Statistical analysis

Landing manoeuvres predict roost-site preferences in bats

 

Purpose

• R code use for data manipulation and statistical analyses of the manuscript:

  • Gloriana Chaverri, Marcelo Araya-Salas, Jose Pablo Barrantes, Tere Uribe-Etxebarria, Marcela Peña-Acuña, Angie Liz Varela, Joxerra Aihartza. In review. Landing manoeuvres predict roost-site preferences in bats. Journal of Experimental Biology

 

Abstract

Roosts are vital for the survival of many species, and how individuals choose one site over another is affected by various factors. In bats, for example, species may use stiff roosts such as caves or compliant ones such as leaves; each type requires not only specific morphological adaptations but also different landing manoeuvres. Selecting a suitable roost within those broad categories may increase landing performance, reducing accidents and decreasing exposure time to predators. We address whether bats select specific roost sites based on the availability of a suitable landing surface, which could increase landing performance. Our study focuses on Spix’s disc-winged bats (Thyroptera tricolor), a species known to roost within developing tubular leaves. Since previous studies show that this species relies on the leaves’ apex for safe landing and rapid post-landing settlement, we predict that bats will prefer to roost in tubular structures with a longer apex and that landing will be consistently more effective on those leaves. Field observations showed that T. tricolor predominantly used two species for roosting, Heliconia imbricata and Calathea lutea, but they preferred roosting in the former. The main difference between these two plant species was the length of the leaf’s apex (longer in H. imbricata). Experiments in a flight cage also show that bats use more consistent approach and landing tactics when accessing leaves with a longer apex. Our results suggest that biomechanics may strongly influence resource selection, especially when complex manoeuvres are needed to acquire those resources.

 

Load packages

## add 'developer/' to packages to be installed from github
x <- c("RColorBrewer", "corrplot", "ggplot2", "readxl", "ranger", "caret", "pbapply", "viridis", "MCMCglmm", "MuMIn", "MASS", "smacof", "vegan", "kableExtra", "tidyr", "knitr", "tuneRanger", "brms", "bayestestR", "loo", "bayesplot", "ggalt")

aa <- lapply(x, function(y) {
  
  # get pakage name
  pkg <- strsplit(y, "/")[[1]]
  pkg <- pkg[length(pkg)]
  
  # check if installed, if not then install 
  if (!pkg %in% installed.packages()[,"Package"])  {

      if (grepl("/", y))  devtools::install_github(y, force = TRUE) else
    install.packages(y) 
    }

  # load package
  try(require(pkg, character.only = T), silent = T)
})

Set functions and global parameters

cols <- viridis(10, alpha = 0.6)

extract_proximity_oob <- function(fit, olddata) {
  pred = predict(fit, olddata, type = "terminalNodes")$predictions
  prox = matrix(NA, nrow(pred), nrow(pred))
  ntree = ncol(pred)
  n = nrow(prox)
  
  if (is.null(fit$inbag.counts)) {
    stop("call ranger with keep.inbag = TRUE")
  }
  
  # Get inbag counts
  inbag = simplify2array(fit$inbag.counts)
  
  for (i in 1:n) {
    for (j in 1:n) {
      # Use only trees where both obs are OOB
      tree_idx = inbag[i, ] == 0 & inbag[j, ] == 0
      prox[i, j] = sum(pred[i, tree_idx] == pred[j, tree_idx]) / sum(tree_idx)
    }
  }
  
  return(prox)
}

Flight trajectories

Calculate flight trajectory descriptors

## find inflection points in z vs distance

traj.dat <- read.csv("trajectories pooled data.csv", stringsAsFactors = FALSE)

# use butterworth filtered height
traj.dat$Z <- traj.dat$bw.Z

traj.list <- split(traj.dat, f = traj.dat$file)

out <- lapply(traj.list, function(Y) {
    
    ts <- Y$Z  

    # a <- c(1:10, 9:0)
    # as.numeric(c(FALSE, diff(diff(a) > 0) == -1))  

    # count up-down inflections
    Y$inflections <- as.numeric(c(FALSE, diff(diff(ts) > 0) == -1, FALSE))  
    
    Y$infl.time <- ifelse(Y$inflections > 0, Y$time, NA) 
    Y$infl.dist <- ifelse(Y$inflections > 0, Y$distance, NA) 
    Y$infl.height <- ifelse(Y$inflections > 0, Y$Z, NA) 

    return(Y)  
  })

traj.infl <- do.call(rbind, out)

# head(traj.infl)

dscnt.cutoff <- -0.11

summ.l <- lapply(unique(traj.infl$file), function(x){
  X <- traj.infl[traj.infl$file == x, ]
  
  # distance to entry at last inflection
  dist.last.infl <- X$distance[which.max(X$infl.time)]  
  
  # height to entry at last inflection
  height.last.infl <- X$Z[which.max(X$infl.time)]  
  
# mean speed after last inflection
  speed.last.infl <- mean(X$speed[which.max(X$infl.time):nrow(X)], na.rm = TRUE)
  
  # mean bw speed after last inflection
  bw.speed.last.infl <- mean(X$bw.speed[which.max(X$infl.time):nrow(X)], na.rm = TRUE) 

   # mean  acceleration
  accel.last.infl <- mean(X$acceleration[which.max(X$infl.time):nrow(X)], na.rm = TRUE)

   # mean bw  acceleration
    bw.accel.last.infl <- mean(X$bw.acceleration[which.max(X$infl.time):nrow(X)], na.rm = TRUE)
  
   # mean angle in y
    xy.angle.last.infl <- mean(X$ang.xy[(which.max(X$infl.time) - 3):nrow(X)], na.rm = TRUE)

        yz.angle.last.infl <- mean(X$ang.yz[(which.max(X$infl.time) - 3):nrow(X)], na.rm = TRUE)
    
      # distance to entry at start of descent fase
  dist.str.dscnt <- min(X$distance[X$time >= dscnt.cutoff], na.rm = TRUE)  

  # height to entry at start of descent fase
  height.strt.dscnt <- X$Z[which(X$time >= dscnt.cutoff)[1]]  
  
  # mean speed after last inflection
  speed.dscnt <- mean(X$speed[X$time >= dscnt.cutoff], na.rm = TRUE)   

  # mean bw speed after last inflection
  bw.speed.dscnt <- mean(X$bw.speed[X$time >= dscnt.cutoff], na.rm = TRUE)   
  
  # mean  acceleration at descent phase
  accel.dscnt <- mean(X$acceleration[X$time >= dscnt.cutoff], na.rm = TRUE)

  # mean bw acceleration at descent phase
  bw.accel.dscnt <- mean(X$bw.acceleration[X$time >= dscnt.cutoff], na.rm = TRUE)
  
     # mean angle in y
    xy.angle.dscnt <- mean(X$ang.xy[(which(X$time >= dscnt.cutoff) - 3)[1]:nrow(X)], na.rm = TRUE)

     # mean angle in z,y
    yz.angle.dscnt <- mean(X$ang.yz[(which(X$time >= dscnt.cutoff) - 3)[1]:nrow(X)], na.rm = TRUE)
  
  # number of inflections at descent
  num.infl.dscnt <- sum(X$inflections[X$time >= dscnt.cutoff], na.rm = TRUE)
  
  df <- data.frame(event = x, 
                   leave.type = X$leave.type[1], 
                   dist.last.infl, 
                   height.last.infl,
                   bw.speed.last.infl, 
                   bw.accel.last.infl, 
                   xy.angle.last.infl,
                   yz.angle.last.infl,
                   dist.str.dscnt, 
                   height.strt.dscnt, 
                   bw.speed.dscnt, 
                   bw.accel.dscnt, 
                   num.infl.dscnt,
                   xy.angle.dscnt,
                   yz.angle.dscnt)

  return(df)
  
})

summ.traj <- do.call(rbind, summ.l)

write.csv(summ.traj, "flying_trajectory_descriptors.csv", row.names = FALSE)

Format data for analysis

summ.traj <- read.csv("flying_trajectory_descriptors.csv", stringsAsFactors = FALSE)

summ.traj2 <- summ.traj[summ.traj$leave.type < 3, -1]

summ.traj2$leave.type <- as.factor(summ.traj2$leave.type)

 # run random forest
pca.trans <- princomp(summ.traj2[,-1], cor = TRUE)

trans.traj <- preProcess(summ.traj2[, -1], method=c("center", "scale", "BoxCox", "corr"))

summ.traj3 <- predict(trans.traj, summ.traj2)

summ.traj3$leave.type <- as.numeric(summ.traj3$leave.type) 

summ.traj3$leave.type[summ.traj3$leave.type == 1] <- "Truncate"
summ.traj3$leave.type[summ.traj3$leave.type == 2] <- "Acuminate"
summ.traj3$leave.type <- as.factor(summ.traj3$leave.type)

Random forest (and randomization test) on flight trajectories

print("variables")
names(summ.traj3)

# tune random forest
rf_task <- makeClassifTask(data = summ.traj3, target = "leave.type")
 
# Estimate runtime
estimateTimeTuneRanger(rf_task)
# Tuning
tuning.results <- tuneRanger(rf_task, measure = list(multiclass.brier), num.trees = 10000, num.threads = 10, iters = 1000, save.file.path = NULL, show.info = FALSE)
  
# Model with the new tuned hyperparameters
rf <- ranger(leave.type ~ ., data = summ.traj3, num.trees = 10000, importance = "impurity", keep.inbag = TRUE, mtry = tuning.results$recommended.pars$mtry, min.node.size = tuning.results$recommended.pars$min.node.size, sample.fraction = tuning.results$recommended.pars$sample.fraction)

rf.error <- rf$prediction.error

pboptions(type = "timer")
  
rnd.error <- pbsapply(1:10000, cl = 10, function(x){

  Y <- summ.traj3

  Y$leave.type <- sample(Y$leave.type)

  rf <- ranger(leave.type ~ ., data = Y, num.trees = 10000, importance = "impurity", mtry = tuning.results$recommended.pars$mtry, min.node.size = tuning.results$recommended.pars$min.node.size, sample.fraction = tuning.results$recommended.pars$sample.fraction)

  rf.error <- rf$prediction.error

  return(rf.error)
  }
  )

prx.mat <- extract_proximity_oob(fit = rf, olddata = summ.traj3)

diss <- dist(t(prx.mat))   ## Euclidean distances 
fit <- mds(diss, ndim = 2)        ## 2D interval MDS

set.seed(123)
rf.mds <- bootmds(fit, prx.mat, method.dat = "euclidean", nrep = 50)

rf.random.res <- list(rf.error = rf.error, rnd.error = rnd.error, rf.model = rf, prx.mat = prx.mat, rf.mds = rf.mds, tuning.results = tuning.results, leave.type = summ.traj3$leave.type)


saveRDS(rf.random.res, "Random forest randomization test resutls.RDS")

rf.random.res <- readRDS("Random forest randomization test resutls.RDS")

print("Tunning parameters")

## [1] "Tunning parameters"

rf.random.res$tuning.results

## Recommended parameter settings: 
##   mtry min.node.size sample.fraction
## 1    1             7       0.8673217
## Results: 
##   multiclass.brier exec.time
## 1        0.3881766 0.1731429

print("Confusion matrix")

## [1] "Confusion matrix"

rf.random.res$rf.model$confusion.matrix

##            predicted
## true        Acuminate Truncate
##   Acuminate        21        3
##   Truncate          7        7

print("Random forest error")

## [1] "Random forest error"

(rf.error <- rf.random.res$rf.error)

## [1] 0.2631579

rnd.error <- rf.random.res$rnd.error
hist(rnd.error, main = " Random error 10000 iterations", col = cols[5], xlab = "Classification error")
abline(v = rf.error, col = cols[10], lty = 2, lwd = 3)  

#p value
print("p-value")

## [1] "p-value"

sum(rnd.error < rf.error) / length(rnd.error)

## [1] 0.0067

Flight trajectory space based on Random Forest proximity

mds.shp <- data.frame(leave.type = as.character(rf.random.res$leave.type), rf.random.res$rf.mds$conf, stringsAsFactors = FALSE)

ggplot(mds.shp, aes(x = D1, y = D2, color = leave.type, shape = leave.type)) +
 geom_point(size = 7)+
  scale_shape_manual(values = c(15, 19)) +
  scale_color_manual(values = viridis(10, alpha = 0.6)[c(4, 8)]) +
  theme_classic() +
  labs(x = "Dimension 1", y = "Dimension 2", color = "Leaf type", shape = "Leaf type") +
  theme(text = element_text(size=20), legend.position = c(0.15, 0.9),  legend.text = element_text(face="italic")) 

 

• Discrimination of flight trajectories of the 2 leaf types is significantly higher than expected by chance

 

Compare variance of trajectory descriptors for the two leaf types

• Multivariate homogeneity of group dispersion (variances) test (Andersson’s PERMDISP2)

dis <- vegdist(summ.traj3[, -1], method = "euclidean")

## Calculate multivariate dispersions
mod <- betadisper(dis, summ.traj3$leave.type)

anova(mod)

## Analysis of Variance Table
## 
## Response: Distances
##           Df Sum Sq Mean Sq F value  Pr(>F)  
## Groups     1 11.775 11.7750  6.8016 0.01318 *
## Residuals 36 62.324  1.7312                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

pcoas <- as.data.frame(mod$vectors)
pcoas$leaf.type <- summ.traj3$leave.type

# original graph
# plot(mod, main = "")

# converted to ggplot
ggplot(pcoas, aes(x = PCoA1, y = PCoA2, color = leaf.type)) +
geom_point(size = 3) + 
    scale_color_manual(values = viridis(10, alpha = 0.6)[c(4, 8)], labels = c("Acuminate (n = 24)", "Truncate (n = 14)")) +
  scale_fill_manual(values = viridis(10, alpha = 0.6)[c(4, 8)]) +
  theme_classic() + 
  labs(x = "MDS dimension 1", y = "MDS dimension 2", color = "Leaf type") +
  geom_encircle(aes(fill = leaf.type), s_shape = 1, expand = 0,
                alpha = 0.2, show.legend = FALSE)

 

• Significant differences in mulitivariate dispersion of flight trajectories: flight towards truncated leaves are more variable

 

Roost shape variation

Random forest (and randomization test) on leaf shape among species

Colinearity

lvs.msrs <- readxl::read_excel("leaf_shape_measures.xls")  

cm <- cor(lvs.msrs[,sapply(lvs.msrs, is.numeric)])

corrplot.mixed(cm, lower = "number", upper = "ellipse", tl.col = "black", lower.col = cols, upper.col = cols, tl.pos = "lt", tl.cex = 1.4)

Tune Random Forest

lvs.msrs <- readxl::read_excel("leaf_shape_measures.xls")  

pp <- preProcess(x = as.matrix(lvs.msrs[, -1]), method=c("center", "scale", "BoxCox", "corr"))

trans.lvs.msrs <- data.frame(Species = lvs.msrs$Species, predict(pp, as.matrix(lvs.msrs[, - 1])), stringsAsFactors = FALSE)

trans.lvs.msrs$Species[trans.lvs.msrs$Species == 2] <- "Calathea lutea"
# trans.lvs.msrs$rdn.var <- rnorm(nrow(trans.lvs.msrs))

trans.lvs.msrs$Species <- as.factor(trans.lvs.msrs$Species)

# tune random forest
rf_task <- makeClassifTask(data = trans.lvs.msrs, target = "Species")
 
# Estimate runtime
estimateTimeTuneRanger(rf_task)

# Tuning
tuning.results <- tuneRanger(rf_task, measure = list(multiclass.brier), num.trees = 10000, num.threads = 10, iters = 1000, save.file.path = NULL, show.info = FALSE)
  
# Model with the new tuned hyperparameters
lvs.rf <- ranger(Species ~ ., data = trans.lvs.msrs, num.trees = 10000, importance = "impurity", keep.inbag = TRUE, mtry = tuning.results$recommended.pars$mtry, min.node.size = tuning.results$recommended.pars$min.node.size, sample.fraction = tuning.results$recommended.pars$sample.fraction)

lvs.rf <- ranger(as.factor(Species) ~ ., data = trans.lvs.msrs, num.trees = 10000, importance = "permutation", keep.inbag = TRUE)

imp_pvals <- importance_pvalues(x = lvs.rf, formula = as.factor(Species) ~ ., data = trans.lvs.msrs, method = "altman", num.permutations = 1000)

prx.mat <- extract_proximity_oob(fit = lvs.rf, olddata = trans.lvs.msrs)

diss <- dist(t(prx.mat))   ## Euclidean distances 
fit <- mds(diss, ndim = 2)        ## 2D interval MDS

set.seed(123)
rf.mds <- bootmds(fit, prx.mat, method.dat = "euclidean", nrep = 50)

pboptions(type = "timer")
  
rnd.error <- pbsapply(1:10000, cl = 20, function(x){

  Y <- trans.lvs.msrs

  Y$Species <- sample(Y$Species)

  rf <- ranger(Species ~ ., data = Y, num.trees = 10000, keep.inbag = FALSE, mtry = tuning.results$recommended.pars$mtry, min.node.size = tuning.results$recommended.pars$min.node.size, sample.fraction = tuning.results$recommended.pars$sample.fraction)

  rf.error <- rf$prediction.error

  return(rf.error)
  }
  )

rf.random.res <- list(rf.error = lvs.rf$prediction.error, rnd.error = rnd.error, rf.model = lvs.rf, prx.mat = prx.mat, rf.mds = rf.mds, trans.lvs.msrs = trans.lvs.msrs, imp_pvals = imp_pvals, tuning.results = tuning.results)

saveRDS(rf.random.res, "Random forest leaf shape randomization test results.RDS")

rf.random.res <- readRDS("Random forest leaf shape randomization test results.RDS")

print("Tunning parameters")

## [1] "Tunning parameters"

rf.random.res$tuning.results

## Recommended parameter settings: 
##   mtry min.node.size sample.fraction
## 1    2             2       0.8987571
## Results: 
##   multiclass.brier exec.time
## 1       0.04946783 0.2914808

print("Confusion matrix")

## [1] "Confusion matrix"

rf.random.res$rf.model$confusion.matrix

##                      predicted
## true                  Calathea lutea Heliconia imbricata
##   Calathea lutea                  25                   0
##   Heliconia imbricata              2                  32

print("Random forest error")

## [1] "Random forest error"

(rf.error <- rf.random.res$rf.error)

## [1] 0.03389831

hist(rf.random.res$rnd.error, main = " Random error 10000 iterations", col = cols[5], xlab = "Classification error", xlim = c(0, 0.8))
abline(v = rf.error, col = cols[9], lty = 2, lwd = 3)  

#p value
print("p-value")

## [1] "p-value"

sum(rnd.error < rf.error) / length(rnd.error)

## [1] 0

 

• H. imbricata and C. lutea differ significantly in leaf shape

 

Leaf shape space based on Random Forest proximity

mds.shp <- data.frame(Species = rf.random.res$trans.lvs.msrs$Species, rf.random.res$rf.mds$conf, stringsAsFactors = FALSE)

mds.shp$Species[mds.shp$Species == 2] <- "Calathea lutea"

ggplot(mds.shp, aes(x = D1, y = D2, color = Species, shape = Species)) +
 geom_point(size = 7)+
  scale_shape_manual(values = c(15, 19), labels = c("Calathea lutea (n = 25)", "Heliconia imbricata (n = 34)")) +
  scale_color_manual(values = viridis(10, alpha = 0.6)[c(4, 8)], labels = c("Calathea lutea (n = 25)", "Heliconia imbricata (n = 34)")) +
  theme_classic() +
  labs(x = "Dimension 1", y = "Dimension 2") +
  theme(text = element_text(size=15), legend.position = c(0.4, 0.9),  legend.text = element_text(face="italic")) 

Random forest variable importance

imp <- data.frame(var = names(ranger::importance(rf.random.res$rf.model)), imp = ranger::importance(rf.random.res$rf.model), stringsAsFactors = FALSE)

imp <- imp[order(-imp$imp), ]

imp$var <- factor(imp$var, levels = imp$var[order(imp$imp)])

rf.pval <- rf.random.res$imp_pvals
rf.pval  <- data.frame(rf.pval, var = rownames(rf.pval), p = ifelse(rf.random.res$imp_pvals[, "pvalue"] < 0.05, "*", ""))


ggplot(imp, aes(x = var, y = imp)) + 
  geom_bar(stat = "identity", fill = viridis(10, alpha = 0.6)[6] ) +
  theme_classic(base_size = 22) +
  labs(y = "Importance", x = "Variable") +
  scale_x_discrete(labels=c("Roost height", "Leaf length", "Tip length", "Tip length/\ncircumference", "Tip\ncircumference")) +
   geom_text(col = "black", size = 10, data = rf.pval, mapping = aes(x = var, y = importance + 0.01, label = p)) +
  coord_flip()

print("Importance p values")

## [1] "Importance p values"

rf.random.res$imp_pvals

##                                       importance      pvalue
## Leaf.length                          0.013404988 0.173826174
## Tip.length                           0.054664114 0.003996004
## Tip.circumference                    0.239664183 0.000999001
## Ratio.of.tip.length.to.circumference 0.126814860 0.000999001
## Roost.height                         0.002688351 0.409590410

lvs.msrs <- readxl::read_excel("leaf_shape_measures.xls")  

lvs.msrs$Species[lvs.msrs$Species == 2] <- "Calathea lutea"

lvs.msrs.gat <-gather(lvs.msrs, key = "variable", value = "value", names(lvs.msrs)[-1])

lvs.msrs.gat$Species <-  ifelse(lvs.msrs.gat$Species == "Calathea lutea", "C. lutea", "H. imbricata")

used.vars <- gsub("\\.", " ",  names(rf.random.res$trans.lvs.msrs))

lvs.msrs.gat <- lvs.msrs.gat[lvs.msrs.gat$variable %in% used.vars,]

lvs.msrs.gat$variable[lvs.msrs.gat$variable == "Tip circumference"] <- "Tip\ncircumference"

lvs.msrs.gat$variable[lvs.msrs.gat$variable == "Ratio of tip length to circumference"] <- "Tip length/\ncircumference"

lvs.msrs.gat$variable <- factor(lvs.msrs.gat$variable, levels = c("Leaf length", "Roost height", "Tip length", "Tip\ncircumference",  "Tip length/\ncircumference"))

sig <- data.frame(variable = unique(lvs.msrs.gat$variable), label = c("", "*", "*", "*", ""), x = rep(1.5, 5), y = c(0, 34.5, 42, 0.98, 200))
  
agg.msrs <- aggregate(value ~ Species + variable, data = lvs.msrs.gat, FUN = mean)

ggplot(lvs.msrs.gat, aes(x = Species, y = value)) + 
  geom_violin(fill =cols[7]) + 
   geom_point(size = 5, data = agg.msrs, aes(x = Species, y = value), col = "black", pch = 21, fill = "white") +
  geom_text(col = "black", size = 6, data = sig, mapping = aes(x = x, y = y, label = label)) +
  facet_wrap(~ variable, nrow = 1, scales = "free_y") +
  theme_classic() +
  labs(y = "Value") +
  theme(axis.text.x = element_text(face = "italic", angle = 45, hjust = 1))

 

• Leaf tip parameters (tip circumference, tip length and ratio of tip length to circumference) but no overall leaf parameters (leaf length and roost height) contributed significantly to species discrimination with Random Forest

 

## Species preference

sp.pref <- read.csv("leave_preference_data.csv", stringsAsFactors = FALSE)

table(sp.pref$Lugar)

names(sp.pref)


usadas <- sp.pref[, c("him.usadas", "clu.usadas", "otros.usadas")]
disp <- sp.pref[, c("him.disponibles", "clu.disponibles", "otros.disponible")]


names(disp) <- names(usadas) <- c("Him", "Clu", "otros")

pref <- compana(usadas, disp, test = "randomisation")

pref


print(pref$rm, quote = FALSE)

sp.pref <- sp.pref[sp.pref$Lugar %in%  c("Esquinas", "Finca Km23", "Lecheria", "Naranjal", "Urena"), ]

### aggregating
sp.pref.agg <- aggregate(cbind(him.usadas, clu.usadas, otros.usadas, him.disponibles, clu.disponibles, otros.disponible)  ~ Lugar, data = sp.pref,  FUN = sum)


usadas <- sp.pref.agg[, c("him.usadas", "clu.usadas", "otros.usadas")]
disp <- sp.pref.agg[, c("him.disponibles", "clu.disponibles", "otros.disponible")]



names(disp) <- names(usadas) <- c("Him", "Clu", "otros")

pref <- compana(usadas, disp, test = "randomisation", alpha =  0.05, nrep = 10000)

print(pref$rm, quote = FALSE)

(pref)


# sin otros
pref <- compana(usadas[, -3], disp[, -3], test = "randomisation", alpha =  0.05, nrep = 10000)

print(pref$rm, quote = FALSE)

(pref)


df.pref <- data.frame(species = rep(c("H. imbricata", "C. lutea", "Others"), each = 5), site = rep(sp.pref.agg$Lugar, 3), used = unlist(usadas), available = unlist(disp))

agg.df.pref <- aggregate(cbind(used, available) ~ species, data = df.pref, FUN = sum)

agg.df.pref$site <- "All"

df.pref <- rbind(df.pref, agg.df.pref)

df.pref.gg <- data.frame(df.pref[, c("species", "site")], type = rep(c("used", "available"), each = nrow(df.pref)), count = c(df.pref$used, df.pref$available), stringsAsFactors = FALSE, row.names = NULL)

df.pref.gg[order(df.pref.gg$species,  df.pref.gg$type, df.pref.gg$site), ]


df.pref.gg$species <- factor(df.pref.gg$species, levels = unique(df.pref.gg$species))

ggplot(df.pref.gg, aes(species, count, fill = type)) + 
  geom_bar(stat = "identity", position = "dodge") + 
  scale_fill_manual(values = viridis(10)[c(3, 8)]) +
  facet_wrap(~site, scales = "free_y") +
  theme_classic() +
  labs(x = "Species", y = "Frequency") +
  theme(legend.justification=c(0,0), legend.position=c(0.87, 0.8), text = element_text(size=20)) 

Roost preference

Correlation among variables

sp.pref <- read.csv("leave_preference_data.csv", stringsAsFactors = FALSE)

sp.pref$Lugar <- gsub("Urena", "Ureña", sp.pref$Lugar)

sp.pref <- sp.pref[sp.pref$clu.disponibles != 0 & sp.pref$him.disponibles != 0, ]

usadas <- sp.pref[, c("him.usadas", "clu.usadas", "otros.usadas")]
disp <- sp.pref[, c("him.disponibles", "clu.disponibles", "otros.disponible")]

use.df <- data.frame(site = sp.pref$Lugar, disp = unlist(disp, use.names = FALSE), used = unlist(usadas, use.names = FALSE), area = sp.pref$area, densidad = sp.pref$Densidad, species = rep(c("Him", "Clu", "other"), each = nrow(sp.pref)))

# Selecting between with and without interaction
cc.use.df <- use.df
cc.use.df <- cc.use.df[complete.cases(cc.use.df), ]
cc.use.df <- cc.use.df[cc.use.df$species != "other", ]
cc.use.df <- droplevels(cc.use.df)

levels(cc.use.df$species) <- c("C. lutea", "H. imbricata")

cm <- cor(cc.use.df[,sapply(cc.use.df, is.numeric)])

corrplot.mixed(cm, lower = "number", upper = "ellipse", tl.col = cols, lower.col = cols, upper.col = cols)

Roost abundance and usage by site:

use.df$site <- gsub(" Km23", "", use.df$site)

plot_df_l <- lapply(unique(use.df$site), function(x){
  
  X <- use.df[use.df$site == x, ]
  
  df <- data.frame(Site = x, 
                   Species = c("H. imbricata", "C. lutea", "Others"), 
                   Type = rep(c("Available", "Used"), each = 3),
                   Frequency = c(sapply(unique(use.df$species), function(y) sum(cc.use.df$disp[cc.use.df$specie == y])),  sapply(unique(use.df$species), function(y) sum(cc.use.df$used[cc.use.df$specie == y]))))

  return(df)
    
})

plot_df <- do.call(rbind, plot_df_l)

all_df <- aggregate(Frequency ~ Species + Type, plot_df, sum)
all_df$Site <- "All"

# plot_df <- rbind(plot_df[plot_df$Site != "Bolivar", ], all_df)
plot_df <- rbind(plot_df, all_df)

plot_df$Species <- factor(plot_df$Species, levels = c("H. imbricata", "C. lutea", "Others"))

ggplot(plot_df, aes(x = Species, y = Frequency, fill = Type, group = Type)) + 
  geom_bar(stat = "identity", position = "dodge") +
  labs(x = "Species", y = "Number of individuals") +
  facet_wrap( ~ Site, scales = "free_y", nrow = 2) + 
  scale_fill_viridis_d(begin = 0.3, end = 0.8, alpha = 0.7) +
  theme_classic()+
  theme(legend.position = c(0.87, 0.2), axis.text.x = element_text(face = "italic", angle = 45, hjust = 1))

Density by species:

agg.dens <- aggregate(densidad ~ species, data = cc.use.df, mean)

ggplot(cc.use.df, aes(x = species, y = densidad)) + geom_violin(fill =cols[5]) + 
   geom_point(size = 6, data = agg.dens, fill = "white", pch = 21, col = "black") +
  theme_classic() +
  labs(y = "Density") +
  theme(text = element_text(size=20)) 

cc.use.df$densidad_sc <- scale(cc.use.df$densidad)

 

• Area and density highly correlated; area was excluded

• Variation in density very similar between C. lutea and H. imbricata so no interaction between density and species was included

 

Bayesian generalized linear mixed models were used to fit binomial models on furled leaf occupancy with site as a random effect and plant species and density as predictors. We tested 4 models:

1. only species as predictor: \[Occupancy \sim species + (1 | site)\]

2. only density as predictor: \[Occupancy \sim density + (1 | site)\]

3. both species and density as predictors: \[Occupancy \sim species + density + (1 | site)\]

• Only sampling events in which furled leaves from both species were found are included
• Model averaging was used to obtained effect size estimates
• Models were created with a binomial link function

iterations <- 20000
burnin <- 10000

priors <- c(set_prior("normal(0, 1.5)", class = "Intercept"), set_prior("normal(0, 1.5)", class = "b"))

mod.sp.dns <- brm(used | trials(disp) ~ species + densidad + (1 | site), data = cc.use.df, family = binomial, save_pars = save_pars(all = TRUE), prior = priors, iter = iterations, warmup = burnin, cores = 3, chains = 3, silent = 2, control = list(adapt_delta = 0.99))

check_prior(mod.sp.dns)

mod.sp <- brm(used | trials(disp) ~ species + (1 | site), data = cc.use.df, family = binomial, save_pars = save_pars(all = TRUE), prior = priors, iter = iterations, warmup = burnin, cores = 3, chains = 3, silent = 2, control = list(adapt_delta = 0.99))

mod.dns <- brm(used | trials(disp) ~ densidad + (1 | site), data = cc.use.df, family = binomial, save_pars = save_pars(all = TRUE), prior = priors, iter = iterations, warmup = burnin, cores = 3, chains = 3, silent = 2, control = list(adapt_delta = 0.99))

models <- list(mod.sp.dns = mod.sp.dns, mod.sp = mod.sp, mod.dns = mod.dns)

saveRDS(models, "brms_models_leave_occupancy.RDS")

attach(usage_models <- readRDS("brms_models_leave_occupancy.RDS"))

# calculate average posteriors and model
post_avrg_sp <- posterior_average(mod.sp.dns, mod.sp, weights = "loo")
post_avrg_dns <- posterior_average(mod.sp.dns, mod.dns, weights = "loo")
post_avrg_intcpt <- posterior_average(mod.sp.dns, mod.sp, mod.dns, weights = "loo")
post_avg <- cbind(post_avrg_intcpt[, "b_Intercept"], post_avrg_sp[, "b_speciesHim"], post_avrg_dns[, "b_densidad"])
colnames(post_avg) <- c("b_Intercept", "b_speciesHim", "b_densidad")

print("priors")

## [1] "priors"

check_prior(mod.sp.dns)

##      Parameter Prior_Quality
## 1  b_Intercept   informative
## 2 b_speciesHim   informative
## 3   b_densidad uninformative

describe_prior(mod.sp.dns)

##            Parameter Prior_Distribution Prior_Location Prior_Scale Prior_df
## 1        b_Intercept             normal              0         1.5       NA
## 2       b_speciesHim             normal              0         1.5       NA
## 3         b_densidad             normal              0         1.5       NA
## 4 sd_site__Intercept          student_t              0         2.5        3

print("model results")

## [1] "model results"

describe_posterior(as.data.frame(post_avg), ci_method = "HDI")

## Summary of Posterior Distribution
## 
## Parameter    |   Median |         95% CI |     pd |          ROPE | % in ROPE
## -----------------------------------------------------------------------------
## b_Intercept  |    -2.64 | [-3.19, -2.04] |   100% | [-0.10, 0.10] |        0%
## b_speciesHim |     1.30 | [ 0.93,  1.66] |   100% | [-0.10, 0.10] |        0%
## b_densidad   | 3.70e-04 | [-0.01,  0.01] | 53.52% | [-0.10, 0.10] |      100%

Leaf occupancy by species:

 

• Only species significantly explained variation in occupancy (i.e. proportion of used leaves)

 

Paired experiments on leaf-landing performance

Odd landing occurrence

 

Regression model

1. tip type as predictor: \[landing.type \sim tip.type + (1 | individual)\]

landing_model <- brm(Land ~ Apex + (1 | Bat), data = land_data, family = "bernoulli", save_pars = save_pars(all = TRUE), iter = iterations, warmup = burnin, cores = 3, chains = 3, silent = 2)

saveRDS(landing_model, "brms_model_landing.RDS")

landing_model <- readRDS("brms_model_landing.RDS")

print("priors")

## [1] "priors"

check_prior(landing_model)

##        Parameter    Prior_Quality
## 1    b_Intercept      informative
## 2 b_Apextruncate not determinable

describe_prior(landing_model)

##           Parameter Prior_Distribution Prior_Location Prior_Scale Prior_df
## 1       b_Intercept          student_t              0         2.5        3
## 2    b_Apextruncate            uniform             NA          NA       NA
## 3 sd_Bat__Intercept          student_t              0         2.5        3

print("model results")

## [1] "model results"

describe_posterior(landing_model, ci_method = "HDI")

## Summary of Posterior Distribution
## 
## Parameter    | Median |        95% CI |     pd |          ROPE | % in ROPE |  Rhat |      ESS
## ---------------------------------------------------------------------------------------------
## (Intercept)  |  -1.59 | [-3.99, 0.16] | 97.48% | [-0.18, 0.18] |     2.75% | 1.000 |  9669.00
## Apextruncate |   3.28 | [ 1.01, 6.23] | 99.97% | [-0.18, 0.18] |        0% | 1.000 | 11590.00

• Odd landing is significantly more common on truncated leaves

 

Latency to hide

agg.lat <- aggregate(Time ~ Land + Apex, data = land_data, FUN = mean)
agg.lat$n <- aggregate(Time ~ Land + Apex, data = land_data, FUN = length)$Time

#Plot for time to enter by apex and landing
ggplot(land_data, aes(x=Land, y=Time, fill=Land)) +
  geom_violin(alpha = 0.7) +
  geom_point(size = 5, data = agg.lat, aes(y = Time, x = Land), col = "black", pch = 21, fill = "white") +
  facet_wrap(~Apex) +
    theme(strip.text = element_text(face="bold", size=9),
        strip.background = element_rect(colour="black",size=1))+ 
  scale_fill_viridis_d(begin = 0.3, end = 0.8, alpha = 0.8) + 
    labs( x = "Type of landing", y = "Time from landing\nto hiding") + theme(legend.position = "none", panel.background = element_blank(), panel.border = element_rect(colour = "black", fill=NA, size=1)) + theme_classic(base_size = 22) + ylim(-50, 1750) +
          geom_text(data=agg.lat, aes(label=paste0("n = ", n)),
                y=rep(-40, 4), colour="grey20", size=5)

Regression models

1. only landing type as predictor: \[Latency \sim landing.type + (1 | individual)\]

2. only tip type as predictor: \[Latency \sim tip.type + (1 | individual)\]

• Both predictors were not included on a single model as they are closely assocaited (see previous section) and contain similar information, which will result in canceling out there effects

mod.land <- brm(Time ~ Land + (1 | Bat), data = land_data, save_pars = save_pars(all = TRUE), iter = iterations, warmup = burnin, cores = 3, chains = 3, silent = 2, control = list(adapt_delta = 0.99))

mod.ap <- brm(Time ~ Apex + (1 | Bat), data = land_data, save_pars = save_pars(all = TRUE), iter = iterations, warmup = burnin, cores = 3, chains = 3, silent = 2, control = list(adapt_delta = 0.99))

latency_models <- list(mod.land = mod.land, mod.ap = mod.ap)

saveRDS(latency_models, "brms_models_leaf_entry_timing.RDS")

attach(latency_models <- readRDS("brms_models_leaf_entry_timing.RDS"))

print("priors")

## [1] "priors"

describe_prior(mod.land)

##           Parameter Prior_Distribution Prior_Location Prior_Scale Prior_df
## 1       b_Intercept          student_t            380       226.8        3
## 2         b_Landodd            uniform             NA          NA       NA
## 3 sd_Bat__Intercept          student_t              0       226.8        3
## 4             sigma          student_t              0       226.8        3

describe_prior(mod.ap)

##           Parameter Prior_Distribution Prior_Location Prior_Scale Prior_df
## 1       b_Intercept          student_t            380       226.8        3
## 2    b_Apextruncate            uniform             NA          NA       NA
## 3 sd_Bat__Intercept          student_t              0       226.8        3
## 4             sigma          student_t              0       226.8        3

print("model results")

## [1] "model results"

describe_posterior(mod.land, ci_method = "HDI")

## Summary of Posterior Distribution
## 
## Parameter   | Median |           95% CI |     pd |            ROPE | % in ROPE |  Rhat |      ESS
## -------------------------------------------------------------------------------------------------
## (Intercept) | 387.98 | [161.79, 615.13] | 99.92% | [-40.26, 40.26] |        0% | 1.000 | 21397.00
## Landodd     | 205.51 | [-88.54, 495.01] | 91.82% | [-40.26, 40.26] |     8.60% | 1.000 | 21443.00

describe_posterior(mod.ap, ci_method = "HDI")

## Summary of Posterior Distribution
## 
## Parameter    | Median |            95% CI |     pd |            ROPE | % in ROPE |  Rhat |      ESS
## ---------------------------------------------------------------------------------------------------
## (Intercept)  | 477.07 | [ 248.33, 714.35] | 99.98% | [-40.26, 40.26] |        0% | 1.000 | 19578.00
## Apextruncate |  31.52 | [-245.13, 306.49] | 59.48% | [-40.26, 40.26] |    24.15% | 1.000 | 32938.00

 

• There is a non-significant trend on the latency to hide between odd and normal landings

• There is no effect of leaf shape

 

---

---

Diagnostic plots for bayesian regresion models

Includes:

1. Model summary
2. Rhats: Rhat values as points
3. Trace: overlaid chain traces and posterior density plots
4. Autocorrelation: autocorrelation plot for posterior samples
5. Pairs: square plot matrix with univariate marginal distributions along the diagonal (as histograms) and bivariate distributions off the diagonal

Occupancy models

color_scheme_set("viridis")
  
for(x in 2:length(usage_models)){
  
  print(names(usage_models)[x])
  
  mod <- usage_models[[x]]
  
  print("Model Summary:")
  print(summary(mod))
  
  print("Rhats:")
  print(mcmc_rhat(rhat = rhat(mod)) + yaxis_text(hjust = 0))

  print("Traces:")
  plot(mod) 

  print("Autocorrelation:")
  print(mcmc_plot(mod, type = "acf"))

  print("Pairs:")
  if (nrow(mod$prior) > 1)
    print(pairs(mod))
}

## [1] "mod.sp"
## [1] "Model Summary:"
##  Family: binomial 
##   Links: mu = logit 
## Formula: used | trials(disp) ~ species + (1 | site) 
##    Data: cc.use.df (Number of observations: 114) 
##   Draws: 3 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 30000
## 
## Group-Level Effects: 
## ~site (Number of levels: 6) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.45      0.25     0.14     1.08 1.00     6195     8599
## 
## Population-Level Effects: 
##            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept     -2.63      0.28    -3.14    -2.03 1.00     9150     8894
## speciesHim     1.30      0.18     0.94     1.67 1.00    18188    17389
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## [1] "Rhats:"

## [1] "Traces:"

## [1] "Autocorrelation:"

## [1] "Pairs:"

## [1] "mod.dns"
## [1] "Model Summary:"
##  Family: binomial 
##   Links: mu = logit 
## Formula: used | trials(disp) ~ densidad + (1 | site) 
##    Data: cc.use.df (Number of observations: 114) 
##   Draws: 3 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 30000
## 
## Group-Level Effects: 
## ~site (Number of levels: 6) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.63      0.33     0.25     1.47 1.00     6694     9076
## 
## Population-Level Effects: 
##           Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept    -1.44      0.32    -2.09    -0.80 1.00    10030    11001
## densidad     -0.00      0.00    -0.01     0.01 1.00    12827    15796
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## [1] "Rhats:"

## [1] "Traces:"

## [1] "Autocorrelation:"

## [1] "Pairs:"

Landing model

mod <- landing_model

print("Model Summary:")

## [1] "Model Summary:"

print(summary(mod))

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: Land ~ Apex + (1 | Bat) 
##    Data: land_data (Number of observations: 30) 
##   Draws: 3 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 30000
## 
## Group-Level Effects: 
## ~Bat (Number of levels: 9) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.67      1.22     0.09     4.69 1.00     7508    11966
## 
## Population-Level Effects: 
##              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept       -1.73      1.08    -4.27     0.00 1.00    12040     7805
## Apextruncate     3.45      1.36     1.25     6.65 1.00    14583     8870
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

print("Rhats:")

## [1] "Rhats:"

print(mcmc_rhat(rhat = rhat(mod)) + yaxis_text(hjust = 0))

print("Traces:")

## [1] "Traces:"

plot(mod) 

print("Autocorrelation:")

## [1] "Autocorrelation:"

print(mcmc_plot(mod, type = "acf"))

print("Pairs:")

## [1] "Pairs:"

if (nrow(mod$prior) > 1)
  print(pairs(mod))

Hidding latency models

for(x in 1:length(latency_models)){
  
  print(names(latency_models)[x])

  mod <- latency_models[[x]]
  
  print("Model Summary:")
  print(summary(mod))
  
  print("Rhats:")
  print(mcmc_rhat(rhat = rhat(mod)) + yaxis_text(hjust = 0))

  print("Traces:")
  plot(mod) 
  
  print("Autocorrelation:")
  print(mcmc_plot(mod, type = "acf"))

  print("Pairs:")
  if (nrow(mod$prior) > 1)
    print(pairs(mod))
  }

## [1] "mod.land"
## [1] "Model Summary:"
##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: Time ~ Land + (1 | Bat) 
##    Data: land_data (Number of observations: 30) 
##   Draws: 3 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 30000
## 
## Group-Level Effects: 
## ~Bat (Number of levels: 9) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)   151.60    109.80     6.75   409.19 1.00     8190    11309
## 
## Population-Level Effects: 
##           Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept   388.68    114.16   164.71   619.52 1.00    21854    19255
## Landodd     206.00    148.85   -85.34   499.63 1.00    21573    18507
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma   373.27     55.46   279.12   495.03 1.00    17373    18218
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## [1] "Rhats:"

## [1] "Traces:"

## [1] "Autocorrelation:"

## [1] "Pairs:"

## [1] "mod.ap"
## [1] "Model Summary:"
##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: Time ~ Apex + (1 | Bat) 
##    Data: land_data (Number of observations: 30) 
##   Draws: 3 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 30000
## 
## Group-Level Effects: 
## ~Bat (Number of levels: 9) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)   188.56    122.93     9.57   459.22 1.00     7217    10435
## 
## Population-Level Effects: 
##              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept      476.51    118.44   240.80   707.85 1.00    20105    18603
## Apextruncate    32.05    140.36  -243.00   310.24 1.00    33148    20854
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma   377.78     59.83   276.62   508.22 1.00    12708    16180
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## [1] "Rhats:"

## [1] "Traces:"

## [1] "Autocorrelation:"

## [1] "Pairs:"

---

R session information

## R version 4.1.0 (2021-05-18)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.2 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/atlas/libblas.so.3.10.3
## LAPACK: /usr/lib/x86_64-linux-gnu/atlas/liblapack.so.3.10.3
## 
## locale:
##  [1] LC_CTYPE=pt_BR.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=es_CR.UTF-8        LC_COLLATE=pt_BR.UTF-8    
##  [5] LC_MONETARY=es_CR.UTF-8    LC_MESSAGES=pt_BR.UTF-8   
##  [7] LC_PAPER=es_CR.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=es_CR.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] parallel  stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] ggalt_0.4.0        bayesplot_1.8.1    loo_2.4.1.9000     bayestestR_0.11.5 
##  [5] brms_2.16.3        Rcpp_1.0.8.3       tuneRanger_0.5     lhs_1.1.3         
##  [9] lubridate_1.7.10   mlrMBO_1.1.5       smoof_1.6.0.2      checkmate_2.0.0   
## [13] mlr_2.19.0         ParamHelpers_1.14  knitr_1.39         tidyr_1.1.3       
## [17] kableExtra_1.3.1   vegan_2.5-7        permute_0.9-5      smacof_2.1-3      
## [21] e1071_1.7-7        colorspace_2.0-2   plotrix_3.8-1      MASS_7.3-54       
## [25] MuMIn_1.43.17      MCMCglmm_2.32      ape_5.5            coda_0.19-4       
## [29] Matrix_1.3-4       viridis_0.6.2      viridisLite_0.4.0  pbapply_1.5-0     
## [33] caret_6.0-88       lattice_0.20-44    ranger_0.13.1      readxl_1.3.1      
## [37] ggplot2_3.3.5      corrplot_0.90      RColorBrewer_1.1-2
## 
## loaded via a namespace (and not attached):
##   [1] ModelMetrics_1.2.2.2 dygraphs_1.1.1.6     data.table_1.14.0   
##   [4] rpart_4.1-15         inline_0.3.19        doParallel_1.0.16   
##   [7] generics_0.1.0       callr_3.7.0          mice_3.13.0         
##  [10] proxy_0.4-26         webshot_0.5.2        xml2_1.3.2          
##  [13] httpuv_1.6.1         StanHeaders_2.21.0-7 assertthat_0.2.1    
##  [16] gower_0.2.2          xfun_0.31            hms_1.1.0           
##  [19] jquerylib_0.1.4      evaluate_0.15        promises_1.2.0.1    
##  [22] fansi_1.0.0          igraph_1.2.6         DBI_1.1.1           
##  [25] htmlwidgets_1.5.3    tensorA_0.36.2       stats4_4.1.0        
##  [28] purrr_0.3.4          ellipsis_0.3.2       heplots_1.3-8       
##  [31] crosstalk_1.1.1      dplyr_1.0.7          backports_1.3.0     
##  [34] V8_3.4.2             insight_0.14.5       markdown_1.1        
##  [37] RcppParallel_5.1.4   vctrs_0.3.8          abind_1.4-5         
##  [40] withr_2.4.3          xts_0.12.1           prettyunits_1.1.1   
##  [43] weights_1.0.4        cluster_2.1.2        lazyeval_0.2.2      
##  [46] crayon_1.5.1         candisc_0.8-5        ellipse_0.4.2       
##  [49] labeling_0.4.2       recipes_0.1.16       pkgconfig_2.0.3     
##  [52] nlme_3.1-152         wordcloud_2.6        nnet_7.3-16         
##  [55] rlang_1.0.2          RJSONIO_1.3-1.4      lifecycle_1.0.1     
##  [58] miniUI_0.1.1.1       colourpicker_1.1.0   extrafontdb_1.0     
##  [61] cellranger_1.1.0     distributional_0.2.2 tcltk_4.1.0         
##  [64] matrixStats_0.61.0   datawizard_0.2.1     carData_3.0-4       
##  [67] boot_1.3-28          zoo_1.8-9            base64enc_0.1-3     
##  [70] gamm4_0.2-6          ggridges_0.5.3       processx_3.5.2      
##  [73] png_0.1-7            KernSmooth_2.23-20   pROC_1.17.0.1       
##  [76] stringr_1.4.0        jpeg_0.1-8.1         shinystan_2.5.0     
##  [79] scales_1.1.1         magrittr_2.0.3       plyr_1.8.6          
##  [82] gdata_2.18.0         threejs_0.3.3        compiler_4.1.0      
##  [85] rstantools_2.1.1     ash_1.0-15           lme4_1.1-27.1       
##  [88] cli_3.1.0            ps_1.6.0             Brobdingnag_1.2-6   
##  [91] htmlTable_2.2.1      Formula_1.2-4        mgcv_1.8-36         
##  [94] tidyselect_1.1.1     stringi_1.7.6        forcats_0.5.1       
##  [97] projpred_2.0.2       highr_0.9            proj4_1.0-10.1      
## [100] yaml_2.3.5           latticeExtra_0.6-29  bridgesampling_1.1-2
## [103] grid_4.1.0           sass_0.4.0           fastmatch_1.1-0     
## [106] polynom_1.4-0        tools_4.1.0          rio_0.5.27          
## [109] rstudioapi_0.13      foreach_1.5.1        foreign_0.8-81      
## [112] gridExtra_2.3        cubature_2.0.4.2     prodlim_2019.11.13  
## [115] posterior_1.1.0      farver_2.1.0         digest_0.6.29       
## [118] shiny_1.6.0          lava_1.6.9           car_3.0-11          
## [121] broom_0.7.8          later_1.2.0          mco_1.15.6          
## [124] httr_1.4.2           rsconnect_0.8.18     rvest_1.0.0         
## [127] splines_4.1.0        shinythemes_1.2.0    plotly_4.10.0       
## [130] xtable_1.8-4         jsonlite_1.8.0       nloptr_1.2.2.2      
## [133] BBmisc_1.11          corpcor_1.6.9        timeDate_3043.102   
## [136] rstan_2.21.2         ipred_0.9-11         R6_2.5.1            
## [139] Hmisc_4.5-0          pillar_1.6.4         htmltools_0.5.2     
## [142] mime_0.11            nnls_1.4             glue_1.6.2          
## [145] fastmap_1.1.0        minqa_1.2.4          DT_0.18             
## [148] class_7.3-19         codetools_0.2-18     maps_3.3.0          
## [151] pkgbuild_1.2.0       mvtnorm_1.1-2        utf8_1.2.2          
## [154] bslib_0.2.5.1        tibble_3.1.6         DiceKriging_1.6.0   
## [157] curl_4.3.2           gtools_3.9.2         misc3d_0.9-1        
## [160] Rttf2pt1_1.3.8       zip_2.2.0            shinyjs_2.0.0       
## [163] openxlsx_4.2.4       survival_3.2-11      parallelMap_1.5.1   
## [166] rmarkdown_2.13       munsell_0.5.0        plot3D_1.4          
## [169] iterators_1.0.13     haven_2.4.1          reshape2_1.4.4      
## [172] gtable_0.3.0         extrafont_0.17