Links

GitHub repository

Data

Set working directory and load data.

setwd("~/Documents/Work/Spring_2025/Corvid Efficiency/crow_efficiency/docs")
data <- read.csv("data/sequences.csv")
demo <- read.csv("data/demographics.csv")

data <- data[-which(data$length < 2), ]
data <- data.frame(individual = data$individual,
                   sequence_id = as.numeric(factor(paste0(data$filename, data$sequence_id))),
                   duration = data$duration,
                   length = data$length,
                   date = as.Date(data$date, format = "%d.%m.%y"),
                   sex = demo$sex[match(data$individual, demo$name)],
                   species = demo$species[match(data$individual, demo$name)],
                   population = demo$population[match(data$individual, demo$name)],
                   group = tolower(data$Group),
                   group_size = data$Groupsize,
                   birth_year = as.numeric(demo$birth[match(data$individual, demo$name)]),
                   age = as.numeric(paste0(20, substr(data$date, 7, 8))) - as.numeric(demo$birth[match(data$individual, demo$name)]),
                   elo_rating = demo$elo_rating[match(data$individual, demo$name)],
                   csi = demo$csi[match(data$individual, demo$name)])
data$age[which(is.na(data$age))] <- mean(data$age, na.rm = TRUE)

avg_data <- aggregate(duration ~ sequence_id + length + species + sex, data = data, FUN = median)

Print structure of the data.

library(knitr)
library(dplyr)
library(stringr)

summary <- data %>%
  group_by(individual, group) %>%
  summarize(
    recording_duration_s = sum(duration, na.rm = TRUE),
    dates = paste0(min(date), " to ", max(date)),
    Vocalizations = n(),
    Sequences = n_distinct(sequence_id),
    .groups = "drop"
  ) %>%
  left_join(data %>% select(individual, birth_year, species, sex, population) %>% distinct(), by = "individual") %>%
  arrange(individual, group)

summary$individual <- str_to_title(summary$individual)
summary$species <- str_to_title(summary$species)
summary$sex <- str_to_title(summary$sex)
summary$population <- str_to_title(summary$population)
summary$group <- str_to_title(summary$group)

summary$recording_duration_s <- as.character(round(summary$recording_duration_s, 1))

colnames(summary) <- c(
  "Individual", "Group", "Recording Time (s)", "Dates", "# Calls", "# Sequences",
  "Birth Year", "Species", "Sex", "Population"
)

kable(summary, format = "markdown")

Individual	Group	Recording Time (s)	Dates	# Calls	# Sequences	Birth Year	Species	Sex	Population
Alicante	Hl	66.6	2013-01-06 to 2013-11-15	126	50	2010	Carrion	F	Spain
Baerchen	Baerchenpeter	643.9	2010-04-11 to 2015-07-04	1214	399	2008	Carrion	M	Austria
Bluepoint	Vr	29.7	2013-01-11 to 2013-09-25	68	22	2012	Carrion	M	Spain
Bluestripes	Vr	13	2013-01-12 to 2013-06-16	29	11	2012	Carrion	M	Spain
Cabezon	Vl	357.5	2012-12-27 to 2014-04-19	524	175	2010	Carrion	M	Spain
Franz	Franztoeffel	74	2010-04-22 to 2012-07-26	162	53	2007	Carrion	M	Austria
Gabi	Gabi	72.4	2012-11-10 to 2012-11-15	168	58	2007	Carrion	F	Austria
Gabi	Hugoklausgabiresa	160	2010-04-09 to 2010-09-10	341	118	2007	Carrion	F	Austria
Gabi	Klausgabiresa	127	2011-09-10 to 2012-09-10	315	88	2007	Carrion	F	Austria
Gertrude	Waltergertrude	34.4	2012-07-10 to 2013-11-27	54	17	2011	Hooded	F	Austria
Greeno	Greenowhitestripes	19.9	2013-11-12 to 2014-04-15	63	20	2011	Carrion	M	Spain
Greeno	Hl	62	2012-12-30 to 2013-04-26	191	56	2011	Carrion	M	Spain
Greeno	Hl3	200	2013-05-04 to 2013-09-24	519	148	2011	Carrion	M	Spain
Greenz	Greenz&White	151.4	2014-01-31 to 2014-04-19	251	72	2011	Carrion	M	Spain
Greenz	Hl	50.9	2013-01-06 to 2014-04-19	104	37	2011	Carrion	M	Spain
Greenz	Hl3	149.8	2013-05-11 to 2013-11-15	260	89	2011	Carrion	M	Spain
Hugo	Hugoklausgabiresa	19.7	2010-04-09 to 2010-09-08	59	15	NA	Carrion	M	Austria
Ibiza	Hr	386.6	2012-12-31 to 2013-05-09	951	293	2010	Carrion	F	Spain
Ibiza	Hr4	300.3	2013-07-01 to 2014-12-25	837	214	2010	Carrion	F	Spain
Klaus	Klausgabi	68.4	2012-01-14 to 2012-09-21	128	44	2009	Carrion	M	Austria
Klaus	Klausgabiresa	151.3	2011-09-07 to 2012-01-10	290	89	2009	Carrion	M	Austria
Martinez	Hr	178.8	2012-12-31 to 2013-06-16	320	98	2010	Carrion	M	Spain
Martinez	Hr4	302.3	2013-06-25 to 2014-12-25	534	150	2010	Carrion	M	Spain
Munin	Momomuninwilli	2.7	2015-05-28 to 2015-05-30	6	3	2014	Hybrid	F	Austria
Nino	Nino	19.1	2012-07-29 to 2012-07-29	50	19	2011	Hooded	M	Austria
Olaf	Ruedigerolaf	123.3	2010-04-12 to 2010-05-01	230	86	NA	Hybrid	F	Austria
Peter	Baerchenpeter	25.2	2010-05-13 to 2015-07-01	32	11	2007	Carrion	F	Austria
Pobla	Vl	472.8	2013-01-15 to 2014-04-19	1119	332	2010	Carrion	F	Spain
Redcross	Vr	18.8	2013-01-11 to 2013-09-15	58	18	2012	Carrion	F	Spain
Redpoint	Vr	321.5	2013-01-06 to 2013-09-25	628	157	2012	Carrion	M	Spain
Redstripes	Vr	0.9	2013-01-06 to 2013-01-06	2	1	2012	Carrion	M	Spain
Resa	Hugoklausgabiresa	2.4	2012-01-14 to 2012-07-17	6	2	2009	Carrion	F	Austria
Ruediger	Ruedigerolaf	14.2	2010-04-28 to 2012-07-12	30	6	NA	Carrion	M	Austria
Toeffel	Franztoeffel	259	2010-04-22 to 2012-11-11	648	204	2008	Carrion	F	Austria
Valencia	Hr4	246.4	2013-06-25 to 2014-12-25	588	159	2013	Carrion	M	Spain
Walter	Walterbaerbel	44	2015-05-27 to 2015-07-05	77	20	2011	Carrion	M	Austria
Walter	Waltergertrude	194.2	2011-09-07 to 2013-11-27	338	116	2011	Carrion	M	Austria
Walter	Waltergertrude	16.4	2012-07-10 to 2012-07-20	31	10	2011	Carrion	M	Austria
White	Greenz&White	11.1	2014-01-31 to 2014-04-16	18	5	2008	Carrion	F	Spain
White	Hl	170.5	2012-12-30 to 2013-03-28	379	119	2008	Carrion	F	Spain
White	Hl3	144.5	2013-05-04 to 2013-11-15	267	101	2008	Carrion	F	Spain
Whitecross	Vr	9.1	2013-01-23 to 2013-09-21	20	7	2012	Carrion	M	Spain
Whitecross	Wild	17.9	2014-04-12 to 2014-04-18	28	12	2012	Carrion	M	Spain
Whitepoint	Vr	4.5	2013-09-10 to 2013-09-21	7	3	2012	Carrion	M	Spain
Whitestripes	Vr	2.6	2013-01-11 to 2014-04-15	6	3	2012	Carrion	F	Spain
Willi	Momomuninwilli	4.1	2015-07-04 to 2015-07-04	6	2	2012	Carrion	M	Austria
Willi	Willitoeffel	19.2	2013-11-26 to 2013-11-27	30	11	2012	Carrion	M	Austria
Xufa	Hr4	6.5	2013-06-25 to 2013-06-25	11	3	2013	Carrion	F	Spain

Models

Run and save all models.

carrion_menz_model <- lme4::lmer(scale(log(duration)) ~ scale(log(length)) + (1|individual/sequence_id), data = data[which(data$species == "carrion"), ])
hooded_menz_model <- lme4::lmer(scale(log(duration)) ~ scale(log(length)) + (1|individual/sequence_id), data = data[which(data$species == "hooded"), ])
hybrid_menz_model <- lme4::lmer(scale(log(duration)) ~ scale(log(length)) + (1|individual/sequence_id), data = data[which(data$species == "hybrid"), ])

menz_models <- list(carrion = carrion_menz_model, hooded = hooded_menz_model, hybrid = hybrid_menz_model)
save(menz_models, file = "models/menz_models.RData")

carrion_m_model <- lme4::lmer(scale(log(duration)) ~ scale(log(length)) + (1|individual/sequence_id), data = data[which(data$species == "carrion" & data$sex == "m"), ])
carrion_f_model <- lme4::lmer(scale(log(duration)) ~ scale(log(length)) + (1|individual/sequence_id), data = data[which(data$species == "carrion" & data$sex == "f"), ])

sex_models <- list(m = carrion_m_model, f = carrion_f_model)
save(sex_models, file = "models/sex_models.RData")

#https://blasbenito.github.io/collinear/articles/how_it_works.html
collinear::collinear(df = data, response = "duration", predictors = c("length", "sex", "group_size", "age", "elo_rating", "csi"), max_cor = NULL, max_vif = 5)

model_all_a <- lme4::lmer(scale(log(duration)) ~ 
                            scale(log(length)) + sex + scale(group_size) + scale(age) + scale(elo_rating) + scale(csi) + 
                            (1|population/group/individual/sequence_id),
                          data = data[which(data$species == "carrion"), ])
model_all_b <- lme4::lmer(scale(log(duration)) ~ 
                            scale(log(length))*(sex + scale(group_size) + scale(age) + scale(elo_rating) + scale(csi)) + 
                            (1|population/group/individual/sequence_id),
                          data = data[which(data$species == "carrion"), ])
model_all_c <- lme4::lmer(scale(log(duration)) ~ 
                            scale(log(length))*(sex + scale(group_size) + scale(age) + scale(elo_rating) + scale(csi)) +
                            (1|population/group/individual/sequence_id) + (0 + scale(log(length))|population:group:individual),
                          data = data[which(data$species == "carrion"), ])

ind_var_models <- list(base = model_all_a, inter_a = model_all_b, inter_b = model_all_c)
save(ind_var_models, file = "models/ind_var_models.RData")

Load models.

Menzerath’s Law

Plot and assess Menzerath’s law.

#load libraries
library(ggplot2)
library(rphylopic)

#img_coords: x, y, height
menz_plot <- function(data, avg_data, intercept, effect, bounds, color = "black", alpha = 1, effects_panel = 0.15, limits, title){
  #get original scaling from data
  og_scaled_x <- scale(log(data$length))
  og_scaled_y <- scale(log(data$duration))
  
  #function that predicts durations from lengths, based on intercepts, effects, and means and sds from scaling
  pred_durations <- function(intercept, effect, length, mean_log_length, sd_log_length, mean_log_dur, sd_log_dur){
    return(exp((intercept + effect*((log(length) - mean_log_length)/sd_log_length))*sd_log_dur + mean_log_dur))
  }
  
  #compute best fit line for plotting
  best_fit_data <- data.frame(x = seq(from = min(avg_data$length), to = max(avg_data$length), length.out = 1000))
  best_fit_data$y <- pred_durations(intercept, effect, length = best_fit_data$x,
                                    mean_log_length = attr(og_scaled_x, "scaled:center"), sd_log_length = attr(og_scaled_x, "scaled:scale"),
                                    mean_log_dur = attr(og_scaled_y, "scaled:center"), sd_log_dur = attr(og_scaled_y, "scaled:scale"))
  
  #get summary stats for titles
  n_inds <- format(length(unique(data$individual)), big.mark = ",", scientific = FALSE)
  n_seqs <- format(length(unique(data$sequence_id)), big.mark = ",", scientific = FALSE)
  n_calls <- format(nrow(data), big.mark = ",", scientific = FALSE)
  
  #construct base plot
  base_plot <- ggplot(avg_data, aes(x = length, y = duration)) + 
    geom_jitter(colour = color, size = 1, stroke = 0, height = 0, width = 0.1) + 
    geom_line(data = best_fit_data, aes(x = x, y = y), colour = color, linewidth = 0.5) +
    theme_linedraw(base_size = 8, base_family = "Avenir") +
    scale_x_continuous(breaks = 2:max(avg_data$length)) + 
    scale_y_continuous(breaks = scales::pretty_breaks(n = 6)) + 
    ggtitle(paste0(title, " (", n_inds, " Birds, ", n_calls, " Calls, ", n_seqs, " Sequences)")) + 
    xlab("# of Calls in Sequence") + ylab("Median Call Duration (s)")
  
  #construct effects plot
  effects_plot <- ggplot() + 
    geom_point(aes(x = 1, y = effect), stroke = 1, colour = color) + 
    geom_linerange(aes(x = 1, ymin = bounds[1], ymax = bounds[2]), colour = color) + 
    theme_linedraw(base_size = 8, base_family = "Avenir") + 
    geom_hline(yintercept = 0, lty = "dashed") + 
    scale_y_continuous(name = "Slope", position = "right", labels = scales::number_format(accuracy = 0.1), breaks = scales::pretty_breaks(n = 6), limits = limits) + 
    scale_x_continuous(name = "...", breaks = c(1), labels = c("A"), limits = c(0.5, 1.5)) + 
    ggtitle(" ") + 
    theme(panel.grid.major.x = element_blank(), panel.grid.minor.x = element_blank(), 
          axis.ticks.x = element_blank(),
          legend.position = "none",
          axis.title.x = element_text(colour = "white"),
          axis.text.x = element_text(colour = "white"))
  
  #combine and return
  return(cowplot::plot_grid(base_plot, effects_plot, rel_widths = c(1, effects_panel)))
}

#combined plot
png("plots/combined_plot.png", width = 6, height = 6, units = "in", res = 600)
cowplot::plot_grid(
  menz_plot(data[which(data$species == "carrion"), ], avg_data = avg_data[which(avg_data$species == "carrion"), ],
            intercept = summary(menz_models$carrion)$coefficients[1, 1],
            effect = summary(menz_models$carrion)$coefficients[2, 1], limits = c(-0.65, 0.1), title = "Carrion Crows",
            bounds = as.numeric(confint(menz_models$carrion, method = "Wald", parm = "scale(log(length))")), color = "black") +
  cowplot::draw_image("imgs/Carrion_crow.png", 
                      x = 0.7, y = 0.65, height = 0.2, width = 0.2),
  menz_plot(data[which(data$species == "hooded"), ], avg_data = avg_data[which(avg_data$species == "hooded"), ],
            intercept = summary(menz_models$hooded)$coefficients[1, 1],
            effect = summary(menz_models$hooded)$coefficients[2, 1], limits = c(-0.65, 0.1), title = "Hooded Crows",
            bounds = as.numeric(confint(menz_models$hooded, method = "Wald", parm = "scale(log(length))")), color = "black") +
  cowplot::draw_image("imgs/Hooded_crow.png", 
                      x = 0.7, y = 0.65, height = 0.2, width = 0.2),
  menz_plot(data[which(data$species == "hybrid"), ], avg_data = avg_data[which(avg_data$species == "hybrid"), ],
            intercept = summary(menz_models$hybrid)$coefficients[1, 1],
            effect = summary(menz_models$hybrid)$coefficients[2, 1], limits = c(-0.65, 0.1), title = "Hybrid Crows",
            bounds = as.numeric(confint(menz_models$hybrid, method = "Wald", parm = "scale(log(length))")), color = "black") +
  cowplot::draw_image("imgs/Carrion_crow.png", 
                      x = 0.63, y = 0.65, height = 0.2, width = 0.2) + 
  cowplot::draw_image("imgs/Hooded_crow.png", 
                      x = 0.7, y = 0.65, height = 0.2, width = 0.2),
  nrow = 3)
invisible(dev.off())

#sex plot
png("plots/sex_plot.png", width = 6, height = 4, units = "in", res = 600)
cowplot::plot_grid(
  menz_plot(data[which(data$species == "carrion" & data$sex == "f"), ], avg_data = avg_data[which(avg_data$species == "carrion" & avg_data$sex == "f"), ],
            intercept = summary(sex_models$f)$coefficients[1, 1],
            effect = summary(sex_models$f)$coefficients[2, 1], limits = c(-0.65, 0.1), title = "Female Carrion Crows",
            bounds = as.numeric(confint(sex_models$f, method = "Wald", parm = "scale(log(length))")), color = "black") +
  cowplot::draw_image("imgs/female.png", 
                    x = 0.67, y = 0.69, height = 0.14, width = 0.14) + 
  cowplot::draw_image("imgs/Carrion_crow.png", 
                      x = 0.7, y = 0.65, height = 0.2, width = 0.2),
  menz_plot(data[which(data$species == "carrion" & data$sex == "m"), ], avg_data = avg_data[which(avg_data$species == "carrion" & avg_data$sex == "m"), ],
            intercept = summary(sex_models$m)$coefficients[1, 1],
            effect = summary(sex_models$m)$coefficients[2, 1], limits = c(-0.65, 0.1), title = "Male Carrion Crows",
            bounds = as.numeric(confint(sex_models$m, method = "Wald", parm = "scale(log(length))")), color = "black") +
  cowplot::draw_image("imgs/male.png", 
                      x = 0.67, y = 0.69, height = 0.12, width = 0.12) + 
  cowplot::draw_image("imgs/Carrion_crow.png", 
                      x = 0.7, y = 0.65, height = 0.2, width = 0.2),
  nrow = 2)
invisible(dev.off())

The distribution of element durations and sequence lengths (left) and the slope of Menzerath's law (right), for each of the three crow species. The bars in the slope plot (right) mark the 95% confidence intervals around the point estimates.

Figure 1: The distribution of element durations and sequence lengths (left) and the slope of Menzerath’s law (right), for each of the three crow species. The bars in the slope plot (right) mark the 95% confidence intervals around the point estimates.

Menzerath’s law in carrion crows.
Parameter	Estimate	2.5% (Lower)	97.5% (Upper)
Intercept	0.018	-0.161	0.197
Length	-0.533	-0.559	-0.507	*

Menzerath’s law in hooded crows.
Parameter	Estimate	2.5% (Lower)	97.5% (Upper)
Intercept	-0.034	-1.609	1.542
Length	-0.195	-0.363	-0.027	*

Menzerath’s law in hybrid crows.
Parameter	Estimate	2.5% (Lower)	97.5% (Upper)
Intercept	-0.218	-0.930	0.494
Length	-0.409	-0.637	-0.182	*

Individual Variation

Investigate individual variation, including plots of interaction effects.

#load libraries
library(ggeffects)
library(ggplot2)

#get marginal predictions for different ages
predictions <- ggpredict(ind_var_models$inter_b, c("length", "age [1, 3, 5, 7]"), back_transform = FALSE)
predictions$predicted <- exp((predictions$predicted*sd(log(data$duration))) + mean(log(data$duration)))
predictions$conf.low <- exp((predictions$conf.low*sd(log(data$duration))) + mean(log(data$duration)))
predictions$conf.high <- exp((predictions$conf.high*sd(log(data$duration))) + mean(log(data$duration)))

#construct age effect plot
age_effect <- predictions %>% plot(line_size = 0.5)
colors <- c("#0072B2", "#D55E00", "#009E73", "#CC79A7", "#BDB10F", "#38A6E5", "#E09900")
age_effect <- age_effect + 
  ggtitle("Carrion Crows: Age Effect") + 
  scale_colour_manual(values = colors[1:4]) + 
  scale_fill_manual(values = colors[1:4]) + 
  scale_x_continuous(breaks = 2:max(avg_data$length)) + 
  scale_y_continuous(breaks = scales::pretty_breaks(n = 6)) + 
  labs(colour = "Age") + xlab("# of Calls in Sequence") + ylab("Median Call Duration (s)") + 
  theme_linedraw(base_size = 8, base_family = "Avenir")
age_effect$layers[[2]]$show.legend <- FALSE
age_effect$layers[[1]]$aes_params$linewidth <- 0.5

#get marginal predictions for different sexes
predictions <- ggpredict(ind_var_models$inter_b, c("length", "sex"), back_transform = FALSE)
predictions$predicted <- exp((predictions$predicted*sd(log(data$duration))) + mean(log(data$duration)))
predictions$conf.low <- exp((predictions$conf.low*sd(log(data$duration))) + mean(log(data$duration)))
predictions$conf.high <- exp((predictions$conf.high*sd(log(data$duration))) + mean(log(data$duration)))

#construct age effect plot
sex_effect <- predictions %>% plot(line_size = 0.5)
colors <- c("#0072B2", "#D55E00", "#009E73", "#CC79A7", "#BDB10F", "#38A6E5", "#E09900")
sex_effect <- sex_effect + 
  ggtitle("Carrion Crows: Sex Effect") + 
  scale_colour_manual(values = colors[1:2], labels = c("F", "M")) + 
  scale_fill_manual(values = colors[1:2], labels = c("F", "M")) + 
  scale_x_continuous(breaks = 2:max(avg_data$length)) + 
  scale_y_continuous(breaks = scales::pretty_breaks(n = 6)) +
  labs(colour = "Sex") + xlab("# of Calls in Sequence") + ylab("Median Call Duration (s)") + 
  theme_linedraw(base_size = 8, base_family = "Avenir")
sex_effect$layers[[2]]$show.legend <- FALSE
sex_effect$layers[[1]]$aes_params$linewidth <- 0.5

#save plot
png("plots/interact_plot.png", width = 6, height = 4, units = "in", res = 600)
cowplot::plot_grid(
  cowplot::plot_grid(age_effect, ggplot(NULL) + theme_void(), rel_widths = c(1, 0)) + cowplot::draw_image("imgs/Carrion_crow.png", x = 0.737, y = 0.65, height = 0.2, width = 0.2),
  cowplot::plot_grid(sex_effect, ggplot(NULL) + theme_void(), rel_widths = c(1, 0)) + cowplot::draw_image("imgs/Carrion_crow.png", x = 0.737, y = 0.65, height = 0.2, width = 0.2),
  nrow = 2
)
invisible(dev.off())

aic_table <- as.data.frame(AIC(ind_var_models$base, ind_var_models$inter_a, ind_var_models$inter_b))
aic_table$AIC <- round(aic_table$AIC)
aic_table <- cbind(Model = c("No Interactions", "Simple Interactions", "Complex Interactions"), aic_table)
flextable::flextable(aic_table) %>% 
  flextable::set_caption("Comparison of models of individual variation.", autonum = officer::run_autonum()) %>%
  flextable::theme_vanilla() %>% flextable::set_table_properties(layout = "autofit")

Comparison of models of individual variation.
Model	df	AIC
No Interactions	12	14,813
Simple Interactions	17	14,698
Complex Interactions	18	14,653

p_values <- c(anova(ind_var_models$base, ind_var_models$inter_a)$`Pr(>Chisq)`[2], anova(ind_var_models$inter_a, ind_var_models$inter_b)$`Pr(>Chisq)`[2])
p_values

## [1] 4.491468e-32 1.812487e-09

ind_var_table <- as.data.frame(summary(ind_var_models$inter_b)$coefficients)
ind_var_table <- cbind(ind_var_table$Estimate, as.data.frame(confint(ind_var_models$inter_b, method = "Wald", parm = c(7:18))))
ind_var_table <- round(ind_var_table, 3)
ind_var_table <- cbind(c("Intercept", "Length", "Sex (M vs. F)", "Group Size", "Age", "ELO", "CSI", "Length : Sex (M vs. F)", "Length : Group Size", "Length : Age", "Length : ELO", "Length : CSI"), ind_var_table, sapply(1:nrow(ind_var_table), function(x){ifelse(ind_var_table[x, 2]*ind_var_table[x, 3] > 0, "*", "")}))
colnames(ind_var_table) <- c("Parameter", "Estimate", "2.5% (Lower)", "97.5% (Upper)", " ")
flextable::flextable(ind_var_table) %>% 
  flextable::set_caption("Individual variation in Menzerath's law in carrion crows.", autonum = officer::run_autonum()) %>%
  flextable::theme_vanilla() %>% flextable::set_table_properties(layout = "autofit")

Individual variation in Menzerath’s law in carrion crows.
Parameter	Estimate	2.5% (Lower)	97.5% (Upper)
Intercept	-0.267	-0.494	-0.040	*
Length	-0.678	-0.796	-0.560	*
Sex (M vs. F)	0.541	0.254	0.827	*
Group Size	-0.107	-0.214	0.001
Age	0.142	0.086	0.198	*
ELO	0.201	0.078	0.324	*
CSI	0.081	-0.087	0.250
Length : Sex (M vs. F)	0.338	0.183	0.494	*
Length : Group Size	-0.043	-0.108	0.022
Length : Age	0.066	0.014	0.119	*
Length : ELO	0.045	-0.019	0.109
Length : CSI	-0.033	-0.114	0.048

The distribution of element durations and sequence lengths (left) and the slope of Menzerath's law (right), for female and male carrion crows. The bars in the slope plot (right) mark the 95% confidence intervals around the point estimates.

Figure 2: The distribution of element durations and sequence lengths (left) and the slope of Menzerath’s law (right), for female and male carrion crows. The bars in the slope plot (right) mark the 95% confidence intervals around the point estimates.

The predicted relationship between element durations and sequence lengths for different levels of age (top) and sex (bottom), from the fitted version of INSERT MODEL.

Figure 3: The predicted relationship between element durations and sequence lengths for different levels of age (top) and sex (bottom), from the fitted version of INSERT MODEL.

Vocal efficiency in crows

Claudia Wascher, Anglia Ruskin University, claudia.wascher@gmail.com

Mason Youngblood, Stony Brook University, masonyoungblood@gmail.com

Links

Data

Models

Menzerath’s Law

Individual Variation