Statistical analysis
# print link to github repo if any
if (file.exists("./.git/config")) {
config <- readLines("./.git/config")
url <- grep("url", config, value = TRUE)
url <- gsub("\\turl = |.git$", "", url)
cat("\nSource code and data found at [", url, "](", url, ")", sep = "")
}Source code and data found at https://github.com/maRce10/thick_billed_parrots_vocal_variation
# options to customize chunk outputs
knitr::opts_chunk$set(
tidy.opts = list(width.cutoff = 65),
tidy = TRUE,
message = FALSE
)
options(
DT.options = list(
pageLength = 200,
scrollX = TRUE,
scrollY = "800px",
dom = 'Bfrtip',
buttons = c('copy', 'csv', 'excel')
)
)
datatable2 <- function(x, ...) datatable(data = x, extensions = 'Buttons', ...)# ggplot font size
bs <- 12
# custom functions
part_var <- function(model) {
var_components_pc1 <- as.data.frame(VarCorr(model))
total_variance <- sum(var_components_pc1$vcov)
var_components_pc1$proportion <- var_components_pc1$vcov / total_variance
return(var_components_pc1)
}
# plot variance partitioning results
graph_part_var <- function(levels,
data,
by = NULL,
response,
full = TRUE,
tick.labels = levels) {
if (!is.null(by)) {
if (full) {
by_levels <- c(unique(data[, by]), "full")
} else {
by_levels <- unique(data[, by])
}
} else
by_levels <- "full"
# scale response
if (is.numeric(data[, response])) {
data[, response] <- scale(data[, response])
} else {
stop("Response variable must be numeric")
}
var_by_list <- lapply(by_levels, function(x) {
if (x != "full") {
formula <- paste0(response, " ~ (1 | ", paste(levels, collapse = " / "), ")")
cat(paste0(x, ":", formula), "\n")
dat <- droplevels(data[data[, by] == x, ])
} else {
dat <- droplevels(data)
if (!is.null(by)) {
formula <- paste0(response,
" ~ (1 | ",
paste(levels, collapse = " / "),
") + (1 | ",
by,
")")
} else {
formula <- paste0(response,
" ~ (1 | ",
paste(levels, collapse = " / "),
")")
}
cat("full:", formula, "\n")
}
model <- lmer(
formula,
data = dat,
control = lmerControl(
optimizer = "bobyqa",
optCtrl = list(maxfun = 2e5)
)
)
var_components <- part_var(model)
print(var_components)
var_components <- var_components[var_components$grp != "Residual", ]
if (!is.null(by)) {
var_components <- var_components[var_components$grp != by, ]
}
var_components$level <- factor(rev(levels), levels = rev(levels))
# sample sizes
var_components$n <- sapply(var_components$level, function(y)
length(unique(dat[, names(dat) == y])))
var_components$prop <- as.character(round(var_components$proportion, 2))
var_components$prop[var_components$prop == "0"] <- "< 0.01"
var_components$prop <- paste(var_components$prop,
" (n = ",
var_components$n,
")",
sep = "")
var_components$by_levels <- x
var_components$perc <- paste(
round(var_components$proportion * 100, 0),
"% (n = ",
var_components$n,
")",
sep = ""
)
return(var_components)
})
var_by_df <- do.call(rbind, var_by_list)
var_by_df$by_levels <- factor(var_by_df$by_levels, levels = by_levels)
# set X tick labels
xlabs <- tick.labels
names(xlabs) <- levels
gg_out <- ggplot(var_by_df, aes(x = level, y = proportion, fill = level)) +
geom_bar(stat = "identity") +
theme_classic(base_size = 20) +
labs(x = "Level", y = "Explained variance (%)", fill = "Factor") +
facet_wrap(~ by_levels, ncol = 1) +
theme(axis.text.x = element_text(
angle = 45,
vjust = 1,
hjust = 1
)) +
geom_text(aes(label = perc), vjust = -0.5, size = 5) +
scale_fill_viridis_d(
option = "G",
begin = 0.1,
end = 0.9,
guide = "none",
direction = -1
) +
scale_y_continuous(labels = label_percent(), limits = c(0, max(var_by_df$proportion) + 0.16)) +
scale_x_discrete(labels = xlabs)
# Data for the nested ovals
oval_data <- data.frame(
# label = c("A", "B", "C", "D"),
x0 = c(0, 0, 0, 0, 0),
# Center x position for all ovals
y0 = c(-1.7, -0.4, 0.7, 2.2, 3.3),
# Center y position for all ovals
b = c(1.5, 3, 4.5, 6, 7.5),
# Semi-major axis (horizontal radius)
a = c(2, 4, 6, 8, 10) + 1,
# Semi-minor axis (vertical radius)
text.pos = c(-4.7, -2, 1, 3.2, 6) + 3 # Radius for each circle
)
oval_data <- oval_data[seq_along(levels), ]
oval_data$label <- rev(xlabs)
oval_data$size <- oval_data$a * oval_data$b
# oval_data <- oval_data[oval_data$label %in% c("Site", "Bird"), ] # Order by y0 for correct layering
# oval_data$label <- factor(oval_data$label, levels = rev(oval_data$label))
oval_data$label <- factor(oval_data$label, levels = oval_data$label[order(oval_data$size, decreasing = FALSE)])
oval_data$label.color <- viridis::mako(
nrow(oval_data),
begin = 0.1,
end = 0.9,
direction = -1,
alpha = 1
)
oval_data$label.color <- factor(oval_data$label.color, levels = oval_data$label.color[order(oval_data$size, decreasing = TRUE)])
# oval_data <- oval_data[1:4,]
# Plot using ggplot2 and ggforce
gg_oval <- ggplot(oval_data, group = label) +
geom_ellipse(aes(
x0 = x0,
y0 = y0,
a = a,
b = b,
angle = 0,
fill = label.color
),
color = "white") +
geom_text(
aes(x = x0, y = text.pos, label = label),
size = 7,
color = c(rep("black", nrow(oval_data) - 1), "white")
) +
# scale_fill_viridis_d(option = "G", begin = 0.1, end = 0.9, guide = "none", direction = 1) + # Add labels in the center
scale_fill_identity() + # Use the colors as specified in the data
theme_void() + # Remove background, axes, and grid
theme(legend.position = "none") +
coord_fixed() #+ # Keep aspect ratio fixed for true ovals
#ylim(c(-12, 6))
print(gg_oval)
return(gg_out)
}flowchart LR A(Read data) --> B(Plot acoustic space) B --> C(Regression models<br>to partition variance) C --> D(Plot variance partition) style A fill:#44015466 style B fill:#3E4A894D style C fill:#26828E4D style D fill:#6DCD594D
# install/ load packages
sketchy::load_packages(packages = c("knitr", "formatR", "warbleR",
"ggplot2", "maRce10/PhenotypeSpace", "lme4", "scales", "Rtsne",
"umap", "ggforce", "DT", "viridis", "readxl"))tbp_calls <- readRDS("./data/processed/extended_selection_table_tpb_calls.rds")
tbp_mfcc <- readRDS("./data/processed/mfcc_tpb_calls.rds")
tbp_calls$PC1.mfcc <- NA
tbp_calls$PC2.mfcc <- NA
for (i in unique(tbp_calls$type)) {
pca <- prcomp(tbp_mfcc[tbp_calls$type == i, -c(1:2)], center = TRUE,
scale. = TRUE)
tbp_calls$PC1.mfcc[tbp_calls$type == i] <- pca$x[, 1]
tbp_calls$PC2.mfcc[tbp_calls$type == i] <- pca$x[, 2]
# umap_l <- umap(tbp_mfcc[tbp_calls$type == i, -c(1:2)])
# tbp_calls$PC1.mfcc[tbp_calls$type == i] <- umap_l$layout[,
# 1] tbp_calls$PC2.mfcc[tbp_calls$type == i] <-
# umap_l$layout[, 2]
}mod_barks <- lmer(PC1.mfcc ~ (1 | Site/UniqueBird), data = tbp_calls[tbp_calls$type ==
"barks", ])
graph_part_var(levels = c("Site", "UniqueBird"), data = as.data.frame(tbp_calls),
by = "type", response = "PC1.mfcc", full = FALSE, tick.labels = c("Site",
"Individual"))laughs:PC1.mfcc ~ (1 | Site / UniqueBird) grp var1 var2 vcov sdcor proportion
1 UniqueBird:Site (Intercept) <NA> 0.3422145 0.5849910 0.3674321
2 Site (Intercept) <NA> 0.0000000 0.0000000 0.0000000
3 Residual <NA> <NA> 0.5891536 0.7675634 0.6325679
barks:PC1.mfcc ~ (1 | Site / UniqueBird)
grp var1 var2 vcov sdcor proportion
1 UniqueBird:Site (Intercept) <NA> 0.6301692 0.7938320 0.4744282
2 Site (Intercept) <NA> 0.3966465 0.6297988 0.2986187
3 Residual <NA> <NA> 0.3014552 0.5490493 0.2269531Warning: Using the `size` aesthetic in this geom was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` in the `default_aes` field and elsewhere instead.
yna_mfcc <- readRDS("./data/processed/mfcc_yna_calls.rds")
yna_calls <- readRDS("./data/processed/extended_selection_table_yna_calls.rds")# pca
pca <- prcomp(yna_mfcc[, -c(1:2)], center = TRUE, scale. = TRUE)
yna_calls$PC1.mfcc <- pca$x[, 1]
yna_calls$PC2.mfcc <- pca$x[, 2]
# yna_calls$PC1.mfcc <- NA yna_calls$PC2.mfcc <- NA for (i in
# unique(yna_calls$type)){ pca <- prcomp(yna_mfcc[yna_calls$type
# == i, -c(1:2)], center = TRUE, scale. = TRUE)
# yna_calls$PC1.mfcc[yna_calls$type == i] <- pca$x[, 1]
# yna_calls$PC2.mfcc[yna_calls$type == i] <- pca$x[, 2] # umap_l
# <- umap(yna_mfcc[yna_calls$type == i, -c(1:2)]) #
# yna_calls$PC1.mfcc[yna_calls$type == i] <- umap_l$layout[, 1]
# # yna_calls$PC2.mfcc[yna_calls$type == i] <- umap_l$layout[,
# 2] }
yna_calls <- yna_calls[!is.na(yna_calls$Site), ]graph_part_var(levels = c("Dialect", "Site", "UniqueBird"), data = as.data.frame(yna_calls),
by = "type", response = "PC1.mfcc", full = TRUE, tick.labels = c("Dialect",
"Site", "Individual"))1994:PC1.mfcc ~ (1 | Dialect / Site / UniqueBird)
grp var1 var2 vcov sdcor proportion
1 UniqueBird:Site:Dialect (Intercept) <NA> 0.2085083 0.4566271 0.2700217
2 Site:Dialect (Intercept) <NA> 0.0812762 0.2850898 0.1052540
3 Dialect (Intercept) <NA> 0.1956841 0.4423619 0.2534141
4 Residual <NA> <NA> 0.2867222 0.5354645 0.3713101
2005:PC1.mfcc ~ (1 | Dialect / Site / UniqueBird)
grp var1 var2 vcov sdcor proportion
1 UniqueBird:Site:Dialect (Intercept) <NA> 0.4342576 0.6589822 0.4072297
2 Site:Dialect (Intercept) <NA> 0.2354432 0.4852249 0.2207894
3 Dialect (Intercept) <NA> 0.1658560 0.4072542 0.1555332
4 Residual <NA> <NA> 0.2308133 0.4804303 0.2164477
full: PC1.mfcc ~ (1 | Dialect / Site / UniqueBird) + (1 | type)
grp var1 var2 vcov sdcor proportion
1 UniqueBird:Site:Dialect (Intercept) <NA> 0.3696672 0.6080026 0.3030462
2 Site:Dialect (Intercept) <NA> 0.1727707 0.4156570 0.1416342
3 Dialect (Intercept) <NA> 0.1940531 0.4405146 0.1590811
4 type (Intercept) <NA> 0.2357404 0.4855311 0.1932556
5 Residual <NA> <NA> 0.2476062 0.4976005 0.2029829
yna_calls$PC1.mfcc <- NA
yna_calls$PC2.mfcc <- NA
for (i in unique(yna_calls$type)) {
pca <- prcomp(yna_mfcc[yna_calls$type == i, -c(1:2)], center = TRUE,
scale. = TRUE)
yna_calls$PC1.mfcc[yna_calls$type == i] <- pca$x[, 1]
yna_calls$PC2.mfcc[yna_calls$type == i] <- pca$x[, 2]
# umap_l <- umap(yna_mfcc[yna_calls$type == i, -c(1:2)])
# yna_calls$PC1.mfcc[yna_calls$type == i] <- umap_l$layout[,
# 1] yna_calls$PC2.mfcc[yna_calls$type == i] <-
# umap_l$layout[, 2]
}
yna_calls <- yna_calls[!is.na(yna_calls$Site), ]graph_part_var(levels = c("Dialect", "Site", "UniqueBird"), data = as.data.frame(yna_calls),
by = "type", response = "PC1.mfcc", full = TRUE, tick.labels = c("Dialect",
"Site", "Individual"))1994:PC1.mfcc ~ (1 | Dialect / Site / UniqueBird)
grp var1 var2 vcov sdcor proportion
1 UniqueBird:Site:Dialect (Intercept) <NA> 0.1116152 0.3340886 0.0839091
2 Site:Dialect (Intercept) <NA> 0.1430501 0.3782196 0.1075410
3 Dialect (Intercept) <NA> 0.8251574 0.9083817 0.6203298
4 Residual <NA> <NA> 0.2503687 0.5003686 0.1882201
2005:PC1.mfcc ~ (1 | Dialect / Site / UniqueBird) grp var1 var2 vcov sdcor proportion
1 UniqueBird:Site:Dialect (Intercept) <NA> 0.4474666 0.6689294 0.4849532
2 Site:Dialect (Intercept) <NA> 0.2768944 0.5262075 0.3000913
3 Dialect (Intercept) <NA> 0.0000000 0.0000000 0.0000000
4 Residual <NA> <NA> 0.1983396 0.4453534 0.2149556
full: PC1.mfcc ~ (1 | Dialect / Site / UniqueBird) + (1 | type) grp var1 var2 vcov sdcor proportion
1 UniqueBird:Site:Dialect (Intercept) <NA> 0.3573140 0.5977575 0.3160685
2 Site:Dialect (Intercept) <NA> 0.3951709 0.6286262 0.3495555
3 Dialect (Intercept) <NA> 0.1640521 0.4050335 0.1451152
4 type (Intercept) <NA> 0.0000000 0.0000000 0.0000000
5 Residual <NA> <NA> 0.2139585 0.4625565 0.1892608
mpa_mfcc <- readRDS("./data/processed/mfcc_mpa_calls.rds")
mpa_calls <- readRDS("./data/processed/monk_parakeet_contactCalls_rangeComparison_extSelTable.RDS")Sample sizes:
ids <- mpa_calls$Bird_ID
ids[is.na(ids)] <- "UNIDENTIFIED"
tbid <- table(ids)
tbidids
INT-UM1 INT-UM10 INT-UM11 INT-UM12 INT-UM13 INT-UM15
23 7 1 1 1 1
INT-UM16 INT-UM17 INT-UM18 INT-UM19 INT-UM2 INT-UM3
9 6 1 12 1 1
INT-UM4 INT-UM5 INT-UM6 INT-UM7 INT-UM8 INT-UM9
1 21 25 29 1 6
NAT-AAT NAT-RAW NAT-UM1 NAT-UM2 NAT-UM3 NAT-UM4
13 5 26 24 6 18
NAT-UM5 NAT-ZW8 UNIDENTIFIED
8 9 1340 mpa_calls$country.region <- paste(mpa_calls$country, mpa_calls$region,
sep = "-")Data set for those from marked individuals with more than 1 call:
mpa_mfcc <- mpa_mfcc[mpa_calls$Bird_ID %in% names(tbid[tbid > 1]),
]
mpa_calls <- mpa_calls[mpa_calls$Bird_ID %in% names(tbid[tbid > 1]),
]
# pca
pca <- prcomp(mpa_mfcc[, -c(1:2)], center = TRUE, scale. = TRUE)
mpa_calls$PC1.mfcc <- pca$x[, 1]
mpa_calls$PC2.mfcc <- pca$x[, 2]
# mpa_calls$PC1.mfcc <- NA mpa_calls$PC2.mfcc <- NA for (i in
# unique(mpa_calls$country)){ pca <-
# prcomp(mpa_mfcc[mpa_calls$country == i, -c(1:2)], center =
# TRUE, scale. = TRUE) mpa_calls$PC1.mfcc[mpa_calls$country ==
# i] <- pca$x[, 1] mpa_calls$PC2.mfcc[mpa_calls$country == i] <-
# pca$x[, 2] # umap_l <- umap(mpa_mfcc[mpa_calls$type == i,
# -c(1:2)]) # mpa_calls$PC1.mfcc[mpa_calls$type == i] <-
# umap_l$layout[, 1] # mpa_calls$PC2.mfcc[mpa_calls$type == i]
# <- umap_l$layout[, 2] }mpa_calls <- as.data.frame(mpa_calls)
mpa_calls$city_site <- mpa_calls$introduced_city
mpa_calls$city_site[mpa_calls$country == "Uruguay"] <- mpa_calls$site[mpa_calls$country ==
"Uruguay"]
graph_part_var(levels = c("city_site", "region", "Bird_ID"), data = mpa_calls,
response = "PC1.mfcc", full = TRUE, by = "range", tick.labels = c("City",
"Region", "Individual"))Native:PC1.mfcc ~ (1 | city_site / region / Bird_ID)
grp var1 var2 vcov sdcor proportion
1 Bird_ID:region:city_site (Intercept) <NA> 0.23403508 0.4837717 0.49226484
2 region:city_site (Intercept) <NA> 0.02062357 0.1436091 0.04337921
3 city_site (Intercept) <NA> 0.07698449 0.2774608 0.16192769
4 Residual <NA> <NA> 0.14378200 0.3791860 0.30242827
Introduced:PC1.mfcc ~ (1 | city_site / region / Bird_ID) grp var1 var2 vcov sdcor proportion
1 Bird_ID:region:city_site (Intercept) <NA> 0.3369851 0.5805042 0.5410605
2 region:city_site (Intercept) <NA> 0.0000000 0.0000000 0.0000000
3 city_site (Intercept) <NA> 0.0000000 0.0000000 0.0000000
4 Residual <NA> <NA> 0.2858382 0.5346384 0.4589395
full: PC1.mfcc ~ (1 | city_site / region / Bird_ID) + (1 | range) Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: large eigenvalue ratio
- Rescale variables? grp var1 var2 vcov sdcor proportion
1 Bird_ID:region:city_site (Intercept) <NA> 0.28937387 0.5379348 0.23343631
2 region:city_site (Intercept) <NA> 0.02275861 0.1508596 0.01835925
3 city_site (Intercept) <NA> 0.03278378 0.1810629 0.02644649
4 range (Intercept) <NA> 0.67125831 0.8193036 0.54150039
5 Residual <NA> <NA> 0.22345207 0.4727072 0.18025756
budgie_dat <- read.csv("./data/processed/budgie_tsne_acoustic_space.csv")
metadat <- read_xlsx("./data/processed/budgie_experiment_metadata.xlsx")
metadat$flock <- paste(metadat$Treatment, metadat$`Treatment Room`,
sep = "-")
budgie_dat$flock <- sapply(budgie_dat$ID, function(x) {
metadat$flock[metadat$`Bird ID` == x][1]
})
budgie_dat <- budgie_dat[, c("ID", "treatment", "flock", "week", "TSNE1",
"TSNE2")]budgie_dat_week_1_4 <- budgie_dat[budgie_dat$week %in% c(1, 4), ]
budgie_dat_week_1_4$week <- paste("week", budgie_dat_week_1_4$week,
sep = " ")
graph_part_var(levels = c("flock", "ID"), data = budgie_dat_week_1_4,
response = "TSNE1", full = TRUE, by = "week", tick.labels = c("Flock",
"Individual"))week 1:TSNE1 ~ (1 | flock / ID) grp var1 var2 vcov sdcor proportion
1 ID:flock (Intercept) <NA> 0.3586982 0.5989142 0.3356301
2 flock (Intercept) <NA> 0.0000000 0.0000000 0.0000000
3 Residual <NA> <NA> 0.7100327 0.8426344 0.6643699
week 4:TSNE1 ~ (1 | flock / ID)
grp var1 var2 vcov sdcor proportion
1 ID:flock (Intercept) <NA> 0.40827684 0.6389654 0.37821256
2 flock (Intercept) <NA> 0.02903974 0.1704105 0.02690134
3 Residual <NA> <NA> 0.64217384 0.8013575 0.59488610
full: TSNE1 ~ (1 | flock / ID) + (1 | week) grp var1 var2 vcov sdcor proportion
1 ID:flock (Intercept) <NA> 0.322583389 0.56796425 0.302336148
2 flock (Intercept) <NA> 0.000000000 0.00000000 0.000000000
3 week (Intercept) <NA> 0.006257408 0.07910378 0.005864656
4 Residual <NA> <NA> 0.738128508 0.85914406 0.691799196
gg_var_pc1 <- readRDS("~/Dropbox/Projects/lbh_cultural_evolution_pattern_and_process/output/plots/song_variance_contribution_spectro.RDS")
# gg_var_pc1 <- gg_var_pc1 + scale_fill_manual(values = mako(4, begin = 0.1, end = 0.9, direction = 1, alpha = 0.9)[c(1, 3, 2, 4)]) + theme(legend.position = "none")
# Data for the nested ovals
oval_data <- data.frame(
# label = c("A", "B", "C", "D"),
x0 = c(0, 0, 0, 0), # Center x position for all ovals
y0 = c(-1.7, -0.4, 0.7, 2.2), # Center y position for all ovals
b = c(1.5, 3, 4.5, 6), # Semi-major axis (horizontal radius)
a = c(2, 4, 6, 8) + 1, # Semi-minor axis (vertical radius)
text.pos = c(-4.7, -2, 1, 3.2) + 3, # Radius for each circle
label = rev(c("Site", "Lek", "Song neighborhood", "Individual")) #
)
oval_data$label <- factor(oval_data$label, levels = (c("Site", "Lek", "Song neighborhood", "Individual")))
oval_data$label.color <- viridis::mako(
nrow(oval_data),
begin = 0.1,
end = 0.9,
direction = -1,
alpha = 1
)
oval_data$label.color <- factor(oval_data$label.color, levels = oval_data$label.color[order(oval_data$b, decreasing = TRUE)])
# Plot using ggplot2 and ggforce
oval_plot <- ggplot(oval_data) +
geom_ellipse(aes(x0 = x0, y0 = y0, a = a, b = b, angle = 0, fill = label.color), color = "white") +
geom_text(aes(x = x0, y = text.pos, label = label), size = c(6, 5, 6, 6), color = rev(c( "white",rep("black", 3)))) +
scale_fill_viridis_d(option = "G", begin = 0.1, end = 0.9, guide = "none", direction = -1, alpha = 0.6) + # Add labels in the center
scale_fill_identity() + # Use the colors as specified in the data
theme_void() + # Remove background, axes, and grid
theme(legend.position = "none") +
coord_fixed() #+ # Keep aspect ratio fixed for true ovals
#ylim(c(-12, 6))
oval_plot
gg_var_pc1 + theme(legend.position = "none") + theme_classic() + labs(x = "Level", y = "Explained variance (%)") +
scale_x_discrete(labels = c("Individuo" = "Individual", "Vecindario de canto" = "Song neighborhood", "Corral" = "Lek", "Sitio" = "Site")) + facet_wrap(~ feature, nrow = 1, labeller= as_labeller(c("Rasgos espectro-temporales" = "Full")))
# cowplot::plot_grid(gg_var_pc1 + scale_y_continuous(labels = label_percent(), limits = c(0, 0.7)), oval_plot, nrow = 1, rel_widths = c(1, 0.7))─ Session info ───────────────────────────────────────────────────────────────
setting value
version R version 4.5.0 (2025-04-11)
os Ubuntu 22.04.5 LTS
system x86_64, linux-gnu
ui X11
language (EN)
collate en_US.UTF-8
ctype en_US.UTF-8
tz America/Costa_Rica
date 2025-08-01
pandoc 3.2 @ /usr/lib/rstudio/resources/app/bin/quarto/bin/tools/x86_64/ (via rmarkdown)
quarto 1.7.31 @ /usr/local/bin/quarto
─ Packages ───────────────────────────────────────────────────────────────────
package * version date (UTC) lib source
abind 1.4-8 2024-09-12 [1] CRAN (R 4.5.0)
askpass 1.2.1 2024-10-04 [3] CRAN (R 4.5.0)
bitops 1.0-9 2024-10-03 [3] CRAN (R 4.5.0)
boot 1.3-31 2024-08-28 [4] CRAN (R 4.4.2)
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* ── Packages attached to the search path.
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