_p < 0.001 ~ "***",
interaction_p < 0.01 ~ "**",
interaction_p < 0.05 ~ "*",
TRUE ~ "ns"
),
genotype_sig = case_when(
genotype_p < 0.001 ~ "***",
genotype_p < 0.01 ~ "**",
genotype_p < 0.05 ~ "*",
TRUE ~ "ns"
),
environment_sig = case_when(
environment_p < 0.001 ~ "***",
environment_p < 0.01 ~ "**",
environment_p < 0.05 ~ "*",
TRUE ~ "ns"
)
)
print("GxE Interaction Summary:")## [1] "GxE Interaction Summary:"print(gxe_interaction_summary)## trait interaction_p interaction_eta2 genotype_p environment_p interaction_sig
## 1 PH 4.258027e-06 0.29902143 NA 5.088033e-27 ***
## 2 DTA 3.392581e-02 0.07281053 NA 4.070043e-27 *
## 3 DTS 8.266769e-02 0.04935305 NA 3.765287e-26 ns
## genotype_sig environment_sig
## 1 ns ***
## 2 ns ***
## 3 ns ***4. Phase 3: Comprehensive Visualization
4.1 Interaction Plots
# Calculate means and SE for interaction plots
interaction_stats <- gxe_data %>%
pivot_longer(cols = all_of(shared_phenotypes),
names_to = "trait", values_to = "value") %>%
group_by(trait, genotype, environment) %>%
summarise(
mean_value = mean(value, na.rm = TRUE),
se_value = sd(value, na.rm = TRUE) / sqrt(n()),
n = n(),
.groups = "drop"
)
pheno_theme <- ggpubr::theme_classic2(base_size = 20) +
ggplot2::theme(
plot.title = ggtext::element_markdown(hjust = 0.5, face ="bold"),
axis.title.y = ggtext::element_markdown(),
axis.title.x = element_blank(),
axis.text.x = element_text( angle=45, face="bold", color= "black", hjust = 1),
strip.background = element_blank(),
strip.text = ggtext::element_markdown(size=20),
legend.position = "top")
interaction_stats$trait <- factor(interaction_stats$trait, levels = c("PH","DTA","DTS"))
interaction_stats$environment <- factor(interaction_stats$environment,
levels = c( "CLY2025","PSU2022_HighP"))
# Create interaction plots
interaction_plot <- ggplot(interaction_stats,
aes(x = environment, y = mean_value,
color = genotype, group = genotype)) +
geom_line(size = 1.2, alpha = 0.8) +
geom_point(size = 3) +
geom_errorbar(aes(ymin = mean_value - se_value, ymax = mean_value + se_value),
width = 0.1, size = 1) +
scale_color_manual(values = c("CTRL" = "gold", "Inv4m" = "purple4")) +
facet_wrap(~ trait, scales = "free_y", ncol = 3) +
labs(
title = "**Genotype × Environment Interaction Effects, Mi21 donor**",
subtitle = "Genotype means ± SE across environments",
x = "Environment",
y = "Trait Value",
color = "Genotype"
) + pheno_theme
print(interaction_plot)
4.2 Effect Size Comparisons
# Calculate environment-specific effect sizes
env_effect_sizes <- bind_rows(
psu2022_cohens_d %>% mutate(environment = "PSU2022_HighP"),
cly2025_cohens_d %>% mutate(environment = "CLY2025")
) %>%
select(trait, environment, magnitude, effsize, conf.low, conf.high) %>%
mutate(trait = factor(trait, levels = c( "DTS","DTA","PH")))
pheno_theme2 <- ggpubr::theme_classic2(base_size = 20) +
ggplot2::theme(
plot.title = ggtext::element_markdown(hjust = 0.5, face ="bold"),
axis.title.y = ggtext::element_markdown(),
axis.title.x = element_blank(),
axis.text.x = element_text( face="bold", color= "black"),
strip.background = element_blank(),
strip.text = ggtext::element_markdown(size=20),
legend.position = "top")
# Forest plot of effect sizes
forest_plot <- env_effect_sizes %>%
ggplot(aes(x = effsize, y = trait, color = environment)) +
geom_vline(xintercept = 0, linetype = "dashed", alpha = 0.6) +
geom_errorbarh(aes(xmin = conf.low,
xmax = conf.high),
height = 0.2, position = position_dodge(width = 0.4)) +
geom_point(size = 4, position = position_dodge(width = 0.4)) +
geom_text(aes(label = paste0("(", magnitude, ")")),
position = position_dodge(width = 0.4),
hjust = -0.2, size = 3) +
scale_color_manual(values= c("tomato", "royalblue")) +
labs(
title = "**Effect Sizes (Cohen's d) of inv4m Across Environments**",
subtitle = "Positive values indicate Inv4m > CTRL",
x = "Cohen's d (Effect Size)",
y = "Trait",
color = "Environment"
) +
pheno_theme2
print(forest_plot)
5. Summary and Export Results
5.1 Summary Tables
# Create comprehensive summary table
final_summary <- list(
PSU2022_HighP = psu2022_summary,
CLY2025_MI21 = cly2025_summary,
GxE_Interactions = gxe_interaction_summary,
Effect_Sizes_by_Environment = env_effect_sizes
)
# Print final summary
cat("=== FINAL SUMMARY ===\n\n")## === FINAL SUMMARY ===cat("1. PSU2022 High-P:\n")## 1. PSU2022 High-P:print(final_summary$PSU2022_HighP)## # A tibble: 3 × 13
## trait .y. group1 group2 n1 n2 statistic df p p.adj
## <chr> <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <dbl>
## 1 DTA value CTRL Inv4m 16 16 3.56 28.9 0.00129 0.00129
## 2 DTS value CTRL Inv4m 16 16 4.83 29.1 0.0000408 0.000122
## 3 PH value CTRL Inv4m 16 16 -3.57 29.7 0.00123 0.00129
## # ℹ 3 more variables: p.adj.signif <chr>, effsize <dbl>, magnitude <ord>cat("\n2. CLY2025 MI21:\n") ##
## 2. CLY2025 MI21:print(final_summary$CLY2025_MI21)## # A tibble: 3 × 13
## trait .y. group1 group2 n1 n2 statistic df p p.adj
## <chr> <chr> <chr> <chr> <int> <int> <dbl> <dbl> <dbl> <dbl>
## 1 DTA value CTRL Inv4m 16 16 2.19 29.7 0.0362 0.0362
## 2 DTS value CTRL Inv4m 16 16 3.16 30.0 0.00357 0.00536
## 3 PH value CTRL Inv4m 16 16 3.62 29.7 0.00109 0.00327
## # ℹ 3 more variables: p.adj.signif <chr>, effsize <dbl>, magnitude <ord>cat("\n3. GxE Interaction Effects:\n")##
## 3. GxE Interaction Effects:print(final_summary$GxE_Interactions)## trait interaction_p interaction_eta2 genotype_p environment_p interaction_sig
## 1 PH 4.258027e-06 0.29902143 NA 5.088033e-27 ***
## 2 DTA 3.392581e-02 0.07281053 NA 4.070043e-27 *
## 3 DTS 8.266769e-02 0.04935305 NA 3.765287e-26 ns
## genotype_sig environment_sig
## 1 ns ***
## 2 ns ***
## 3 ns ***cat("\n4. Effect Sizes by Environment:\n")##
## 4. Effect Sizes by Environment:print(final_summary$Effect_Sizes_by_Environment)## # A tibble: 6 × 6
## trait environment magnitude effsize conf.low conf.high
## <fct> <chr> <ord> <dbl> <dbl> <dbl>
## 1 DTA PSU2022_HighP large -1.26 -2.31 -0.6
## 2 DTS PSU2022_HighP large -1.71 -2.84 -1.06
## 3 PH PSU2022_HighP large 1.26 0.52 2.21
## 4 DTA CLY2025 moderate -0.776 -1.64 -0.05
## 5 DTS CLY2025 large -1.12 -2.1 -0.41
## 6 PH CLY2025 large -1.28 -2.11 -0.645.2 Export Results
# Export summary tables
write.csv(final_summary$PSU2022_HighP, "PSU2022_HighP_inv4m_results.csv", row.names = FALSE)
write.csv(final_summary$CLY2025_MI21, "CLY2025_MI21_inv4m_results.csv", row.names = FALSE)
write.csv(final_summary$GxE_Interactions, "GxE_interaction_results.csv", row.names = FALSE)
write.csv(final_summary$Effect_Sizes_by_Environment, "effect_sizes_by_environment.csv", row.names = FALSE)
# Export combined dataset
write.csv(gxe_data, "combined_gxe_dataset.csv", row.names = FALSE)
cat("Results exported to CSV files:\n")## Results exported to CSV files:cat("- PSU2022_HighP_inv4m_results.csv\n")## - PSU2022_HighP_inv4m_results.csvcat("- CLY2025_MI21_inv4m_results.csv\n") ## - CLY2025_MI21_inv4m_results.csvcat("- GxE_interaction_results.csv\n")## - GxE_interaction_results.csvcat("- effect_sizes_by_environment.csv\n")## - effect_sizes_by_environment.csvcat("- combined_gxe_dataset.csv\n")## - combined_gxe_dataset.csv6. Key Findings
cat("=== KEY FINDINGS ===\n\n")## === KEY FINDINGS ===# Identify significant GxE interactions
sig_interactions <- gxe_interaction_summary %>%
filter(interaction_p < 0.05) %>%
pull(trait)
if (length(sig_interactions) > 0) {
cat("Traits with significant GxE interactions (p < 0.05):\n")
cat(paste(sig_interactions, collapse = ", "), "\n\n")
} else {
cat("No significant GxE interactions detected (p < 0.05)\n\n")
}## Traits with significant GxE interactions (p < 0.05):
## PH, DTA# Identify consistent effects across environments
consistent_effects <- env_effect_sizes %>%
group_by(trait) %>%
summarise(
same_direction = all(sign(effsize) == sign(effsize[1])),
min_effect = min(abs(effsize)),
max_effect = max(abs(effsize)),
.groups = "drop"
)
cat("Traits with consistent inv4m effects across environments:\n")## Traits with consistent inv4m effects across environments:if (nrow(consistent_effects) > 0) {
print(consistent_effects)
} else {
cat("No traits show consistent effects across environments\n")
}## # A tibble: 3 × 4
## trait same_direction min_effect max_effect
## <fct> <lgl> <dbl> <dbl>
## 1 DTS TRUE 1.12 1.71
## 2 DTA TRUE 0.776 1.26
## 3 PH FALSE 1.26 1.28