O1 Veg Diversity Quadratic Linear Model

pacman::p_load(tidyverse, readxl, raster, vegan, ggplot2,
               tigris, sf, sp, plotly, ggrepel, rstanarm, mgcv,
               brms, lme4, caret, MuMIn, VSURF, loo, patchwork)

EnvironmentalOutputs <- read_excel("C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/03_Biodiversity/06_Processing/Environmental_Outputs.xlsx")

# Tree PCQ Data
tree_data <- read_excel("C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/05_SharedData/Field_Data_FL_AL_MS.xlsx",
                        sheet = "Tree_PCQ")

# Veg Data
Veg_Cover <- read_excel("C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/05_SharedData/Field_Data_FL_AL_MS.xlsx",
                        sheet = "Veg_Cover")

# Shrub Cover Data
shrub_data <- read_excel("C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/05_SharedData/Field_Data_FL_AL_MS.xlsx",
                         sheet = "Shrub_Cover")

# Site Data
CogonSites <- read_excel("C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/05_SharedData/CogonSites_FL_AL_MS.xlsx")

Number of quadrats sampled per plot

# Count the total number of quadrats per plot
quadrat_count <- Veg_Cover %>%
  group_by(Plot) %>%
  summarize(total_quadrats = n_distinct(Quadrat), .groups = "drop")

Filter All data to only include specified species (Per PLANTS database)

#Filter tree data to only include trees with "tree" in the growth column
tree_data <- dplyr::filter(tree_data, Growth == "Tree")

#Filter Veg Cover to exclude Shrubs and Trees
Veg_Cover <- dplyr::filter(Veg_Cover, Growth != "Shrub" & Growth != "Tree")

#Filter Shrub Cover to only include Shrubs and Trees
shrub_data <- dplyr::filter(shrub_data, Growth == "Shrub" | Growth == "Tree")

Shrub Cover Conversion

# Total length of Shrub cover at a site
shrub_cover <- shrub_data %>%
  mutate(Cover = Line_End - Line_Start) %>%
  group_by(Species_Name, Plot, InvStatus) %>%
  summarise(Total_Cover = sum(Cover, na.rm = TRUE), .groups = "drop") %>%
  mutate(Percent_Cover = Total_Cover / 3000 * 100)

Herbacous Cover Conversion

# Combine Plot and Quadrat columns
Veg_Cover <- Veg_Cover %>%
  mutate(Plot_Quadrat = paste(Plot, Quadrat, sep = '_'))

# Join with CogonSites to get site information
Veg_Cover <- Veg_Cover %>%
  left_join(CogonSites, by = "Plot")

# Sum species cover across quadrats for each species at each plot
veg_cover_summed <- Veg_Cover %>%
  group_by(Plot, Species_Name, InvStatus) %>%
  summarize(total_cover = sum(Cover_Per, na.rm = TRUE), .groups = "drop")

# Calculate average herbaceous species cover
avg_species_cover <- veg_cover_summed %>%
  left_join(quadrat_count, by = "Plot") %>%
  mutate(avg_cover = total_cover / total_quadrats)

Merging Herb cover with Shrub

This species matrix includes herbaceous and shrub species

# Merge shrub cover with herbaceous average cover
combined_cover <- avg_species_cover %>%
  full_join(
    shrub_cover %>%
      select(Plot, Species_Name, Percent_Cover, InvStatus),
    by = c("Plot", "Species_Name")
  ) %>%
  mutate(
    overlap_flag = ifelse(!is.na(avg_cover) & !is.na(Percent_Cover), TRUE, FALSE), # Flag overlaps
    final_cover = case_when(
      !is.na(avg_cover) & is.na(Percent_Cover) ~ avg_cover,  # Use herbaceous cover if no shrub data
      is.na(avg_cover) & !is.na(Percent_Cover) ~ Percent_Cover, # Use shrub cover if no herbaceous data
      TRUE ~ NA_real_ # Leave as NA where overlaps exist
    )
  )

Extract Cogongrass Cover

# Extract cogongrass cover
cogongrass_cover <- combined_cover %>%
  filter(Species_Name == "Imperata_cylindrica") %>%
  select(Plot, final_cover) %>%
  rename(Cogongrass_Cover = final_cover)

Species Matrix

combined_cover <- combined_cover %>%
  filter(Species_Name != "Imperata_cylindrica" , Species_Name != "Imperata_cylindrica_Live") # Remove cogongrass from species matrix

## Remove any non_native species
combined_cover <- combined_cover %>%
  filter(InvStatus.x != "Non_Native") # Remove non-native species from species matrix

species_matrix <- combined_cover %>%
  select(Plot, Species_Name, final_cover) %>%
  pivot_wider(
    names_from = Species_Name,
    values_from = final_cover,
    values_fill = 0
  )

Shannon Diversity

# Calculate Shannon diversity index for each site
shannon_diversity <- species_matrix %>%
  select(-Plot) %>%
  vegan::diversity(index = "shannon") %>%
  as.data.frame() %>%
  setNames("Shannon_Diversity") %>%
  mutate(Plot = species_matrix$Plot)

Merge Shannon Diversity with Cogongrass Cover and Environmental Data

# Merge Shannon diversity with cogongrass cover, tree canopy cover, and environmental outputs
model_data <- shannon_diversity %>%
  left_join(cogongrass_cover, by = "Plot") %>%
  left_join(EnvironmentalOutputs, by = "Plot") %>%
  mutate(Cogongrass_Cover = ifelse(is.na(Cogongrass_Cover), 0, Cogongrass_Cover))

# Inspect to see if there are any columns with only one level
model_data$Site <- as.factor(model_data$Site)
summary(model_data)

##  Shannon_Diversity     Plot           Cogongrass_Cover       Site   
##  Min.   :0.000     Length:206         Min.   : 0.00    WSF     :44  
##  1st Qu.:2.065     Class :character   1st Qu.: 0.00    Jay     :42  
##  Median :2.407     Mode  :character   Median : 0.00    BCNWR   :32  
##  Mean   :2.333                        Mean   :17.08    DSNF    :24  
##  3rd Qu.:2.720                        3rd Qu.:29.82    CNF     :23  
##  Max.   :3.552                        Max.   :92.14    Escambia:11  
##                                                        (Other) :30  
##     BurnYear       Camera             Latitude       Longitude     
##  Min.   :2000   Length:206         Min.   :28.48   Min.   :-89.80  
##  1st Qu.:2014   Class :character   1st Qu.:29.56   1st Qu.:-88.91  
##  Median :2022   Mode  :character   Median :30.77   Median :-87.14  
##  Mean   :2018                      Mean   :30.38   Mean   :-86.72  
##  3rd Qu.:2022                      3rd Qu.:30.98   3rd Qu.:-83.58  
##  Max.   :2024                      Max.   :31.59   Max.   :-81.94  
##  NA's   :42                                                        
##     Muname          NLCD_LandCover        Region            SoilType        
##  Length:206         Length:206         Length:206         Length:206        
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##                                                                             
##     Status          TreeCanopy_NLCD     aspect        elevation     
##  Length:206         Min.   : 0.00   Min.   :  0.0   Min.   : 17.00  
##  Class :character   1st Qu.:51.50   1st Qu.: 90.0   1st Qu.: 38.00  
##  Mode  :character   Median :75.50   Median :180.0   Median : 59.00  
##                     Mean   :66.22   Mean   :171.7   Mean   : 57.68  
##                     3rd Qu.:86.75   3rd Qu.:270.0   3rd Qu.: 75.00  
##                     Max.   :98.00   Max.   :350.6   Max.   :111.00  
##                                                                     
##       ndvi              pr            slope             sph         
##  Min.   :0.2728   Min.   :3.850   Min.   : 0.000   Min.   :0.01051  
##  1st Qu.:0.4303   1st Qu.:4.345   1st Qu.: 2.149   1st Qu.:0.01074  
##  Median :0.4624   Median :4.592   Median : 2.984   Median :0.01091  
##  Mean   :0.4503   Mean   :4.566   Mean   : 3.601   Mean   :0.01145  
##  3rd Qu.:0.4846   3rd Qu.:4.796   3rd Qu.: 4.688   3rd Qu.:0.01183  
##  Max.   :0.5357   Max.   :5.294   Max.   :18.429   Max.   :0.01325  
##                                                                     
##       srad            tmmn            agb        
##  Min.   :204.7   Min.   :285.7   Min.   :  5.00  
##  1st Qu.:206.8   1st Qu.:286.6   1st Qu.: 74.00  
##  Median :207.0   Median :287.2   Median : 96.00  
##  Mean   :210.6   Mean   :287.4   Mean   : 99.92  
##  3rd Qu.:216.6   3rd Qu.:288.6   3rd Qu.:133.00  
##  Max.   :224.2   Max.   :290.3   Max.   :211.00  
## 

Model Fit

shannon_lmer_ml <- lmer(Shannon_Diversity ~ Cogongrass_Cover +
                          (1 | Site),
                        data = model_data, REML = FALSE)

shannon_lmer_quad_ml <- lmer(Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2) +
                               (1 | Site),
                             data = model_data, REML = FALSE)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

Model Comparison

aic_tab <- AIC(shannon_lmer_ml, shannon_lmer_quad_ml)
aic_tab$delta <- aic_tab$AIC - min(aic_tab$AIC)
print(aic_tab)

##                      df      AIC    delta
## shannon_lmer_ml       4 313.5426 11.47665
## shannon_lmer_quad_ml  5 302.0660  0.00000

summary(shannon_lmer_quad_ml)

## Linear mixed model fit by maximum likelihood  ['lmerMod']
## Formula: Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2) +  
##     (1 | Site)
##    Data: model_data
## 
##       AIC       BIC    logLik -2*log(L)  df.resid 
##     302.1     318.7    -146.0     292.1       201 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.5448 -0.5122  0.0852  0.6761  2.5135 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 0.07534  0.2745  
##  Residual             0.22048  0.4695  
## Number of obs: 206, groups:  Site, 10
## 
## Fixed effects:
##                         Estimate Std. Error t value
## (Intercept)            2.267e+00  9.992e-02  22.688
## Cogongrass_Cover       9.878e-03  3.874e-03   2.550
## I(Cogongrass_Cover^2) -1.962e-04  5.251e-05  -3.736
## 
## Correlation of Fixed Effects:
##             (Intr) Cgng_C
## Cgngrss_Cvr -0.229       
## I(Cgng_C^2)  0.158 -0.934
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling

LOOCV

sites <- levels(model_data$Site)
obs_all <- pred_lmer_all <- pred_quad_all <- c()

for (s in sites) {
  train <- subset(model_data, Site != s)
  test  <- subset(model_data, Site == s)

  fit_lmer <- lmer(Shannon_Diversity ~ Cogongrass_Cover + (1 | Site),
                   data = train, REML = FALSE)
  fit_quad <- lmer(Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2) + (1 | Site),
                   data = train, REML = FALSE)

  obs_all       <- c(obs_all,       test$Shannon_Diversity)
  pred_lmer_all <- c(pred_lmer_all, predict(fit_lmer, newdata = test, re.form = NA))
  pred_quad_all <- c(pred_quad_all, predict(fit_quad, newdata = test, re.form = NA))
}

## Warning: Some predictor variables are on very different scales: consider
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rmse   <- function(y, yhat) sqrt(mean((y - yhat)^2))
mae    <- function(y, yhat) mean(abs(y - yhat))
r2_oos <- function(y, yhat) 1 - sum((y - yhat)^2) / sum((y - mean(y))^2)

metrics <- list(
  LMM_Linear = c(
    RMSE = rmse(obs_all, pred_lmer_all),
    MAE  = mae(obs_all,  pred_lmer_all),
    R2   = r2_oos(obs_all, pred_lmer_all)
  ),
  LMM_Quadratic = c(
    RMSE = rmse(obs_all, pred_quad_all),
    MAE  = mae(obs_all,  pred_quad_all),
    R2   = r2_oos(obs_all, pred_quad_all)
  )
)

print(metrics)

## $LMM_Linear
##       RMSE        MAE         R2 
##  0.5650397  0.4485244 -0.1101912 
## 
## $LMM_Quadratic
##        RMSE         MAE          R2 
##  0.55213009  0.44305887 -0.06004089

Observed vs. Predicted Plot

plot_data <- data.frame(
  Observed              = obs_all,
  LMM_Predicted         = pred_lmer_all,
  LMM_Quadratic_Predicted = pred_quad_all
)

ggplot(plot_data, aes(x = Observed)) +
  geom_point(aes(y = LMM_Predicted,           color = "LMM Linear"),    alpha = 0.6) +
  geom_point(aes(y = LMM_Quadratic_Predicted, color = "LMM Quadratic"), alpha = 0.6) +
  geom_abline(slope = 1, intercept = 0, linetype = "dashed", color = "black") +
  labs(x = "Observed Shannon Diversity", y = "Predicted Shannon Diversity") +
  scale_color_manual(name = "Model",
                     values = c("LMM Linear" = "blue", "LMM Quadratic" = "orange")) +
  theme_minimal()

Quadratic Smooth Curve

cov_seq  <- seq(min(model_data$Cogongrass_Cover), max(model_data$Cogongrass_Cover), length.out = 200)
pred_df  <- data.frame(Cogongrass_Cover = cov_seq, Site = model_data$Site[1])

# Refit final quadratic model under REML for inference
shannon_lmer_quad_reml <- lmer(Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2) +
                                 (1 | Site),
                               data = model_data, REML = TRUE)

## Warning: Some predictor variables are on very different scales: consider
## rescaling

pred_df$fit <- predict(shannon_lmer_quad_reml, newdata = pred_df, re.form = NA)

# Bootstrap 95% CI (population level)
set.seed(42)
boot_preds <- replicate(500, {
  b_data <- model_data[sample(nrow(model_data), replace = TRUE), ]
  b_fit  <- tryCatch(
    lmer(Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2) + (1 | Site),
         data = b_data, REML = FALSE),
    error = function(e) NULL
  )
  if (is.null(b_fit)) return(rep(NA, nrow(pred_df)))
  predict(b_fit, newdata = pred_df, re.form = NA)
})

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pred_df$lwr <- apply(boot_preds, 1, quantile, 0.025, na.rm = TRUE)
pred_df$upr <- apply(boot_preds, 1, quantile, 0.975, na.rm = TRUE)

smooth_plot <- ggplot() +
  geom_ribbon(data = pred_df,
              aes(x = Cogongrass_Cover, ymin = lwr, ymax = upr),
              fill = "#0072B2", alpha = 0.2) +
  geom_line(data = pred_df,
            aes(x = Cogongrass_Cover, y = fit),
            color = "#0072B2", linewidth = 1) +
  geom_rug(data = model_data,
           aes(x = Cogongrass_Cover),
           sides = "b", length = unit(0.03, "npc"), color = "black", alpha = 0.7) +
  labs(x = "Cogongrass Cover (%)", y = "Shannon Diversity") +
  theme_minimal(base_size = 14) +
  theme(
    axis.title.x    = element_text(margin = margin(t = 10)),
    axis.title.y    = element_text(margin = margin(r = 10)),
    panel.grid.minor = element_blank(),
    panel.grid.major = element_line(color = "grey80", linetype = "dotted"),
    axis.line        = element_line(color = "black")
  )

ggsave("C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/03_Biodiversity/03_Figure/Quadratic_Cogon_Diversity.png",
       plot = smooth_plot, width = 8, height = 6, dpi = 300)

Regional analysis

# --- Regional Groups ---
central_fl <- c("ONF", "WSF")
north_fl   <- c("BRSF", "Escambia", "Jay", "Howell", "Hooper")
south_ms   <- c("CNF", "DSNF", "BCNWR")

run_region_quad <- function(region_sites, data, min_sites = 3) {

  region_data      <- subset(data, Site %in% region_sites)
  region_data$Site <- droplevels(as.factor(region_data$Site))
  n_sites          <- length(unique(region_data$Site))
  use_mixed        <- n_sites >= min_sites

  cat("\n=============================\n")
  cat("Region Sites:", region_sites, "\n")
  cat("Number of Sites:", n_sites, "\n")
  cat("Using mixed effects:", use_mixed, "\n")
  cat("=============================\n")

  # --- Fit both models ---
  if (use_mixed) {
    fit_linear <- lmer(Shannon_Diversity ~ Cogongrass_Cover +
                         (1 | Site),
                       data = region_data, REML = FALSE)  # ML for fair AIC comparison
    fit_quad   <- lmer(Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2) +
                         (1 | Site),
                       data = region_data, REML = FALSE)
  } else {
    fit_linear <- lm(Shannon_Diversity ~ Cogongrass_Cover,
                     data = region_data)
    fit_quad   <- lm(Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2),
                     data = region_data)
  }

  # --- AIC Comparison ---
  aic_tab       <- AIC(fit_linear, fit_quad)
  aic_tab$delta <- aic_tab$AIC - min(aic_tab$AIC)
  rownames(aic_tab) <- c("Linear", "Quadratic")
  cat("\nAIC Comparison:\n")
  print(aic_tab)

  # Select best model by AIC
  best_label <- ifelse(aic_tab["Quadratic", "delta"] < aic_tab["Linear", "delta"],
                       "Quadratic", "Linear")
  cat("Best model by AIC:", best_label, "\n")

  # Refit best model under REML (lmer) for final inference
  if (use_mixed) {
    fit_best <- lmer(
      if (best_label == "Quadratic")
        Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2) + (1 | Site)
      else
        Shannon_Diversity ~ Cogongrass_Cover + (1 | Site),
      data = region_data, REML = TRUE
    )
  } else {
    fit_best <- if (best_label == "Quadratic") fit_quad else fit_linear
  }

  print(summary(fit_best))

  # --- LOOCV for both models ---
  sites <- unique(region_data$Site)
  obs_all <- pred_linear <- pred_quad <- c()

  for (s in sites) {
    train <- subset(region_data, Site != s)
    test  <- subset(region_data, Site == s)

    cv_linear <- tryCatch({
      if (use_mixed)
        lmer(Shannon_Diversity ~ Cogongrass_Cover + (1 | Site),
             data = train, REML = FALSE)
      else
        lm(Shannon_Diversity ~ Cogongrass_Cover, data = train)
    }, error = function(e) { cat("Linear CV failed for site", s, "\n"); NULL })

    cv_quad <- tryCatch({
      if (use_mixed)
        lmer(Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2) + (1 | Site),
             data = train, REML = FALSE)
      else
        lm(Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2), data = train)
    }, error = function(e) { cat("Quadratic CV failed for site", s, "\n"); NULL })

    if (is.null(cv_linear) | is.null(cv_quad)) next

    obs_all    <- c(obs_all,    test$Shannon_Diversity)
    pred_linear <- c(pred_linear, predict(cv_linear, newdata = test,
                                          re.form = if (use_mixed) NA else NULL))
    pred_quad  <- c(pred_quad,  predict(cv_quad,  newdata = test,
                                        re.form = if (use_mixed) NA else NULL))
  }

  metrics <- list(
    Linear = c(
      RMSE = rmse(obs_all, pred_linear),
      MAE  = mae(obs_all,  pred_linear),
      R2   = r2_oos(obs_all, pred_linear)
    ),
    Quadratic = c(
      RMSE = rmse(obs_all, pred_quad),
      MAE  = mae(obs_all,  pred_quad),
      R2   = r2_oos(obs_all, pred_quad)
    )
  )

  cat("\nLOOCV Metrics:\n")
  print(metrics)

  return(list(
    model      = fit_best,
    best_label = best_label,
    aic_table  = aic_tab,
    cv_metrics = metrics,
    use_mixed  = use_mixed
  ))
}

central_mod <- run_region_quad(central_fl, model_data)

## 
## =============================
## Region Sites: ONF WSF 
## Number of Sites: 2 
## Using mixed effects: FALSE 
## =============================
## 
## AIC Comparison:
##           df      AIC     delta
## Linear     3 90.29496 0.2030604
## Quadratic  4 90.09190 0.0000000
## Best model by AIC: Quadratic 
## 
## Call:
## lm(formula = Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2), 
##     data = region_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1707 -0.3365  0.1024  0.3844  1.1104 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            2.3797985  0.0965911  24.638   <2e-16 ***
## Cogongrass_Cover      -0.0001371  0.0095605  -0.014    0.989    
## I(Cogongrass_Cover^2) -0.0001793  0.0001231  -1.456    0.152    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5489 on 49 degrees of freedom
## Multiple R-squared:  0.265,  Adjusted R-squared:  0.235 
## F-statistic: 8.831 on 2 and 49 DF,  p-value: 0.0005305
## 
## 
## LOOCV Metrics:
## $Linear
##       RMSE        MAE         R2 
##  1.1106755  0.9834191 -2.1940762 
## 
## $Quadratic
##      RMSE       MAE        R2 
##  1.221268  1.042377 -2.861826

north_mod   <- run_region_quad(north_fl,   model_data)

## 
## =============================
## Region Sites: BRSF Escambia Jay Howell Hooper 
## Number of Sites: 5 
## Using mixed effects: TRUE 
## =============================

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## 
## AIC Comparison:
##           df      AIC    delta
## Linear     4 101.4567 0.000000
## Quadratic  5 103.4140 1.957266
## Best model by AIC: Linear 
## Linear mixed model fit by REML ['lmerMod']
## Formula: Shannon_Diversity ~ Cogongrass_Cover + (1 | Site)
##    Data: region_data
## 
## REML criterion at convergence: 106
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.4054 -0.5624  0.1082  0.6794  1.7730 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 0.05732  0.2394  
##  Residual             0.18954  0.4354  
## Number of obs: 75, groups:  Site, 5
## 
## Fixed effects:
##                   Estimate Std. Error t value
## (Intercept)      2.215e+00  1.296e-01  17.090
## Cogongrass_Cover 7.374e-05  2.628e-03   0.028
## 
## Correlation of Fixed Effects:
##             (Intr)
## Cgngrss_Cvr -0.280

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## 
## LOOCV Metrics:
## $Linear
##       RMSE        MAE         R2 
##  0.4951540  0.3910515 -0.1587836 
## 
## $Quadratic
##       RMSE        MAE         R2 
##  0.5016398  0.3931736 -0.1893390

south_mod   <- run_region_quad(south_ms,   model_data)

## 
## =============================
## Region Sites: CNF DSNF BCNWR 
## Number of Sites: 3 
## Using mixed effects: TRUE 
## =============================

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## 
## AIC Comparison:
##           df      AIC    delta
## Linear     4 123.3004 8.286584
## Quadratic  5 115.0138 0.000000
## Best model by AIC: Quadratic

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## Linear mixed model fit by REML ['lmerMod']
## Formula: Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2) +  
##     (1 | Site)
##    Data: region_data
## 
## REML criterion at convergence: 135.9
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.00145 -0.44401  0.07645  0.50625  2.14876 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Site     (Intercept) 0.02006  0.1417  
##  Residual             0.22016  0.4692  
## Number of obs: 79, groups:  Site, 3
## 
## Fixed effects:
##                         Estimate Std. Error t value
## (Intercept)            2.432e+00  1.095e-01  22.218
## Cogongrass_Cover       1.680e-02  5.869e-03   2.862
## I(Cogongrass_Cover^2) -2.497e-04  7.617e-05  -3.278
## 
## Correlation of Fixed Effects:
##             (Intr) Cgng_C
## Cgngrss_Cvr -0.351       
## I(Cgng_C^2)  0.239 -0.947
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## 
## LOOCV Metrics:
## $Linear
##       RMSE        MAE         R2 
##  0.5798611  0.4222165 -0.3080590 
## 
## $Quadratic
##        RMSE         MAE          R2 
##  0.52531103  0.40597858 -0.07352551

Regional Plots

# --- Regional Plots ---
plot_region_quad <- function(mod_obj, region_data, region_label, color = "steelblue") {

  fit_mod   <- mod_obj$model
  use_mixed <- mod_obj$use_mixed

  cov_range <- range(region_data$Cogongrass_Cover, na.rm = TRUE)
  pred_df   <- data.frame(
    Cogongrass_Cover = seq(cov_range[1], cov_range[2], length.out = 200),
    Site = region_data$Site[1]
  )

  preds <- predict(fit_mod, newdata = pred_df,
                   re.form = if (use_mixed) NA else NULL,
                   se.fit  = !use_mixed)

  if (use_mixed) {
    set.seed(42)
    boot_formula <- if (mod_obj$best_label == "Quadratic")
      Shannon_Diversity ~ Cogongrass_Cover + I(Cogongrass_Cover^2) + (1 | Site)
    else
      Shannon_Diversity ~ Cogongrass_Cover + (1 | Site)

    boot_p <- replicate(300, {
      b_data <- region_data[sample(nrow(region_data), replace = TRUE), ]
      b_fit  <- tryCatch(
        lmer(boot_formula, data = b_data, REML = FALSE),
        error = function(e) NULL
      )
      if (is.null(b_fit)) return(rep(NA, nrow(pred_df)))
      predict(b_fit, newdata = pred_df, re.form = NA)
    })
    pred_df$fit <- preds
    pred_df$lwr <- apply(boot_p, 1, quantile, 0.025, na.rm = TRUE)
    pred_df$upr <- apply(boot_p, 1, quantile, 0.975, na.rm = TRUE)
  } else {
    pred_df$fit <- preds$fit
    pred_df$lwr <- preds$fit - 1.96 * preds$se.fit
    pred_df$upr <- preds$fit + 1.96 * preds$se.fit
  }

  # Pull CV metrics for the best model
  m             <- mod_obj$cv_metrics[[mod_obj$best_label]]
  subtitle_text <- sprintf("%s model (AIC-selected) | LOOCV — RMSE: %.3f | MAE: %.3f | R²: %.3f",
                           mod_obj$best_label, m["RMSE"], m["MAE"], m["R2"])

  ggplot() +
    geom_point(data = region_data,
               aes(x = Cogongrass_Cover, y = Shannon_Diversity),
               color = color, alpha = 0.6, size = 2) +
    geom_ribbon(data = pred_df,
                aes(x = Cogongrass_Cover, ymin = lwr, ymax = upr),
                fill = color, alpha = 0.2) +
    geom_line(data = pred_df,
              aes(x = Cogongrass_Cover, y = fit),
              color = color, linewidth = 1.2) +
    labs(subtitle = subtitle_text, x = NULL, y = "Shannon Diversity") +
    theme_bw(base_size = 13) +
    theme(
      plot.subtitle   = element_text(size = 10, color = "grey40"),
      legend.position = "right"
    )
}

p_central <- plot_region_quad(central_mod, subset(model_data, Site %in% central_fl),
                               "Central Florida",   color = "steelblue")
p_north   <- plot_region_quad(north_mod,   subset(model_data, Site %in% north_fl),
                               "North Florida",     color = "darkorange")

## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')

p_south   <- plot_region_quad(south_mod,   subset(model_data, Site %in% south_ms),
                               "South Mississippi", color = "forestgreen")

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
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## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

## boundary (singular) fit: see help('isSingular')

## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling
## Warning: Some predictor variables are on very different scales: consider
## rescaling

p_south <- p_south + labs(x = "Cogongrass Cover (%)")

final_plot <- (p_central / p_north / p_south) +
  plot_annotation(tag_levels = "A") &
  theme(plot.tag = element_text(size = 16, face = "bold"))

final_plot

ggsave(
  "C:/Users/DrewIvory/OneDrive - University of Florida/Desktop/School/PHD/01_Projects/03_Biodiversity/03_Figure/Quadratic_Regional_Cogon_Diversity.png",
  plot   = final_plot,
  width  = 10,
  height = 15,
  dpi    = 300
)