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R_script_goshawks.R
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R_script_goshawks.R
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## Script written by Manuela Merling, IZW Berlin
library(readxl)
library(spaMM)
library(DHARMa)
library(lme4)
library(car)
library(purrr)
library(binom)
library(ggplot2)
library(maps)
library(mapdata)
library(dplyr)
library(doSNOW)
library(vegan)
spaMM.options(nb_cores = 3, separation_max = 1)
boot.repl <- 1000 ## put 0 for not parametric bootstrap!
nb_cores <- 3
## Map of study area ###############
rural <- data.frame(long = c(6.12954, 9.563227, 13.699830, 8.5324708),
lat = c(51.786726, 54.5239312, 52.857445, 52.0302285),
names = c('Kleve', 'Schleswig', 'Barnim', 'Bielefeld'), stringsAsFactors = FALSE)
urban <- data.frame(long = c(13.413215, 6.958281, 9.993682),
lat = c(52.521918, 50.941278, 53.551085),
names = c('Berlin', 'Cologne', 'Hamburg'), stringsAsFactors = FALSE)
germany <- map_data("worldHires", "Germany")
Germ <- ggplot() +
geom_polygon(data = germany, aes(x = long, y = lat, group = group), fill = "white", color = "black") +
coord_fixed(1.5) +
geom_point(data = rural, aes(x = long, y = lat), size = 3, shape = 17) +
geom_point(data = urban, aes(x = long, y = lat), size = 3,shape = 15) +
geom_text(data = rural, aes(x = long + 0.1, y = lat + 0.45, label = names, fontface = 2), color = 'black', size = 3) +
geom_text(data = urban, aes(x = long + 0.1, y = lat - 0.33, label = names, fontface = 2), color = 'black', size = 3) +
labs(x = "Longitude") + labs(y = "Latitude") +
theme_light() +
theme(panel.grid.minor = element_blank())
Germ
ggsave(filename = "./figures/figure1.pdf", width = 7, height = 10)
# Behavioural responses #####################################################
table_per_nest <- read_excel("./source_data/goshawk_data_nest.xlsx")
goshawk_nest1 <- subset(table_per_nest, Year == "2015" | Year == "2016")
goshawk_nest <- goshawk_nest1[, c("Year", "Location", "Age_youngest", "No_nestlings",
"Laying_begin_day", "Territory", "Habitat",
"reaction_female", "Rainfall")]
goshawk_nest$Year <- as.factor(goshawk_nest$Year)
goshawk_nest$Location <- as.factor(goshawk_nest$Location)
goshawk_nest$Territory <- as.factor(goshawk_nest$Territory)
goshawk_nest$Habitat <- as.factor(goshawk_nest$Habitat)
goshawk_nest$reaction_female <- factor(goshawk_nest$reaction_female)
goshawk_nest <- as.data.frame(goshawk_nest)
goshawk_nest <- droplevels(na.omit(goshawk_nest))
goshawk_nest$reaction <- goshawk_nest$reaction_female != "no reaction"
goshawk_nest$Age <- ifelse(goshawk_nest$Age_youngest <= 16,"young","old")
goshawk_nest$Age <- as.factor(goshawk_nest$Age)
urban <- subset(goshawk_nest, Habitat == "urban")
rural <- subset(goshawk_nest, Habitat == "rural")
### median Age
median(urban$Age_youngest)
# 21
median(rural$Age_youngest)
# 20
nrow(urban)
# 77
nrow(rural)
# 74
### wilcox age ##
wilcox.test(Age_youngest ~ Habitat, data = table_per_nest)
# Wilcoxon rank sum test with continuity correction
#
# data: Age_youngest by Habitat
# W = 4315.5, p-value = 0.2681
# alternative hypothesis: true location shift is not equal to 0
### behaviour model ###############
### test effects
test_react_int <- fitme(reaction ~ Habitat*Age + No_nestlings + Laying_begin_day +
Year + Rainfall + (1|Location/Territory),
family = binomial(link = "logit"), data = goshawk_nest,
method = "PQL/L") ## FULL MODEL
test_no_Hab_age <- fitme(reaction ~ No_nestlings + Laying_begin_day + Year +
Rainfall + (1|Location/Territory),
family = binomial(link = "logit"), data = goshawk_nest,
method = "PQL/L")
test_noHabitat <- fitme(reaction ~ Age + No_nestlings + Laying_begin_day + Year +
Rainfall + (1|Location/Territory),
family = binomial(link = "logit"), data = goshawk_nest,
method = "PQL/L")
test_nonest <- fitme(reaction ~ Habitat*Age + Laying_begin_day + Year + Rainfall
+ (1|Location/Territory), family = binomial(link = "logit"),
data = goshawk_nest, method = "PQL/L")
test_noYear <- fitme(reaction ~ Habitat*Age + No_nestlings + Laying_begin_day +
Rainfall + (1|Location/Territory),
family = binomial(link = "logit"), data = goshawk_nest,
method = "PQL/L")
test_noDay <- fitme(reaction ~ Habitat*Age + No_nestlings + Year + Rainfall
+ (1|Location/Territory), family = binomial(link = "logit"),
data = goshawk_nest, method = "PQL/L")
test_noRain <- fitme(reaction ~ Habitat*Age + No_nestlings + Laying_begin_day +
Year + (1|Location/Territory), family = binomial(link = "logit"),
data = goshawk_nest, method = "PQL/L")
test_noYoung <- fitme(reaction ~ Habitat + Rainfall + No_nestlings +
Laying_begin_day + Year + (1|Location/Territory),
family = binomial(link = "logit"), data = goshawk_nest,
method = "PQL/L")
### Odds ratioS
rural_young <- data.frame(Habitat = "rural", Age = "young", No_nestlings = 0, Laying_begin_day = 0,
Year = "2015", Rainfall = 0, Location = "new", Territory = "new")
urban_young <- data.frame(Habitat = "urban", Age = "young", No_nestlings = 0, Laying_begin_day = 0,
Year = "2015", Rainfall = 0, Location = "new", Territory = "new")
rural_old <- data.frame(Habitat = "rural", Age = "old", No_nestlings = 0, Laying_begin_day = 0,
Year = "2015", Rainfall = 0, Location = "new", Territory = "new")
urban_old <- data.frame(Habitat = "urban", Age = "old", No_nestlings = 0, Laying_begin_day = 0,
Year = "2015", Rainfall = 0, Location = "new", Territory = "new")
prob_rural_young <- predict(test_react_int, newdata = rural_young, re.form = NA)[[1]]
prob_urban_young <- predict(test_react_int, newdata = urban_young, re.form = NA)[[1]]
prob_rural_old <- predict(test_react_int, newdata = rural_old, re.form = NA)[[1]]
prob_urban_old <- predict(test_react_int, newdata = urban_old, re.form = NA)[[1]]
OR <- function(p1, p2) (p1/(1 - p1))/(p2/(1 - p2))
odd_ratio_urban_young_vs_rural_young <- round(OR(prob_urban_young, prob_rural_young), 2)
odd_ratio_urban_young_vs_rural_young # [1] 10.81
odd_ratio_urban_old_vs_rural_old <- round(OR(prob_urban_old, prob_rural_old), 2)
odd_ratio_urban_old_vs_rural_old # [1] 23.46
odd_ratio_urban_young_vs_urban_old <- round(OR(prob_urban_young, prob_urban_old), 2)
odd_ratio_urban_young_vs_urban_old # [1] 2.87
odd_ratio_rural_young_vs_rural_old <- round(OR(prob_rural_young, prob_rural_old), 2)
odd_ratio_rural_young_vs_rural_old # [1] 6.24
### bootstrap to get p-values of each effect
set.seed(123L)
anova(test_react_int, test_noHabitat, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 1907.8 s.
# chi2_LR df p_value
# p_v 12.26368 2 0.002172577
# Bootstrap results -
# Raw simulated p-value: 0.016
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 9.145138 2 0.01033138
anova(test_react_int, test_nonest, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 3288.4 s.
# chi2_LR df p_value
# p_v 1.036544 1 0.3086266
# Bootstrap results -
# Raw simulated p-value: 0.337
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 0.8949581 1 0.3441372
anova(test_react_int, test_noYear, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 2801.6 s.
# chi2_LR df p_value
# p_v 8.014984 1 0.00463919
# Bootstrap results -
# Raw simulated p-value: 0.011
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 7.454125 1 0.006329123
anova(test_react_int, test_noDay, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 2297.4 s.
# chi2_LR df p_value
# p_v 4.940328 1 0.02623706
# Bootstrap results -
# Raw simulated p-value: 0.03
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 4.569614 1 0.0325439
anova(test_react_int, test_noRain, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 1967.2 s.
# chi2_LR df p_value
# p_v 0.6995435 1 0.4029371
# Bootstrap results -
# Raw simulated p-value: 0.427
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 0.6404846 1 0.4235354
anova(test_react_int, test_noYoung, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 2387 s.
# chi2_LR df p_value
# p_v 5.979197 2 0.05030763
# Bootstrap results -
# Raw simulated p-value: 0.0829
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 4.970473 2 0.08330584
### Odds ratio for Year effect
exp(fixef(test_react_int)["Year2016"])
### behaviour model without interaction ###############
test_no_int <- fitme(reaction ~ Habitat + Age + No_nestlings + Laying_begin_day +
Year + Rainfall + (1|Location/Territory),
family = binomial(link = "logit"), data = goshawk_nest,
method = "PQL/L")
### odds ratio
round(exp(fixef(test_no_int)["Habitaturban"]), 2)
# Habitaturban (Odds-ratio)
# 21.68
CI_behaviour <- confint(test_no_int, "Habitaturban")
exp(CI_behaviour$interval)
# lower Habitaturban upper Habitaturban
# 10.13009 21.9269
### Improve fit for more reliable CI
refit_test_no_int <- test_no_int
for (i in 1:5) {
refit_test_no_int <- update(refit_test_no_int,
init = list(lambda = unique(CI_behaviour$confint_best_fit$ranPars$lambda)),
init.HLfit = list(fixef = CI_behaviour$confint_best_fit$beta_eta))
CI_behaviour <- confint(refit_test_no_int, "Habitaturban")
print(exp(CI_behaviour$interval))
}
exp(CI_behaviour$interval)
# lower Habitaturban upper Habitaturban
# 5.129949 130.546767
cbind(fixef(refit_test_no_int), fixef(test_no_int)) ## the change in parameter estimates remains minimal and will be neglected
# [,1] [,2]
# (Intercept) 6.97399820 6.98972574
# Habitaturban 3.09604863 3.07656847
# Ageyoung 1.62236032 1.63593499
# No_nestlings -0.33113174 -0.32905848
# Laying_begin_day -0.09258641 -0.09263122
# Year2016 1.48054505 1.47856159
# Rainfall -0.06217306 -0.06094037
### test effects
test_no_Habitat <- fitme(reaction ~ Age + No_nestlings + Laying_begin_day + Year +
Rainfall + (1|Location/Territory),
family = binomial(link = "logit"), data = goshawk_nest,
method = "PQL/L")
test_no_Age <- fitme(reaction ~ Habitat + No_nestlings + Laying_begin_day + Year +
Rainfall + (1|Location/Territory),
family = binomial(link = "logit"), data = goshawk_nest,
method = "PQL/L")
### bootstraps
anova(test_react_int, test_no_int, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 2789.7 s.
# chi2_LR df p_value
# p_v 0.2841157 1 0.5940163
# Bootstrap results -
# Raw simulated p-value: 0.736
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 0.2414185 1 0.6231834
anova(test_no_int, test_no_Age, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 2018.7 s.
# chi2_LR df p_value
# p_v 5.695081 1 0.01701252
# Bootstrap results -
# Raw simulated p-value: 0.015
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 5.587429 1 0.01808983
anova(test_no_int, test_no_Habitat, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 1943.1 s.
# chi2_LR df p_value
# p_v 11.97957 1 0.0005378708
# Bootstrap results -
# Raw simulated p-value: 0.005
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 7.658944 1 0.005649156
### figures #####################
#### barplot raw data
total_rural <- nrow(goshawk_nest[goshawk_nest$Habitat == "rural", ])
total_urban <- nrow(goshawk_nest[goshawk_nest$Habitat == "urban", ])
plot_data <- goshawk_nest %>%
group_by(reaction_female, Habitat) %>%
summarise(n = n()) %>%
ungroup() %>%
mutate(total = ifelse(Habitat == "rural", total_rural, total_urban),
prop = n/total,
CI_lwr = map2_dbl(n, total, ~ as.numeric(binom.confint( x = .x, n = .y)[5, 5])), ## method exact
CI_upr = map2_dbl(n, total, ~ as.numeric(binom.confint( x = .x, n = .y)[5, 6]))) ## method exact
plot_data$reaction_female <- relevel(plot_data$reaction_female, ref = "no reaction")
plot_data$Habitat <- relevel(plot_data$Habitat, ref = "urban")
ggplot(plot_data, aes(x = reaction_female, y = prop, fill = Habitat, ymin = CI_lwr, ymax = CI_upr)) +
geom_bar(stat = "identity", position = position_dodge2(preserve = "single", width = 0.9), alpha = 0.8) +
geom_errorbar(width = 0, position = position_dodge(preserve = "total", width = 0.9)) +
scale_fill_grey() +
scale_y_continuous("Proportion of females reacting") +
scale_x_discrete("Reaction") +
theme_bw() +
theme(panel.grid.minor = element_blank(),
panel.grid.major.x = element_blank())
ggsave(filename = "./figures/figure2.pdf", width = 8, height = 7)
#### barplot predictions Habitat/Age
pred_urban_young <- predict(test_react_int,
newdata = expand.grid(Laying_begin_day = median(goshawk_nest$Laying_begin_day, na.rm = TRUE),
Age = "young",
Rainfall = median(goshawk_nest$Rainfall, na.rm = TRUE),
No_nestlings = 3,
Year = "2015",
Habitat = "urban"),
re.form = NA, intervals = "predVar")
pred_1 <- data.frame(pred = pred_urban_young, attr(pred_urban_young, "intervals"),
Habitat = "urban", Age = "young")
pred_urban_old <- predict(test_react_int, newdata = expand.grid(Laying_begin_day = median(goshawk_nest$Laying_begin_day, na.rm = TRUE),
Age = "old",
Rainfall = median(goshawk_nest$Rainfall, na.rm = TRUE),
No_nestlings = 3,
Year = "2015",
Habitat = "urban"),
re.form = NA, intervals = "predVar")
pred_2 <- data.frame(pred = pred_urban_old, attr(pred_urban_old, "intervals"),
Habitat = "urban", Age = "old")
pred_rural_young <- predict(test_react_int, newdata = expand.grid(Laying_begin_day = median(goshawk_nest$Laying_begin_day, na.rm = TRUE),
Age = "young",
Rainfall = median(goshawk_nest$Rainfall, na.rm = TRUE),
No_nestlings = 3,
Year = "2015",
Habitat = "rural"),
re.form = NA, intervals = "predVar")
pred_3 <- data.frame(pred = pred_rural_young, attr(pred_rural_young, "intervals"),
Habitat = "rural", Age = "young")
pred_rural_old <- predict(test_react_int, newdata = expand.grid(Laying_begin_day = median(goshawk_nest$Laying_begin_day, na.rm = TRUE),
Age = "old",
Rainfall = median(goshawk_nest$Rainfall, na.rm = TRUE),
No_nestlings = 3,
Year = "2015",
Habitat = "rural"),
re.form = NA, intervals = "predVar")
pred_4 <- data.frame(pred = pred_rural_old, attr(pred_rural_old, "intervals"),
Habitat = "rural", Age = "old")
pred_Habitat_age <- rbind(pred_1, pred_2, pred_3, pred_4)
pred_Habitat_age$Habitat <- factor(pred_Habitat_age$Habitat, levels = c("urban", "rural"))
pred_Habitat_age$Age <- factor(pred_Habitat_age$Age, levels = c("young", "old"))
ggplot(pred_Habitat_age, aes(x = Age, y = pred, fill = Habitat, ymin = predVar_0.025, ymax = predVar_0.975)) +
geom_bar(stat = "identity", position = position_dodge2(preserve = "single", width = 0.9), alpha = 0.8) +
geom_errorbar(width = 0, position = position_dodge(preserve = "total", width = 0.9)) +
scale_fill_grey() +
scale_y_continuous("Proportion of females reacting") +
scale_x_discrete("Age categorical") +
theme_bw() +
theme(panel.grid.minor = element_blank(),
panel.grid.major.x = element_blank())
ggsave(filename = "./figures/figure3.pdf", width = 8, height = 7)
#### plot prediction laying
predictor_lay <- seq(min(goshawk_nest$Laying_begin_day, na.rm = TRUE), max(goshawk_nest$Laying_begin_day, na.rm = TRUE), length = 30)
pred_lay_obj <- predict(test_no_int,
newdata = expand.grid(Laying_begin_day = predictor_lay,
Age = "young",
Rainfall = median(goshawk_nest$Rainfall, na.rm = TRUE),
No_nestlings = 3,
Year = "2015",
Habitat = "urban"),
re.form = NA, intervals = "predVar")
pred_lay <- data.frame(pred = pred_lay_obj, attr(pred_lay_obj, "intervals"), lay = predictor_lay)
predictor_lay2 <- seq(min(goshawk_nest$Laying_begin_day, na.rm = TRUE),
max(goshawk_nest$Laying_begin_day, na.rm = TRUE),
length = 30)
pred_lay_obj2 <- predict(test_no_int,
newdata = expand.grid(Laying_begin_day = predictor_lay2,
Age = "young",
Rainfall = median(goshawk_nest$Rainfall, na.rm = TRUE),
No_nestlings = 3,
Year = "2015",
Habitat = "rural"),
re.form = NA, intervals = "predVar")
pred_lay2 <- data.frame(pred = pred_lay_obj2, attr(pred_lay_obj2, "intervals"), lay2 = predictor_lay2)
pdf("./figures/figure4.pdf", width = 10, height = 7)
plot(pred_lay$pred ~ pred_lay$lay, type = "l", lwd = 2, ylab = "Proportion of females reacting",
las = 1, ylim = c(0, 1), xlab = "Laying date", axes = FALSE)
points(pred_lay$predVar_0.025~ pred_lay$lay, type = "l", lwd = 2, lty = 2)
points(pred_lay$predVar_0.975~ pred_lay$lay, type = "l", lwd = 2, lty = 2)
rug(x = jitter(urban$Laying_begin_day[!goshawk_nest$reaction]), side = 1)
rug(x = jitter(urban$Laying_begin_day[goshawk_nest$reaction]), side = 3)
lines(pred_lay2$pred ~ pred_lay2$lay2, type = "l", lwd = 2, ylab = "Proportion of females reacting",
las = 1, ylim = c(0, 1), xlab = "Laying date", col = "grey")
points(pred_lay2$predVar_0.025~ pred_lay2$lay2, type = "l", lwd = 2, lty = 2, col = "grey")
points(pred_lay2$predVar_0.975~ pred_lay2$lay2, type = "l", lwd = 2, lty = 2, col = "grey")
box()
rug(x = jitter(rural$Laying_begin_day[!goshawk_nest$reaction]), side = 1, col = "grey")
rug(x = jitter(rural$Laying_begin_day[goshawk_nest$reaction]), side = 3, col = "grey")
labelist <- as.vector(c("March 02","March 12", "March 22", "April 01", "April 11", "April 21", "May 01"))
axis(1, at = seq(60,120, by = 10), labels = labelist)
axis(2, las = 2)
dev.off()
# Diet composition ####################################################################
## figure raw data
Rupfungen_gesamt <- read_excel("./source_data/goshawk_data_diet_plot.xlsx")
n_land <- nrow(Rupfungen_gesamt[Rupfungen_gesamt$Habitat == "Land", ])
n_stadt <- nrow(Rupfungen_gesamt[Rupfungen_gesamt$Habitat == "Stadt", ])
cut_off <- Rupfungen_gesamt %>%
group_by(species, Habitat) %>%
summarise(n = n()) %>%
mutate(n_total = ifelse(Habitat == "Land", n_land, n_stadt),
prop = n / n_total) %>%
ungroup()
cut_off <- cut_off %>%
mutate(CI_lwr = map2_dbl(n, n_total, ~ as.numeric(binom.confint( x = .x, n = .y)[5, 5])), ## method exact
CI_upr = map2_dbl(n, n_total, ~ as.numeric(binom.confint( x = .x, n = .y)[5, 6]))) ## table with all species even < 1%
cut_off2 <- cut_off %>%
filter(prop > 0.01) ## filter to keep only species > 1%
cut_off2$species <- relevel(as.factor(cut_off2$species), ref = "Feral pigeon")
cut_off2$species <- factor(cut_off2$species,
levels = levels(cut_off2$species)[c(1, 22, 12, 20, 9, 3, 10, 14, 6, 4, 8, 5, 18, 15, 13, 21, 7, 16, 19, 17, 2, 11)])
cut_off2$Habitat <- factor(cut_off2$Habitat, levels = c("Stadt", "Land"))
cut_off2$Habitat <- relevel(as.factor(cut_off2$Habitat), ref = "Stadt")
ggplot(cut_off2, aes(x = species, y = prop, fill = Habitat, ymin = CI_lwr, ymax = CI_upr)) +
geom_bar(stat = "identity", position = position_dodge2(preserve = "single", width = 0.9), alpha = 0.8) +
geom_errorbar(position = position_dodge(preserve = "total", width = 0.9), width = 0) +
scale_fill_grey(labels = c("urban", "rural")) +
scale_y_continuous("Proportion of prey species") +
scale_x_discrete("Species") +
geom_vline(xintercept = 4.5, linetype = 2) +
theme_bw() +
theme(panel.grid.minor = element_blank(),
axis.text.x = element_text(angle = 90, hjust = 1),
panel.grid.major.x = element_blank(),
panel.grid.minor.x = element_blank())
ggsave(filename = "./figures/figure5.pdf", width = 10, height = 7)
### pigeons ###################
Rupfungen_per_nest_aktuell <- read_excel("./source_data/goshawk_data_diet.xlsx")
pigeon <- Rupfungen_per_nest_aktuell[, c("Location", "nest_side", "Habitat",
"Species_richness_nest", "Pigeon", "Rest")]
pigeon$Location <- as.factor(pigeon$Location)
pigeon$nest_side <- as.factor(pigeon$nest_side)
pigeon$Habitat <- as.factor(pigeon$Habitat)
pigeon <- as.data.frame(pigeon)
GLMM_pigeon_spaMM_loc <- fitme(cbind(Pigeon, Rest)~Habitat + (1|Location/nest_side),
family = binomial(link = "logit"),
data = pigeon,
method = "PQL/L")
GLMM_0_loc <- fitme(cbind(Pigeon, Rest)~ 1 + (1|Location/nest_side),
family = binomial(link = "logit"),
data = pigeon,
method = "PQL/L")
### Odds ratio
Odds_ratio <- exp(GLMM_pigeon_spaMM_loc$fixef["HabitatUrban"])
Odds_ratio
# HabitatUrban
# 3.637754
CI_diet <- confint(GLMM_pigeon_spaMM_loc, "HabitatUrban")
exp(CI_diet$interval)
# lower HabitatUrban upper HabitatUrban
# 2.436699 5.281086
### Improve fit for more reliable CI
refit_GLMM_pigeon_spaMM_loc <- GLMM_pigeon_spaMM_loc
for (i in 1:5) {
refit_GLMM_pigeon_spaMM_loc <- update(refit_GLMM_pigeon_spaMM_loc,
init = list(lambda = unique(CI_diet$confint_best_fit$ranPars$lambda)),
init.HLfit = list(fixef = CI_diet$confint_best_fit$beta_eta))
CI_diet <- confint(refit_GLMM_pigeon_spaMM_loc, "HabitatUrban")
print(exp(CI_diet$interval))
}
exp(CI_diet$interval)
# lower HabitatUrban upper HabitatUrban
# 2.051880 6.661841
cbind(fixef(refit_GLMM_pigeon_spaMM_loc), fixef(GLMM_pigeon_spaMM_loc)) ## the change in parameter estimates remains minimal and will be neglected
# [,1] [,2]
# (Intercept) -0.665362 -0.6614136
# HabitatUrban 1.295880 1.291366
### bootstrap ###
set.seed(123)
anova(GLMM_0_loc, GLMM_pigeon_spaMM_loc, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 241.8 s.
# chi2_LR df p_value
# p_v 10.16658 1 0.001430096
# Bootstrap results -
# Raw simulated p-value: 0.015
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 5.998557 1 0.01431759
### diversity ###########################
Rupfungen_per_nest_aktuell <- read_excel("./source_data/goshawk_data_diet.xlsx")
diversity <- Rupfungen_per_nest_aktuell[, c("Location", "nest_side", "Habitat",
"diversity_nest")]
diversity$Location <- as.factor(diversity$Location)
diversity$nest_side <- as.factor(diversity$nest_side)
diversity$Habitat <- as.factor(diversity$Habitat)
diversity$diversity_nest <- as.numeric(diversity$diversity_nest)
diversity <- na.omit(diversity)
diversity <- as.data.frame(diversity)
### Here we use lme4 as an interim step to estimate the BoxCox transformation to be applied in spaMM
lmer_diversity <- lmer(diversity_nest ~ Habitat + (1|Location), data = diversity, REML = FALSE)
spaMM_diversity_coor <- fitme(diversity_nest ~ Habitat +(1|Location), data = diversity)
bc_lmer <- powerTransform(lmer_diversity, family = "bcPower")
diversity$diversity_nest_bc <- bcPower(diversity$diversity_nest, bc_lmer$lambda)
lmer_diversity2 <- lmer(diversity_nest_bc ~ Habitat + (1|Location), data = diversity, REML = FALSE)
spaMM_diversity3 <- fitme(diversity_nest_bc ~ Habitat +(1|Location), data = diversity)
logLik(lmer_diversity2)
logLik(spaMM_diversity3) ## same loglik across packages! GOOD
lmer_diversity_0 <- lmer(diversity_nest ~ 1 + (1|Location), data = diversity, REML = FALSE)
spaMM_diversity_0 <- fitme(diversity_nest ~ 1 + (1|Location), data = diversity)
lmer_diversity_upda <- lmer(diversity_nest_bc ~ 1 + (1|Location), data = diversity, REML = FALSE)
spaMM_diversity_upda_0 <- fitme(diversity_nest_bc ~ 1 + (1|Location), data = diversity)
### test effect #
pred_trans_rural <- (spaMM_diversity3$fixef["(Intercept)"] * bc_lmer$lambda + 1)^(1/bc_lmer$lambda)
pred_trans_urban <- ((spaMM_diversity3$fixef["(Intercept)"] + spaMM_diversity3$fixef["HabitatUrban"]) * bc_lmer$lambda + 1)^(1/bc_lmer$lambda)
pred_trans_urban - pred_trans_rural
# (Intercept)
# -0.1099321
### bootstrap
set.seed(123)
anova(spaMM_diversity3, spaMM_diversity_upda_0, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 107.7 s.
# chi2_LR df p_value
# p_v 8.929882 1 0.002805424
# Bootstrap results -
# Raw simulated p-value: 0.00799
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 6.12485 1 0.01332946
### species richness ####################################
Rupfungen_per_nest_aktuell <- read_excel("./source_data/goshawk_data_diet.xlsx")
species <- Rupfungen_per_nest_aktuell[, c("Location","nest_side", "Habitat",
"Species_richness_nest")]
species$Location <- as.factor(species$Location)
species$nest_side <- as.factor(species$nest_side)
species$Habitat <- as.factor(species$Habitat)
species$Species_richness_nest <- as.numeric(species$Species_richness_nest)
species <- na.omit(species)
species <- as.data.frame(species)
glm_species_spaMM <- fitme(Species_richness_nest ~ Habitat+(1|Location),
family = Tnegbin(),
data = species)
glm_0_spaMM <- fitme(Species_richness_nest ~ 1 + (1|Location),
family = Tnegbin, data = species)
### Habitat Effect
predict(glm_species_spaMM, newdata = data.frame(Habitat = c("Urban", "Rural")),
re.form = NA)
# Point predictions:
# 4.017246 5.457141
diff(predict(glm_species_spaMM, newdata = data.frame(Habitat = c("Urban", "Rural")),
re.form = NA))
# Point predictions:
# 1.439895
### bootstrap
set.seed(123)
anova(glm_species_spaMM, glm_0_spaMM, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 302.7 s.
# chi2_LR df p_value
# p_v 5.53247 1 0.01866674
# Bootstrap results -
# Raw simulated p-value: 0.03
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 4.782857 1 0.02874439
# Breeding performance #########################################################################################
## egg laying date ###
table_per_nest <- read_excel("./source_data/goshawk_data_nest.xlsx")
goshawk_nest2 <- table_per_nest[, c("Year", "Location", "No_nestlings", "Laying_begin_day",
"Territory", "Habitat", "Temp_breeding_begin")]
goshawk_nest2$Year <- as.factor(goshawk_nest2$Year)
goshawk_nest2$Location <- as.factor(goshawk_nest2$Location)
goshawk_nest2$Territory <- as.factor(goshawk_nest2$Territory)
goshawk_nest2$Habitat <- as.factor(goshawk_nest2$Habitat)
goshawk_nest2 <- as.data.frame(goshawk_nest2)
goshawk_nest2 <- droplevels(na.omit(goshawk_nest2))
lmm_laying2 <- fitme(Laying_begin_day ~ Habitat + Temp_breeding_begin +
(1|Location/Territory), family = gaussian, data = goshawk_nest2)
### odds ratio
lmm_laying2$fixef["Habitaturban"]
# Habitaturban
# -12.49214
CI_laying <- confint(lmm_laying2, "Habitaturban")
CI_laying
#lower Habitaturban upper Habitaturban
#-17.365852 -7.121119
### test effects
lmm_laying_no_Habitat <- fitme(Laying_begin_day ~ Temp_breeding_begin +
(1|Location/Territory), family = gaussian,
data = goshawk_nest2)
lmm_laying_no_Temp <- fitme(Laying_begin_day ~ Habitat + (1|Location/Territory),
family = gaussian, data = goshawk_nest2)
### bootstrap
set.seed(123)
anova(lmm_laying2, lmm_laying_no_Habitat, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 559.1 s.
# chi2_LR df p_value
# p_v 11.33817 1 0.0007592998
# Bootstrap results -
# Raw simulated p-value: 0.00899
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 6.617723 1 0.01009689
anova(lmm_laying2, lmm_laying_no_Temp, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 465.8 s.
# chi2_LR df p_value
# p_v 1.613375 1 0.2040181
# Bootstrap results -
# Raw simulated p-value: 0.221
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 1.460426 1 0.2268624
### reproductive output (brood size) ############
table_per_nest <- read_excel("./source_data/goshawk_data_nest.xlsx")
### wilcox Number of nestlings
wilcox.test(No_nestlings ~ Habitat, data = table_per_nest)
# Wilcoxon rank sum test with continuity correction
#
# data: No_nestlings by Habitat
# W = 3517.5, p-value = 0.0006975
# alternative hypothesis: true location shift is not equal to 0
### Figure Number of nestlings per nest raw data
n_land <- nrow(table_per_nest[table_per_nest$Habitat == "rural", ])
n_stadt <- nrow(table_per_nest[table_per_nest$Habitat == "urban", ])
cut_off <- table_per_nest %>%
group_by(No_nestlings, Habitat) %>%
summarise(n = n()) %>%
mutate(n_total = ifelse(Habitat == "urban", n_land, n_stadt),
prop = n / n_total) %>%
ungroup()
cut_off <- cut_off %>%
mutate(CI_lwr = map2_dbl(n, n_total, ~ as.numeric(binom.confint( x = .x, n = .y)[5, 5])), ## method exact
CI_upr = map2_dbl(n, n_total, ~ as.numeric(binom.confint( x = .x, n = .y)[5, 6]))) ## method exact
cut_off$No_nestlings <- relevel(as.factor(cut_off$No_nestlings), ref = "1")
cut_off$Habitat <- factor(cut_off$Habitat, levels = c("urban", "rural"))
cut_off$Habitat <- relevel(as.factor(cut_off$Habitat), ref = "urban")
ggplot(cut_off, aes(x = No_nestlings, y = prop, fill = Habitat, ymin = CI_lwr, ymax = CI_upr)) +
geom_bar(stat = "identity", position = position_dodge2(preserve = "single", width = 0.9), alpha = 0.8) +
geom_errorbar(position = position_dodge(preserve = "total", width = 0.9), width = 0) +
scale_fill_grey(labels = c("urban", "rural")) +
scale_y_continuous("Proportion") +
scale_x_discrete("Number of nestlings") +
geom_vline(xintercept = 2.5, linetype = 2) +
theme_bw() +
theme(panel.grid.minor = element_blank(),
axis.text.x = element_text(angle = 0, hjust = 1),
panel.grid.major.x = element_blank(),
panel.grid.minor.x = element_blank())
ggsave(filename = "./figures/figure6.pdf", width = 10, height = 7)
### model brood size ######
goshawk_nest3 <- table_per_nest[, c("Year", "Location", "No_nestlings", "Laying_begin_day",
"Territory", "Habitat", "Temp_breeding_begin")]
goshawk_nest3$Year <- as.factor(goshawk_nest3$Year)
goshawk_nest3$Location <- as.factor(goshawk_nest3$Location)
goshawk_nest3$Territory <- as.factor(goshawk_nest3$Territory)
goshawk_nest3$Habitat <- as.factor(goshawk_nest3$Habitat)
goshawk_nest3 <- as.data.frame(goshawk_nest3)
goshawk_nest3 <- droplevels(na.omit(goshawk_nest3))
goshawk_nest3$No_nestlings_binary <- goshawk_nest3$No_nestlings > 2
glmm_nestlings <- fitme(No_nestlings_binary ~ Habitat + Laying_begin_day +
Temp_breeding_begin + (1|Location/Territory),
family = binomial(link = "logit"), data = goshawk_nest3,
method = "PQL/L")
### test effects
glmm_nestlings_no_Habitat <- fitme(No_nestlings_binary ~ Laying_begin_day +
Temp_breeding_begin + (1|Location/Territory),
family = binomial(link = "logit"), data = goshawk_nest3,
method = "PQL/L")
glmm_nestlings_no_day <- fitme(No_nestlings_binary ~ Habitat + Temp_breeding_begin +
(1|Location/Territory), family = binomial(link = "logit"),
data = goshawk_nest3, method = "PQL/L")
glmm_nestlings_no_Temp <- fitme(No_nestlings_binary ~ Habitat + Laying_begin_day +
(1|Location/Territory), family = binomial(link = "logit"),
data = goshawk_nest3, method = "PQL/L")
### bootstraps
set.seed(123)
anova(glmm_nestlings, glmm_nestlings_no_Habitat, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 3930.3 s.
# chi2_LR df p_value
# p_v 0.005885621 1 0.938848
# Bootstrap results -
# Raw simulated p-value: 0.939
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 0.006440164 1 0.9360379
anova(glmm_nestlings, glmm_nestlings_no_day, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 2176.4 s.
# chi2_LR df p_value
# p_v 6.648189 1 0.009925667
# Bootstrap results -
# Raw simulated p-value: 0.011
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 6.649499 1 0.009918371
anova(glmm_nestlings, glmm_nestlings_no_Temp, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 1819.5 s.
# chi2_LR df p_value
# p_v 0.434495 1 0.5097915
# Bootstrap results -
# Raw simulated p-value: 0.543
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 0.384722 1 0.5350869
### predictive figures ####
urban1 <- subset(goshawk_nest3, Habitat == "urban")
rural1 <- subset(goshawk_nest3, Habitat == "rural")
predictor_day <- seq(min(goshawk_nest3$Laying_begin_day, na.rm = TRUE),
max(goshawk_nest3$Laying_begin_day, na.rm = TRUE),
length = 30)
pred_day_obj <- predict(glmm_nestlings, newdata = expand.grid(Laying_begin_day = predictor_day,
Habitat = "urban",
Temp_breeding_begin = median(goshawk_nest3$Temp_breeding_begin, na.rm = TRUE)),
re.form = NA, intervals = "predVar")
pred_day <- data.frame(pred = pred_day_obj, attr(pred_day_obj, "intervals"), day = predictor_day)
predictor_day2 <- seq(min(goshawk_nest3$Laying_begin_day, na.rm = TRUE), max(goshawk_nest3$Laying_begin_day, na.rm = TRUE), length = 30)
pred_day_obj2 <- predict(glmm_nestlings, newdata = expand.grid(Laying_begin_day = predictor_day2,
Habitat = "rural",
Temp_breeding_begin = median(goshawk_nest3$Temp_breeding_begin, na.rm = TRUE)),
re.form = NA, intervals = "predVar")
pred_day2 <- data.frame(pred2 = pred_day_obj2, attr(pred_day_obj2, "intervals"), day2 = predictor_day2)
pdf("./figures/figure7.pdf", width = 10, height = 7)
plot(pred_day$pred ~ pred_day$day, type = "l", lwd = 2, ylab = "Proportion of large clutches",
las = 1, ylim = c(0, 1), xlab = "Laying date", axes = FALSE)
points(pred_day$predVar_0.025~ pred_day$day, type = "l", lwd = 2, lty = 2)
points(pred_day$predVar_0.975~ pred_day$day, type = "l", lwd = 2, lty = 2)
rug(x = jitter(urban1$Laying_begin_day[!urban1$No_nestlings_binary]), side = 1)
rug(x = jitter(urban1$Laying_begin_day[urban1$No_nestlings_binary]), side = 3)
lines(pred_day2$pred2 ~ pred_day2$day2, type = "l", lwd = 2, ylab = "Proportion of large clutches",
las = 1, ylim = c(0, 1), xlab = "Laying date", col = "grey")
points(pred_day2$predVar_0.025~ pred_day2$day2, type = "l", lwd = 2, lty = 2, col = "grey")
points(pred_day2$predVar_0.975~ pred_day2$day2, type = "l", lwd = 2, lty = 2, col = "grey")
box()
rug(x = jitter(rural1$Laying_begin_day[!rural1$No_nestlings_binary]), side = 1, col = "grey")
rug(x = jitter(rural1$Laying_begin_day[rural1$No_nestlings_binary]), side = 3, col = "grey")
labelist <- as.vector(c("March 02","March 12", "March 22", "April 01", "April 11", "April 21", "May 01"))
axis(1, at = seq(60,120, by = 10), labels = labelist)
axis(2, las = 2)
dev.off()
### brood size model without laying start ################
glmm_nestlings2 <- fitme(No_nestlings_binary ~ Habitat + Temp_breeding_begin +
(1|Location/Territory), family = binomial(link = "logit"),
data = goshawk_nest3, method = "PQL/L")
### Odds ratio
exp(glmm_nestlings2$fixef["Habitaturban"])
# Habitaturban
# 2.217902
CI_nestlings <- confint(glmm_nestlings2, "Habitaturban")
exp(CI_nestlings$interval)
# lower Habitaturban upper Habitaturban
# 1.724201 2.2207
### Improve fit for more reliable CI
refit_glmm_nestlings2 <- glmm_nestlings2
for (i in 1:5) {
refit_glmm_nestlings2 <- update(refit_glmm_nestlings2,
init = list(lambda = unique(CI_nestlings$confint_best_fit$ranPars$lambda)),
init.HLfit = list(fixef = CI_nestlings$confint_best_fit$beta_eta))
CI_nestlings <- confint(refit_glmm_nestlings2, "Habitaturban")
print(exp(CI_nestlings$interval))
}
exp(CI_nestlings$interval)
# lower Habitaturban upper Habitaturban
# 0.9844251 4.7337744
cbind(fixef(refit_glmm_nestlings2), fixef(glmm_nestlings2)) ## the change in parameter estimates remains minimal and will be neglected
# [,1] [,2]
# (Intercept) -0.17167554 -0.17246528
# Habitaturban 0.79670641 0.79656178
# Temp_breeding_begin 0.08200158 0.08220989
### testing effects
glmm_nestlings_no_Habitat2 <- fitme(No_nestlings_binary ~ Temp_breeding_begin +
(1|Location/Territory), family = binomial(link = "logit"),
data = goshawk_nest3, method = "PQL/L")
glmm_nestlings_no_Temp2 <- fitme(No_nestlings_binary ~ Habitat + (1|Location/Territory),
family = binomial(link = "logit"),
data = goshawk_nest3,
method = "PQL/L")
### bootstraps
set.seed(123)
anova(glmm_nestlings2, glmm_nestlings_no_Habitat2, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 1621.8 s.
# chi2_LR df p_value
# p_v 5.543066 1 0.01855405
# Bootstrap results -
# Raw simulated p-value: 0.036
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 4.359898 1 0.0367945
anova(glmm_nestlings2, glmm_nestlings_no_Temp2, boot.repl = boot.repl, nb_cores = nb_cores)
# bootstrap took 1645.6 s.
# chi2_LR df p_value
# p_v 0.2953909 1 0.5867865
# Bootstrap results -
# Raw simulated p-value: 0.551
# Bartlett-corrected LR test:
# chi2_LR df p_value
# p_v 0.2924267 1 0.5886696
#Health status of goshawk nestlings ####################################
### prevalence ####
Tabelle_Statistik_urban_ecology_aktuell <- read_excel("./source_data/goshawk_data_nestlings.xlsx")
goshawk_urban <- Tabelle_Statistik_urban_ecology_aktuell[, c("Year", "Location","No_nestlings", "Sex",
"Age", "Prevalence", "Territory", "Habitat", "laying_day",
"Temp_age", "Clinical_binary")]
goshawk_urban$Year <- as.factor(goshawk_urban$Year)
goshawk_urban$Location <- as.factor(goshawk_urban$Location)
goshawk_urban$Territory <- as.factor(goshawk_urban$Territory)
goshawk_urban$Sex <- as.factor(goshawk_urban$Sex)
goshawk_urban$Habitat <- as.factor(goshawk_urban$Habitat)
goshawk_urban$Clinical_binary <- as.numeric(goshawk_urban$Clinical_binary)
goshawk_urban <- as.data.frame(goshawk_urban)
goshawk_urban <- droplevels(na.omit(goshawk_urban))
urban2 <- subset(goshawk_urban, Habitat == "urban")
rural2 <- subset(goshawk_urban, Habitat == "rural")
### Median age
median(urban2$Age)
# 24
median(rural2$Age)
# 23
### figure prevalence raw data w###
plot_data <- goshawk_urban %>%
group_by(Year, Habitat) %>%
summarise(n = n(),
n_inf = sum(Prevalence == 1, na.rm = T),
n_not_inf = sum(Prevalence == 0, na.rm = T),
prop_inf = n_inf / n) %>%
ungroup() %>%
mutate(CI_lwr = map2_dbl(n_inf, n, ~ as.numeric(binom.confint( x = .x, n = .y)[5, 5])), ## method exact
CI_upr = map2_dbl(n_inf, n, ~ as.numeric(binom.confint( x = .x, n = .y)[5, 6]))) ## method exact
plot_data$Habitat <- relevel(as.factor(plot_data$Habitat), ref = "urban")
ggplot(plot_data, aes(y = prop_inf, x = Year, ymin = CI_lwr, ymax = CI_upr, fill = Habitat)) +
geom_bar(stat = "identity", position = position_dodge(width = 0.9), alpha = 0.8) +
geom_errorbar(width = 0, position = position_dodge(width = 0.9)) +
scale_fill_grey() +
scale_y_continuous("Proportion of infected nestlings") +
theme_bw() +
theme(panel.grid.minor = element_blank(),
panel.grid.major.x = element_blank(),
panel.grid.minor.x = element_blank())
ggsave(filename = "./figures/figure8.pdf", width = 8, height = 8)
## Model trichomonas
glmm_tricho_logit <- fitme(Prevalence ~ Habitat + Age + No_nestlings + Sex + Temp_age +
Year + laying_day +(1|Location/Territory),
family = binomial(link = "logit"),
data = goshawk_urban,
method = "PQL/L")
### odds ratio
exp(glmm_tricho_logit$fixef["Habitaturban"])
# Habitaturban
# 2.833019
CI_tricho <- confint(glmm_tricho_logit, "Habitaturban")
exp(CI_tricho$interval)
# lower Habitaturban upper Habitaturban
# 0.9757569 7.5532315
### Improve fit for more reliable CI
refit_glmm_tricho_logit <- glmm_tricho_logit
for (i in 1:10) {
refit_glmm_tricho_logit <- update(refit_glmm_tricho_logit,
init = list(lambda = unique(CI_tricho$confint_best_fit$ranPars$lambda)),
init.HLfit = list(fixef = CI_tricho$confint_best_fit$beta_eta))
CI_tricho <- confint(refit_glmm_tricho_logit, "Habitaturban")
print(exp(CI_tricho$interval))
}
exp(CI_tricho$interval)
# lower Habitaturban upper Habitaturban
# 1.058916 8.443243
cbind(fixef(refit_glmm_tricho_logit), fixef(glmm_tricho_logit)) ## the change in parameter estimates remains minimal and will be neglected
# [,1] [,2]
# (Intercept) 3.44230963 3.44229931
# Habitaturban 1.04134178 1.04134277
# Age 0.02055114 0.02055125
# No_nestlings 0.03126630 0.03126600
# Sexmale -0.18016419 -0.18016431
# Temp_age -0.09682991 -0.09682992
# Year2015 -1.63311223 -1.63311200
# Year2016 -0.50410795 -0.50410749
# laying_day -0.03120544 -0.03120537
### test effects
glmm_tricho_logit_noHabitat <- fitme(Prevalence ~ Age + No_nestlings + Sex + Temp_age +
Year + laying_day + (1|Location/Territory),
family = binomial(link = "logit"),
data = goshawk_urban, method = "PQL/L")
glmm_tricho_logit_nonest <- fitme(Prevalence ~ Habitat + Age + Sex + Temp_age + Year +
laying_day + (1|Location/Territory),