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MAKEFILE.R
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# R Makefile ####
# This script will sequentially run all the analyses of the accompanying paper:
#
# Almaraz, P. and Green, A.J. (2023) Catastrophic Dynamics of a Threatened Bird Community Triggered by
# a Planetary-Scale Environmental Perturbation. Biological Conservation
#
# Author: Dr. Pablo Almaraz (pablo.almaraz@csic.es), palmaraz.github.io
message(' \n
WARNING!\n
As with all Bayesian numerical integration techniques, either using Gibbs sampling,
HMC-NUTS or other sampling methods, the posterior distribution will always be an approximation
to the target distribution, up to a constant and accounting for MC error. In this case, both
the Bayesian DFA (using HMC-NUTS), and the SSRDLVR model (using Gibbs MCMC sampling), are very
high-dimensional approaches, yielding very high-dimensional posterior distributions.
As a consequence, the values of summaries from the posterior distributions will be somewhat
sensitive not only to prior specification, but also to initial values of the MC chains.
In particular, providing informative initial values for the MC chains (that is, abusing of language,
values that are within the basin of attraction of the target distribution), can greatly speed the
convergence and provide meaningful posterior values. Keep this in mind when modifying the prior or
the initial values of this or other models!\n
The following code is structured with these issues in mind:\n
1. Depending on your computing architecture, the fitting of the Bayesian DFA and the SSRDLVR model
cant take up to several hours (most likely), or even days (unlikely). Therefore, the essential
output from the fitted posterior distributions is saved in the `output` folder, and the analyses
from this file and the `MAKEFILE.R` and `Makefile` files use this default procedure for quickly
producing the figures and compiling the manuscript.\n
2. If you decide to re-fit all the models, set `fit_DFA=TRUE` and `fit_SSRDLVR=TRUE` here and
elsewhere. Keep in mind the issue with initial and prior values described above! In particular,
do not modify the random seeds used in this project. Otherwise, expect slightly diverging
numerical results. In particular, the estimation of the empirical probability of feasibility is
particularly sensitive to these issues. Even depending on the particular version of R, Stan,
JAGS, gcc, etc., slightly different results are expected. This is annoying.\n')
# Load functions
source('code/functions.R')
message('\nLoad functions\n')
# Load libraries ####
message('\nLoad libraries\n')
# You can choose to make a checkpoint to reproduce all the analyses with a
# CRAN snapshot of the day of acceptance of the paper. If so, uncomment the
# two following lines:
# if (!require(checkpoint)) install.packages('checkpoint')
# checkpoint::checkpoint("2024-01-20")
message('\nInstall, if necessary, the "librarian" package...\n')
if (!require(librarian)) install.packages('librarian') # Install, if necessary, the 'librarian' package
# Automatically install, if necessary, from whichever source (CRAN, Bioconductor...), the necessary
# packages to conduct the analyses, and load them
message('\n... and then install (if necessary) and load the necessary packages\n')
librarian::shelf(tidyverse,readr,runjags,rstan,bayesdfa,coda,ggmcmc,bayesplot,qgraph,
imputeTS,ggridges,viridis,bayestestR,cusp,mvtnorm,ggbreak,psych,data.table,
reshape2,patchwork,ggrepel)
# Load data ####
message('\nLoad data\n')
Count_data = read_delim("data/Aerial_count_data.csv",delim = ";", escape_double = FALSE, trim_ws = TRUE)
Sp_names_long = c("Pintail","Shoveler","Common teal","Eurasian wigeon","Mallard",
"Gadwall","Greylag goose","Common pochard","Red-crested pochard","Shelduck")
Sp_names_short = c("Pintail","Shoveler","C. teal","E. wigeon","Mallard",
"Gadwall","G. goose","C. pochard","R-c. pochard","Shelduck")
Env_data = read_delim("data/Environmental_data.csv",delim = ";", escape_double = FALSE, trim_ws = TRUE)
if (!dir.exists("output/figures")) { dir.create("output/figures") }
# Bayesian DFA ####
message('\nBegin the fitting of the Bayesian Dynamic Factor Analysis:\n')
set.seed(498468)
options(mc.cores = parallel::detectCores()) # Use all the available cores (if using a multi-core processor)
## Long format for the waterfowl dataset
years = 1978:2013
WaterfowlData = Count_data[-nrow(Count_data),] %>%
dplyr::mutate(time=rep(1:length(years), each=2)) %>%
dplyr::select(time,
Anas_acuta,
Anas_clypeata,
Anas_crecca,
Anas_penelope,
Anas_platyrhynchos,
Anas_strepera,
Anser_anser,
Aythya_ferina,
Netta_rufina,
Tadorna_tadorna) %>%
reshape2::melt(., id=c("time")) %>%
dplyr::mutate(obs=log(value+1),
ts=as.numeric(variable),
time=time) %>%
dplyr::select(obs,ts,time)
# Specify some items
chains = 3
iter = 6000
n_knots = 16
fit_DFA=FALSE
if(fit_DFA==TRUE){
## DFA with 1 trend ####
message('\nFit a Bayesian DFA with 1 trend\n')
DFA_1trend_PS = fit_dfa(
y = WaterfowlData, num_trends = 1, data_shape = "long", estimation = "sampling",
scale="zscore", trend_model="ps", n_knots = n_knots,
iter = iter, chains = chains, thin = 1, refresh = 100, verbose = T, expansion_prior=T,
seed = 1083941809)
save(DFA_1trend_PS, file = 'output/BDFA_model/DFA_1trend_PS.Rdata')
# LOO cross-validation
loocv_DFA_1trend_PS = loo(DFA_1trend_PS)
rotate_DFA_1trend_PS <- rotate_trends(DFA_1trend_PS, conf_level=0.9, invert = F)
plot_trends(rotate_DFA_1trend_PS, years=years) +
xlab("Year") + ylab("Dynamic factor") + theme_bw() + theme(panel.grid = element_blank())
# DFA with 2 trends ####
message('\nFit a Bayesian DFA with 2 trends\n')
DFA_2trends_PS = fit_dfa(
y = WaterfowlData, num_trends = 2, data_shape = "long", estimation = "sampling",
scale="zscore", trend_model="ps", n_knots = n_knots,
iter = iter, chains = chains, thin = 1, refresh = 100, verbose = T, expansion_prior=T,
seed=4128785653)
save(DFA_2trends_PS, file = 'output/BDFA_model/DFA_2trends_PS.Rdata')
# LOO cross-validation
loocv_DFA_2trends_PS = loo(DFA_2trends_PS)
rotate_DFA_2trends <- rotate_trends(DFA_2trends_PS, conf_level=0.9, invert = F)
# Make some changes to display the major trend first
trends <- dfa_trends(rotate_DFA_2trends)
trends$trend_number = as.factor(trends$trend_number)
levels(trends$trend_number) <- c("Trend 2","Trend 1")
trends$trend_number = as.character(trends$trend_number)
trends$trend_number = factor(trends$trend_number, labels = c("Trend 1","Trend 2"))
trends$year = rep(years,2)
plot_rotate_DFA_2trends = ggplot(trends, aes(x = year, y = estimate)) +
geom_ribbon(aes(ymin = lower, ymax = upper),
alpha = 0.4) + geom_line() + facet_wrap("trend_number") +
xlab("Year") + ylab("Dynamic factor") + theme_bw() + theme(panel.grid = element_blank())
# Plot the major common trends of the community
pdf("output/figures/Common_Trends_raw.pdf",height=4,width=8)
print(plot_rotate_DFA_2trends)
dev.off()
Common_Trends_by_Species_plot = plot_fitted(DFA_2trends_PS, conf_level = 0.9, names=Sp_names_long, time_labels=years, spaghetti=F) +
geom_point(aes(x = time,
y = y), col = "royalblue", size = 1, alpha = 1) +
theme_bw() +
ylab('Abdundance (standardised)') + xlab('Year') + theme(panel.grid = element_blank())
pdf("output/figures/Common_Trends_by_Species.pdf",height=6,width=7)
print(Common_Trends_by_Species_plot)
dev.off()
# Plot the factor loadings
FacLoad = dfa_loadings(rotate_DFA_2trends, summary = FALSE, names = Sp_names_long, conf_level = 0.95)
levels(FacLoad$trend) <- c("Trend 2","Trend 1")
FacLoad$loading = 1*FacLoad$loading
FacLoad$trend = relevel(FacLoad$trend, "Trend 1")
FacLoad_plot = ggplot(FacLoad, aes(x = name, y = loading, fill = trend, alpha = prob_diff0)) +
geom_violin(color = NA) +
scale_fill_manual(values = c("royalblue", "orange2")) +
scale_y_continuous(limits = c(-2.5, 5)) +
geom_hline(yintercept = 0, lty = 2) +
coord_flip() +
xlab("Species") + ylab("Loading")
FacLoad_plot = FacLoad_plot + facet_wrap(~trend, scales = "free_x")
pdf("output/figures/Factor_loadings.pdf",height=5,width=7)
print(FacLoad_plot)
dev.off()
# Fit a Hidden Markov Model to identify regime shifts in the dynamic common trends
message('\nFit a Hidden Markov Model to identify regime shifts in the dynamic common trends:\n')
# HMM with 1 regime
HMM_model_DFA_1trend = fit_regimes(
y = rotate_DFA_2trends$trends_mean[2, ],
sds = (rotate_DFA_2trends$trends_upper - rotate_DFA_2trends$trends_mean)[2, ] / 1.96,
n_regimes = 1,
iter = iter, chains = chains, refresh=iter, verbose = F)
# HMM with 2 regimes
HMM_model_DFA_2trends <- fit_regimes(
y = rotate_DFA_2trends$trends_mean[2, ],
sds = (rotate_DFA_2trends$trends_upper - rotate_DFA_2trends$trends_mean)[2, ] / 1.96,
n_regimes = 2,
iter = iter, chains = chains, refresh=iter, verbose = F)
message(paste0('\nThe looic for the HMM with 1 regime is ',
round(HMM_model_DFA_1trend$looic,3), '\n',
'The looic for the HMM with 2 regimes is ',
round(HMM_model_DFA_2trends$looic,3), '\n',
'The difference is of ', round(HMM_model_DFA_1trend$looic,3) -
round(HMM_model_DFA_2trends$looic,3),'\n',
sep=''))
# Plot the regimes
pdf("output/figures/Regime_shift.pdf",height=5,width=5)
plot_hmm_regimes(HMM_model_DFA_2trends,years=years)
dev.off()
# save(DFA_1trend_PS,DFA_2trends_PS,HMM_model_DFA_1trend,HMM_model_DFA_2trends,
# file='output/BDFA_model/BayesDFA_results.Rdata')
}
if(fit_DFA==FALSE) {
load('output/BDFA_model/BDFA_results.Rdata')
# Plot the major common trends of the community
plot_rotate_DFA_2trends = ggplot(trends, aes(x = year, y = estimate)) +
geom_ribbon(aes(ymin = lower, ymax = upper),
alpha = 0.4) + geom_line() + facet_wrap("trend_number") +
xlab("Year") + ylab("Dynamic factor") + theme_bw() + theme(panel.grid = element_blank())
pdf("output/figures/Common_Trends_raw.pdf",height=4,width=8)
print(plot_rotate_DFA_2trends)
dev.off()
# Difference in looic between models
message(paste0('\nThe looic for the DFA with 1 trend is ',
round(loocv_DFA_1trend_PS$estimates['looic','Estimate'],3), '\n',
'The looic for the DFA with 2 trends is ',
round(loocv_DFA_2trends_PS$estimates['looic','Estimate'],3), '\n',
'The difference is of ', round(loocv_DFA_1trend_PS$estimates['looic','Estimate'],3) -
round(loocv_DFA_2trends_PS$estimates['looic','Estimate'],3),'\n',
sep=''))
Common_Trends_by_Species_plot = ggplot(trends_by_sp) +
geom_ribbon(aes(x = time, ymin = lower, ymax = upper), alpha = 0.4) +
geom_line(aes(x = time, y = estimate)) +
geom_point(col = "royalblue", size = 1, alpha = 1, aes(x = time, y = y)) +
facet_wrap("ID", scales = "free_y") + xlab("Time") +
ylab("") +
theme_bw() +
ylab('Abdundance (standardised)') + xlab('Year') +
theme(panel.grid = element_blank())
pdf("output/figures/Common_Trends_by_Species.pdf",height=6,width=7)
print(Common_Trends_by_Species_plot)
dev.off()
# Plot the factor loadings
FacLoad_plot = ggplot(FacLoad, aes(x = name, y = loading, fill = trend, alpha = prob_diff0)) +
geom_violin(color = NA) +
scale_fill_manual(values = c("royalblue", "orange2")) +
scale_y_continuous(limits = c(-2.5, 5)) +
geom_hline(yintercept = 0, lty = 2) +
coord_flip() +
xlab("Species") + ylab("Loading")
FacLoad_plot = FacLoad_plot + facet_wrap(~trend, scales = "free_x")
pdf("output/figures/Factor_loadings.pdf",height=5,width=7)
print(FacLoad_plot)
dev.off()
# HMM with 2 regimes
HMM_model_DFA_2trends <- fit_regimes(
y = rotate_DFA_2trends_trends_mean,
sds = sds,
n_regimes = 2,
iter = iter, chains = chains, refresh=iter, verbose = F)
message(paste0('\nThe looic for the HMM with 1 regime is ',
round(HMM_model_DFA_1trend_looic,3), '\n',
'The looic for the HMM with 2 regimes is ',
round(HMM_model_DFA_2trends_looic,3), '\n',
'The difference is of ', round(HMM_model_DFA_1trend_looic,3) -
round(HMM_model_DFA_2trends_looic,3),'\n',
sep=''))
# Plot the regimes
pdf("output/figures/Regime_shift.pdf",height=5,width=5)
plot_hmm_regimes(HMM_model_DFA_2trends,years=years)
dev.off()
}
# END Bayesian DFA ####
# State-space regime-dependent LVR model ####
seed=827545
set.seed(seed)
runjags.options(inits.warning=F,
rng.warning=F,
blockignore.warning=F,
blockcombine.warning=F,
nodata.warning=F,
silent.jags=F,
silent.runjags=F)
testjags()
scal_Fact=1000 # Scaling factor for abundance data
NSpecies = 10
WaterfowlData = Count_data[-nrow(Count_data),] %>%
dplyr::mutate(time=rep(1:36, each=2)) %>%
dplyr::select(time,
Anas_acuta,
Anas_clypeata,
Anas_crecca,
Anas_penelope,
Anas_platyrhynchos,
Anas_strepera,
Anser_anser,
Aythya_ferina,
Netta_rufina,
Tadorna_tadorna) %>%
reshape2::melt(., id=c("time")) %>%
dplyr::mutate(obs=value,
ts=as.numeric(variable),
time=time) %>%
dplyr::select(obs,ts,time)
Period = c('PrePinatubo', 'PostPinatubo')
## Loop ####
for(period in Period) {
message(paste0('\nFit the regime-dependent SSLVR model to the ', period, ' period\n'))
## Data ####
if(period=='PrePinatubo') NYears=length(1978:1991)
if(period=='PostPinatubo') {
FirstYear = 21
FinalYear = max(WaterfowlData$time)
NYears = FinalYear-FirstYear
}
if(period=='PrePinatubo') {
est.k = WaterfowlData %>% dplyr::filter(time < NYears) %>% group_by(ts) %>% summarise_all(mean, na.rm=T) %>% select(-ts, -time)
est.k.var = WaterfowlData %>% dplyr::filter(time < NYears) %>% group_by(ts) %>% mutate(obs.var = obs/scal_Fact) %>% select(-obs) %>% summarise_all(var, na.rm=T) %>% select(-ts, -time)
data_list_SSLVR_regime = list(
NSpecies = NSpecies,
NYears = NYears,
n1 = as.matrix((log((Count_data[-1,] %>% dplyr::filter(Month == 12) %>% dplyr::select(-Year, -Month))/scal_Fact + 1)))[1:NYears,],
n2 = as.matrix((log((Count_data[-1,] %>% dplyr::filter(Month == 1) %>% dplyr::select(-Year, -Month))/scal_Fact + 1)))[1:NYears,],
flood = scale(Env_data[1:NYears,'Flood'])[,1],
est.k = est.k$obs/scal_Fact,
est.k.var = est.k.var$obs.var)
}
if(period=='PostPinatubo') {
est.k = WaterfowlData %>% dplyr::filter(time > FirstYear) %>% group_by(ts) %>% summarise_all(mean, na.rm=T) %>% select(-ts, -time)
est.k.var = WaterfowlData %>% dplyr::filter(time > FirstYear) %>% group_by(ts) %>% mutate(obs.var = obs/scal_Fact) %>% select(-obs) %>% summarise_all(var, na.rm=T) %>% select(-ts, -time)
data_list_SSLVR_regime = list(
NSpecies = NSpecies,
NYears = NYears,
n1 = as.matrix((log((Count_data[-1,] %>% dplyr::filter(Month == 12) %>% dplyr::select(-Year, -Month))/scal_Fact + 1)))[(FirstYear+1):FinalYear,],
n2 = as.matrix((log((Count_data[-1,] %>% dplyr::filter(Month == 1) %>% dplyr::select(-Year, -Month))/scal_Fact + 1)))[(FirstYear+1):FinalYear,],
flood = scale(Env_data[(FirstYear+1):FinalYear,'Flood'])[,1],
est.k = est.k$obs/scal_Fact,
est.k.var = est.k.var$obs.var)
}
parameter_list_SSLVR_regime = c("prob_inter","g.alpha","alpha","k","r","b","gamma",
"Corr.sigma","Corr.tau","state","n1_ppc","n2_ppc")
## Inits for the SSLVR model ####
if(period=='PrePinatubo'){
# Informative initial conditions, to speed up convergence
b_mean=c(-0.8544,-1.05,0.6868,0.03144,0.3442,-0.06122,-0.3627,-1.763,-3.054,-1.235)
n1 = matrix(NA, NYears, NSpecies)
n1[12,] = unname(data_list_SSLVR_regime$n1[11,]+data_list_SSLVR_regime$n1[13,])/2
n2 = matrix(NA, NYears, NSpecies)
n2[7,] = unname(data_list_SSLVR_regime$n1[6,]+data_list_SSLVR_regime$n1[8,])/2
inits_list_SSLVR_regime=function(){
list(
prob_inter=rbeta(1,2,8),
active_alpha=replicate(NSpecies,rnorm(NSpecies,0,0.1)) + diag(NA, NSpecies),
g.alpha=replicate(NSpecies,rbinom(NSpecies,1,0.5)) + diag(NA, NSpecies),
Obs.prec.mat=diag(0.1,NSpecies),
Sys.prec.mat=diag(0.1,NSpecies),
k=pmax(rnorm(NSpecies, data_list_SSLVR_regime$est.k, 1), 0.1),
b=rnorm(NSpecies, b_mean,0.1),
gamma=rnorm(NSpecies, b_mean, 0.1),
n1=n1,
n2=n2,
state=matrix(c(NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
1.54,3.06,2.76,3.54,1.99,1.36,3.77,0.87,2,1.15,
1.99,3.82,2.88,3.78,1.8,1.52,4.1,1.49,2.74,1.09,
1.66,2.77,2.44,3.31,1.29,0.76,4.02,0.76,0.9,1.1,
2.49,3.61,2.6,3.89,1.03,0.94,4,1.35,2.03,0.92,
2.37,3.65,3.34,3.66,0.9,0.99,4.08,1.45,2.13,0.96,
2.78,3.41,3.48,3.88,1.41,1.19,4.04,1.78,2.08,1.01,
2.58,3.53,3.47,3.89,1.75,1.5,4.1,1.55,1.95,1.1,
2.5,3.65,3.63,3.61,1.83,1.39,4.07,1.7,2.46,1.07,
2.59,3.41,3.88,3.94,1.6,1.07,3.97,1.65,2.32,1.12,
2.84,3.48,4.23,3.72,2.16,1.53,4,1.67,2.11,1.32,
2.26,3.74,4.06,3.97,2.29,1.85,4.14,1.04,2.42,1.39,
2.73,3.4,4.22,3.72,2.34,1.36,3.79,0.93,2.01,1.25,
2.41,3.92,4.15,3.81,2.24,1.44,3.98,1.07,2.68,1.13),
NYears,NSpecies,byrow = T),
.RNG.seed=seed)
}
}
if(period=='PostPinatubo'){
# Informative initial conditions, to speed up convergence
b_mean=c(-0.8544,-1.05,0.6868,0.03144,0.3442,-0.06122,-0.3627,-1.763,-3.054,-1.235)
inits_list_SSLVR_regime=function(){
list(
prob_inter=rbeta(1,2,8),
active_alpha=replicate(NSpecies,rnorm(NSpecies,0,0.1)) + diag(NA, NSpecies),
g.alpha=replicate(NSpecies,rbinom(NSpecies,1,0.5)) + diag(NA, NSpecies),
Obs.prec.mat=diag(0.1,NSpecies),
Sys.prec.mat=diag(0.1,NSpecies),
k=pmax(rnorm(NSpecies, data_list_SSLVR_regime$est.k, 1), 0.1),
b=rnorm(NSpecies, b_mean,0.1),
gamma=rnorm(NSpecies, b_mean, 0.1),
state=matrix(c(NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
0.5,2.25,1.97,0.91,1.47,0.9,3.08,0.98,3.24,0.77,
1.18,2.87,2.83,1.17,1.69,-2.06,3.62,0.77,0.99,0.47,
2.1,3.09,2.73,1.66,1.91,-2.04,3.85,0.8,0.54,0.37,
2.6,3,2.71,1.92,1.7,-2.24,4.09,0.75,0.8,0.5,
3.12,3.22,2.8,1.93,1.96,-2.19,3.94,0.63,0.86,0.4,
3.47,3.15,2.71,2.03,1.88,-2.21,3.88,0.71,0.59,0.19,
2.63,3.58,2.07,1.96,1.47,-1.86,4.09,0.5,2.3,0.74,
2.42,3.98,2.64,2.09,1.2,-2.24,3.95,0.47,3.11,0.74,
3.09,3.87,2.91,2.12,1.98,-5.99,3.92,0.64,0.6,0.58,
3.23,3.79,2.71,2.19,1.78,-5.95,4.15,0.7,0.68,0.49,
3.33,3.77,2.79,2.15,1.94,-5.94,3.95,0.68,0.89,0.57,
3.39,3.57,2.59,2.2,1.8,-5.98,4.08,0.83,0.64,0.72,
3.64,3.58,2.92,2.24,1.73,-6,3.81,0.88,0.58,0.85,
3.31,3.82,2.57,2.1,1.75,-5.87,4,0.81,0.98,0.8),
NYears,NSpecies,byrow = T),
.RNG.seed=seed)
}
}
## Model fit ####
fit_SSRDLVR=FALSE
if(fit_SSRDLVR==TRUE) {
SSRDLVR_mcmc_analysis = runjags::run.jags(
data=data_list_SSLVR_regime,
inits=inits_list_SSLVR_regime,
monitor=parameter_list_SSLVR_regime,
model=read.jagsfile("code/SSRDLVR_model.JAGS"),
n.chains = 3,
adapt = 5000,
burnin = 100000,
sample = 1000,
thin = 50,
method='parallel',
modules = 'glm',
keep.jags.files=file.path(paste0("output/SSRDLVR_model/","mcmc_run_",period,sep = "")),
summarise=TRUE)
save(SSRDLVR_mcmc_analysis, file = paste0('output/SSRDLVR_model/SSRDLVR_model_results_',period,'.Rdata'))
# Convert the posterior object
post_vars = as.data.frame(combine.mcmc(as.mcmc.list(SSRDLVR_mcmc_analysis)))
nloops = nrow(post_vars)
}
if(fit_SSRDLVR==FALSE) {
load(paste0('output/SSRDLVR_model/SSRDLVR_model_results_',period,'.Rdata'))
if(period=='PrePinatubo') post_vars = as.data.frame(combine.mcmc(as.mcmc.list(SSRDLVR_model_results_PrePinatubo)))
if(period=='PostPinatubo') post_vars = as.data.frame(combine.mcmc(as.mcmc.list(SSRDLVR_model_results_PostPinatubo)))
nloops = nrow(post_vars)
}
## MCMC diagnostics ####
plot=FALSE
if(plot){
if (!dir.exists("output/SSRDLVR_model/MCMC_checks")) { dir.create("output/SSRDLVR_model/MCMC_checks") }
if(period=='PrePinatubo') ggs_object = ggs(as.mcmc.list(SSRDLVR_model_results_PrePinatubo))
if(period=='PostPinatubo') ggs_object = ggs(as.mcmc.list(SSRDLVR_model_results_PostPinatubo))
ggmcmc(ggs_object,family="prob_inter",
file = paste0("output/SSRDLVR_model/MCMC_checks/MCMC_diagnostics_prob_inter_",period,".pdf"),
param_page = 5, width=6, height=6)
ggmcmc(ggs_object,family="b",
file = paste0("output/SSRDLVR_model/MCMC_checks/MCMC_diagnostics_b_",period,".pdf"),
param_page = 11, width=5, height=12)
ggmcmc(ggs_object,family="k",
file = paste0("output/SSRDLVR_model/MCMC_checks/MCMC_diagnostics_k_",period,".pdf"),
param_page = 10, width=5, height=12)
ggmcmc(ggs_object,family="r",
file = paste0("output/SSRDLVR_model/MCMC_checks/MCMC_diagnostics_r_",period,".pdf"),
param_page = 10, width=5, height=12)
ggmcmc(ggs_object,family="alpha",
file = paste0("output/SSRDLVR_model/MCMC_checks/MCMC_diagnostics_alpha_",period,".pdf"),
param_page = 10, width=5, height=12)
}
## Plot prior vs. posterior ####
nu=dplyr::select(post_vars,starts_with("prob_inter"))
pdf(file=paste0('output/figures/Prior_post_',period,'.pdf'), height = 6, width = 6)
prior_vs_posterior(nu$prob_inter, dist = "beta", xlim = c(0, 1), alpha=2, beta=8, pos.legend="right",
title = "Prior vs. posterior distribution")
dev.off()
## PPC plot ####
Obs_mean_Dec = data_list_SSLVR_regime$n1
Obs_mean_Jan = data_list_SSLVR_regime$n2
colnames(Obs_mean_Dec) = colnames(Obs_mean_Jan) = Sp_names_long
yobs_n1_ppc_mcmc = dplyr::select(post_vars, starts_with("n1_ppc"))
yobs_n2_ppc_mcmc = dplyr::select(post_vars, starts_with("n2_ppc"))
ppc_n1_mcmc = array(NA, dim = c(nloops, NYears-1, NSpecies))
for(j in 1:NSpecies){
ppc_n1_mcmc[,,j] = yobs_n1_ppc_mcmc %>%
dplyr::select(bayesplot::param_glue("n1_ppc[{time},{type}]", type = j, time = 2:NYears)) %>%
as.matrix()
}
ppc_n1_yobs = array(NA, dim = c(3, NYears-1, NSpecies))
for(l in 1:NSpecies){
ppc_n1_yobs[,,l] = apply(ppc_n1_mcmc[,,l], 2 , quantile , probs = c(0.10, 0.5, 0.9) , na.rm = TRUE )
}
ppc_n2_mcmc = array(NA, dim = c(nloops, NYears-1, NSpecies))
for(j in 1:NSpecies){
ppc_n2_mcmc[,,j] = yobs_n2_ppc_mcmc %>%
dplyr::select(bayesplot::param_glue("n2_ppc[{time},{type}]", type = j, time = 2:NYears)) %>%
as.matrix()
}
ppc_n2_yobs = array(NA, dim = c(3, NYears-1, NSpecies))
for(l in 1:NSpecies){
ppc_n2_yobs[,,l] = apply(ppc_n2_mcmc[,,l], 2 , quantile , probs = c(0.025, 0.5, 0.975) , na.rm = TRUE )
}
# for December counts
Yobs_n1 = array(NA, dim=c((NYears-1)*NSpecies, 4))
temp = array(NA, dim=c((NYears-1)*NSpecies, 4))
for(l in 1:NSpecies){
if(l==1){
temp = as.data.frame(t(ppc_n1_yobs[,,l])) %>%
dplyr::mutate(Type = rep(Sp_names_long[l], NYears-1),
ppc_Lower95 = V1,
ppc_mean = V2,
ppc_Upper95 = V3) %>%
dplyr::select(Type, ppc_Lower95, ppc_mean, ppc_Upper95)
Yobs_n1 = temp
}
else{
temp = as.data.frame(t(ppc_n1_yobs[,,l])) %>%
dplyr::mutate(Type = rep(Sp_names_long[l], NYears-1),
ppc_Lower95 = V1,
ppc_mean = V2,
ppc_Upper95 = V3) %>%
dplyr::select(Type, ppc_Lower95, ppc_mean, ppc_Upper95)
Yobs_n1 = rbind.data.frame(Yobs_n1, temp)
}
}
# for January counts
Yobs_n2 = array(NA, dim=c((NYears-1)*NSpecies, 4))
temp = array(NA, dim=c((NYears-1)*NSpecies, 4))
for(l in 1:NSpecies){
if(l==1){
temp = as.data.frame(t(ppc_n2_yobs[,,l])) %>%
dplyr::mutate(Type = rep(Sp_names_long[l], NYears-1),
ppc_Lower95 = V1,
ppc_mean = V2,
ppc_Upper95 = V3) %>%
dplyr::select(Type, ppc_Lower95, ppc_mean, ppc_Upper95)
Yobs_n2 = temp
}
else{
temp = as.data.frame(t(ppc_n2_yobs[,,l])) %>%
dplyr::mutate(Type = rep(Sp_names_long[l], NYears-1),
ppc_Lower95 = V1,
ppc_mean = V2,
ppc_Upper95 = V3) %>%
dplyr::select(Type, ppc_Lower95, ppc_mean, ppc_Upper95)
Yobs_n2 = rbind.data.frame(Yobs_n2, temp)
}
}
# Latent states
latent_state_mcmc = dplyr::select(post_vars, starts_with("state"))
state_mcmc = array(NA, dim = c(nloops, NYears-1, NSpecies))
for(j in 1:NSpecies){
state_mcmc[,,j] = latent_state_mcmc %>%
dplyr::select(bayesplot::param_glue("state[{time},{type}]", type = j, time = 2:NYears)) %>%
as.matrix()
}
latent_state = array(NA, dim = c(3, NYears-1, NSpecies))
for(l in 1:NSpecies){
latent_state[,,l] = apply(state_mcmc[,,l], 2 , quantile , probs = c(0.025, 0.5, 0.975) , na.rm = TRUE )
}
state = array(NA, dim=c((NYears-1)*NSpecies, 4))
temp = array(NA, dim=c((NYears-1)*NSpecies, 4))
for(l in 1:NSpecies){
if(l==1){
temp = as.data.frame(t(latent_state[,,l])) %>%
dplyr::mutate(Type = rep(Sp_names_long[l], NYears-1),
state_Lower95 = V1,
state_mean = V2,
state_Upper95 = V3) %>%
dplyr::select(Type, state_Lower95, state_mean, state_Upper95)
state = temp
}
else{
temp = as.data.frame(t(latent_state[,,l])) %>%
dplyr::mutate(Type = rep(Sp_names_long[l], NYears-1),
state_Lower95 = V1,
state_mean = V2,
state_Upper95 = V3) %>%
dplyr::select(Type, state_Lower95, state_mean, state_Upper95)
state = rbind.data.frame(state, temp)
}
}
plot_ppc_ts = as.data.frame(cbind(melt(Obs_mean_Dec[2:NYears,]),
melt(Obs_mean_Jan[2:NYears,])["value"],
Yobs_n1[,c("ppc_Lower95","ppc_mean","ppc_Upper95")],
Yobs_n2[,c("ppc_Lower95","ppc_mean","ppc_Upper95")],
state[,c("state_Lower95", "state_mean", "state_Upper95")]))
colnames(plot_ppc_ts) = c("Year","Species","Dec","Jan",
"ppc_Lower95_Dec","ppc_mean_Dec","ppc_Upper95_Dec",
"ppc_Lower95_Jan","ppc_mean_Jan","ppc_Upper95_Jan",
"state_Lower95", "state_mean", "state_Upper95")
# Plot
if(period=='PrePinatubo') years = 1979:1991
if(period=='PostPinatubo') years = 2000:2013
ppc_ts_plots = plot_ppc_ts %>% group_by(Species = factor(Species, levels = unique(Species))) %>%
group_map(~tibble(plots=list(
ggplot(.) + aes(x= years, y=state_mean) +
geom_line(col="red", linewidth=1.5) +
geom_ribbon(aes(ymax = state_Lower95, ymin = state_Upper95), fill = "red", alpha = 0.2) +
geom_point(aes(x=years,y=Dec),col="blue3",size=1.5) +
geom_point(aes(x=years,y=Jan),col="green4",size=1.5) +
geom_abline(slope=0, intercept=0) +
theme_classic() +
# scale_y_continuous(limits = c(-0.5, 9)) +
scale_y_continuous(limits = c(NA, 10)) +
labs(x="Year",y=expression('Abundance, (' ~ italic(ln) ~ '[' ~ N ~ '/' ~ 1000 ~ '])')) +
annotate("point", x = years[5], y = 8.3, color="blue3", fill="blue3", size=2) +
annotate("text", x = years[7], y = 8.3, label = "December count", color="black", size=3) +
annotate("point", x = years[5], y = 7.3, color="green4", fill="green4", size=2) +
annotate("text", x = years[7], y = 7.3, label = "January count", color="black", size=3) +
annotate("segment", x = years[5]-0.5, xend = years[5], y = 6.3, yend = 6.3, colour = "red", linewidth=1) +
annotate("text", x = years[7], y = 6.3, label = "Latent abundance", color="black", size=3) +
ggtitle(.y[[1]]))))
PPC_TS_fullplot =
(ppc_ts_plots[[1]]$plots[[1]]+ppc_ts_plots[[2]]$plots[[1]])/
(ppc_ts_plots[[3]]$plots[[1]]+ppc_ts_plots[[4]]$plots[[1]])/
(ppc_ts_plots[[5]]$plots[[1]]+ppc_ts_plots[[6]]$plots[[1]])/
(ppc_ts_plots[[7]]$plots[[1]]+ppc_ts_plots[[8]]$plots[[1]])/
(ppc_ts_plots[[9]]$plots[[1]]+ppc_ts_plots[[10]]$plots[[1]]) +
plot_annotation(
title = 'Posterior predicted time series',
# subtitle = 'First stable state, before Mt. Pinatubo eruption',
subtitle = 'Second stable state, after Mt. Pinatubo eruption',
theme = theme(plot.title = element_text(size = 25),
plot.subtitle = element_text(size = 15)))
# print(PPC_TS_fullplot)
ggsave(file=paste0('output/figures/PPC_TS_fullplot_',period,'.pdf'), plot=PPC_TS_fullplot, width = 10, height = 13)
## Plot results ####
### Environmental effects ####
gamma = dplyr::select(post_vars, starts_with("gamma"))
colnames(gamma) = Sp_names_long
gamma_PrePinatubo = ggplot(reshape2::melt(gamma), aes(x=value, y=reorder(variable, desc(variable)), fill= after_stat(x))) +
geom_density_ridges_gradient(stat = "binline", bins = 100, scale = 1.5, draw_baseline = FALSE) +
geom_vline(xintercept=0) +
scale_x_continuous(limits = c(-1.5,1.5)) +
scale_y_discrete(expression(N)) +
scale_fill_viridis(name = "Posterior\nvalue", option = "magma") +
labs(x="Posterior value",
title = "Effect of flooding extension") +
theme_ridges(font_size = 13, grid = TRUE) +
theme(axis.title.y = element_blank(),
plot.title = element_text(size=18))
# gamma_PrePinatubo
ggsave(file=paste0('output/figures/Flooding_impact_',period,'.pdf'), plot=gamma_PrePinatubo,
width=7.5, height=5.5, limitsize = FALSE)
### Stability measures ####
alpha = dplyr::select(post_vars, starts_with("alpha"))
alpha_mean = matrix(colMeans(alpha),NSpecies,NSpecies)
k_vec = dplyr::select(post_vars, starts_with("k"))
k_mean = as.numeric(colMeans(k_vec))
r_vec = dplyr::select(post_vars, starts_with("r"))[,1:NSpecies]
r_mean = as.numeric(colMeans(r_vec))
# Create the objects to be populated:
Resilience=c()
jacobi_mat = matrix(rep(NA,(NSpecies^2)*nloops),ncol=NSpecies^2,nrow=nloops)
Eigenvals = matrix(rep(NA,NSpecies*nloops),ncol=NSpecies,nrow=nloops)
EqAbund = matrix(rep(NA,NSpecies*nloops),ncol=NSpecies,nrow=nloops)
initial_time = proc.time()
pb = txtProgressBar(min = 0, max = nloops, initial = 0, char = "*", width = 60)
for (j in 1:nloops){
# Interaction matrix
alpha_mat = matrix(as.matrix(as.numeric(alpha[j,])), nrow = NSpecies, ncol = NSpecies)
k_vector = as.vector(as.numeric(k_vec[j,]))
r_vector = as.vector(as.numeric(r_vec[j,]))
EqAbund[j, ] = as.vector(solve(alpha_mat) %*% k_vector)
if(all(EqAbund[j, ] >= 0)) {
jacobian = numDeriv::jacobian(function(N) N*exp(r_vector*(1 - (alpha_mat %*% N)/k_vector)), EqAbund[j, ], "complex")
jacobi_mat[j,] = as.vector(jacobian)
Eigenvals[j,] = matrix(eigen(jacobian, only.values = TRUE)$values, nrow=1)
Resilience[j] = 1/max(abs(Re(Eigenvals[j,])))
}
setTxtProgressBar(pb,j)
final_time = proc.time() - initial_time
if (j == nloops*0.25) cat(" 25% completed in", final_time[3], "sec!\n")
final_time = proc.time() - initial_time
if (j == nloops*0.5) cat(" 50% completed in", final_time[3], "sec!\n")
final_time = proc.time() - initial_time
if (j == nloops*0.75) cat(" 75% completed in", final_time[3], "sec!\n")
final_time = proc.time() - initial_time
if (j == nloops) cat(" 100% completed in", final_time[3], "sec!\n")
}
(HDInterval_stability = bayestestR::hdi(as.mcmc(Resilience), credMass = 0.9, allowSplit = TRUE))
### Plot unit circle and prob. of dynamic stability ####
Eigenvals = Eigenvals[complete.cases(Eigenvals),]
ReEigenvals = reshape2::melt(Re(Eigenvals), value.name="Real_part")
ImEigenvals = reshape2::melt(Im(Eigenvals), value.name="Imaginary_part")
Eigenvals_toplot = as.data.frame(cbind(ReEigenvals[,c("Real_part")],ImEigenvals[,c("Imaginary_part")]))
colnames(Eigenvals_toplot) = c("Real_part","Imaginary_part")
Eigenvals_toplot$Modulus = sqrt((Eigenvals_toplot$Real_part)^2 + (Eigenvals_toplot$Imaginary_part)^2)
(EmpProbDynStab = sum(Eigenvals_toplot$Modulus < 1)/length(Eigenvals_toplot$Modulus))
th = seq(-pi, pi, len = 100)
z = exp((0+1i) * th)
UnitCircle=as.data.frame(cbind(Re(z),Im(z)))
Origin=data.frame(x=0,y=0)
unitcircle_plot = ggplot(data=UnitCircle,aes(Re(z),Im(z))) +
geom_path() +
geom_vline(xintercept = 0,lty="dotted") +
geom_hline(yintercept = 0,lty="dotted") +
geom_point(data=Eigenvals_toplot,aes(x=Real_part,y=Imaginary_part),size=0.5,col="red") +
scale_x_continuous(limits = c(-1.5,1.5)) +
scale_y_continuous(limits = c(-1.5,1.5)) +
labs(x="Real", y = "Imaginary") +
theme(
axis.line.x=element_line(linewidth=0.5,colour="Black"),
axis.line.y=element_line(linewidth=0.5,colour="Black"),
axis.text=element_text(size=18,colour="Black"),
axis.title=element_text(size=18,colour="Black"),
plot.title = element_text(size=15),
legend.position = "right",
legend.text = element_text(size = 12),
legend.key = element_blank(),
panel.grid = element_blank(),
panel.grid.minor = element_blank(),
panel.grid.major = element_blank(),
panel.background = element_blank(),
plot.background = element_rect(fill = "transparent", colour = NA)) +
ggtitle(paste0("Resilience: ", round(map_estimate(Resilience)$MAP_Estimate, 3),
" (", round(bayestestR::hdi(Resilience, credMass = 0.9, allowSplit = TRUE)[["CI_low"]], 3),",",
round(bayestestR::hdi(Resilience, credMass = 0.9, allowSplit = TRUE)[["CI_high"]],3), ") MAP, 90% HDI", sep=""),
paste0("Probability of dynamic stability: ", round(EmpProbDynStab, 4),"\n", sep=""))
# unitcircle_plot
ggsave(paste0('output/figures/Probability_of_stability_',period,'.pdf'), unitcircle_plot, height = 6.5, width = 6)
if(period=='PrePinatubo') unitcircle_plot_PrePinatubo = unitcircle_plot
if(period=='PostPinatubo') unitcircle_plot_PostPinatubo = unitcircle_plot
### Plot feasibility and extinction probability ####
EquilAbund = as.data.frame(EqAbund)
colnames(EquilAbund) = Sp_names_long
# Probability of species extinction
ProbSpExtinct=matrix(NA,1,NSpecies)
for(g in 1:NSpecies){
ProbSpExtinct[,g] = length(which(apply(as.data.frame(EquilAbund[,g]), 1, function(row) any(row <= 0))))/nrow(EquilAbund)
}
colnames(ProbSpExtinct) = Sp_names_long
if(period=='PrePinatubo') ProbSpExtinct_PrePinatubo = ProbSpExtinct
if(period=='PostPinatubo') ProbSpExtinct_PostPinatubo = ProbSpExtinct
(EmpProbFeas = (dim(EquilAbund)[1] - length(which(apply(EquilAbund, 1, function(row) any(row < 0)))))/dim(EquilAbund)[1])
k_posterior = as.data.frame(map_estimate(k_vec)$MAP_Estimate)
rownames(k_posterior) = Sp_names_long
k_posterior = as.data.frame(cbind(rownames(k_posterior),as.data.frame(k_posterior)))
colnames(k_posterior) = c("variable","value")
plot_feasibility = ggplot(reshape2::melt(EquilAbund), aes(x=value, y=reorder(variable, desc(variable)), fill = after_stat(x))) +
geom_density_ridges_gradient(stat = "binline", bins = 100, scale = 1.5, draw_baseline = FALSE) +
geom_vline(xintercept=0) +
scale_x_continuous(limits = c(-20,100)) +
scale_y_discrete(expression(N)) +
scale_fill_viridis(name = expression("Equilibrium \nabundance,"~italic(N)^"*"), option = "viridis") +
geom_point(data = k_posterior, aes(col="k_posterior"), size=2) +
scale_color_manual(name = element_blank(),
values = c(k_posterior = "brown"),
labels = "Carrying capacity") +
labs(x="Abundance (n. ind x1000)",
title = paste("Probability of feasibility: ",round(EmpProbFeas,3))) +
theme_ridges(font_size = 13, grid = TRUE) +
theme(axis.title.y = element_blank(),
plot.title = element_text(size=18))
# plot_feasibility
ggsave(file=paste0('output/figures/Prob_of_feasibility_',period,'.pdf'), plot=plot_feasibility,
width=7.5, height=5.5, limitsize = FALSE)
if(period=='PrePinatubo') plot_feasibility_PrePinatubo = plot_feasibility
if(period=='PostPinatubo') plot_feasibility_PostPinatubo = plot_feasibility
}
## Plot wrapped figures ####
### Stability and feasibility ####
Wrapped_stability = wrap_plots(unitcircle_plot_PrePinatubo,
unitcircle_plot_PostPinatubo,
plot_feasibility_PrePinatubo,
plot_feasibility_PostPinatubo) + plot_annotation(tag_levels = 'A', tag_suffix = ')')
# Wrapped_stability
ggsave(file='output/figures/Wrapped_stability.pdf', plot=Wrapped_stability,
width=14.5, height=9, limitsize = FALSE)
## Probability of species extinction ####
probspExt = as.data.frame(t(rbind(ProbSpExtinct_PrePinatubo,ProbSpExtinct_PostPinatubo)))
colnames(probspExt) = c('ProbSpExtinct_pre','ProbSpExtinct_post')
probspExt <- probspExt %>%
mutate(Names = Sp_names_long,
'Before Pinatubo' = ProbSpExtinct_pre,
'After Pinatubo' = ProbSpExtinct_post) %>%
dplyr::select(Names, `Before Pinatubo`, `After Pinatubo`)
SpExtPr = ggplot(reshape2::melt(probspExt, id="Names")) +
geom_vline(xintercept=0) +
geom_point(aes(x=value, y=reorder(Names, desc(Names)), col = variable), size=5) +
scale_color_manual(values = c("purple", "green")) +
scale_x_continuous(limits = c(0,0.4), trans = "sqrt") +
theme_bw() +
theme(axis.title.y = element_blank(),
axis.text.x = element_text(size = 12),
axis.text.y = element_text(size = 12),
plot.title = element_text(size=18)) +
labs(col = "Regime",
x="Species extinction probability",
title = "Probability of extinction at equilibrium")
# SpExtPr
for(i in 1:nrow(probspExt)){
SpExtPr = SpExtPr + geom_segment(data=probspExt[i,],
aes(x=`Before Pinatubo`, xend = `After Pinatubo`, y=Names, yend = Names),
arrow = arrow(type = "closed", length = unit(0.2, "cm"), ends = "last"))
}
# print(SpExtPr)
ggsave(file="output/figures/Prob_of_extinction.pdf", plot=SpExtPr,
width=7, height=6, limitsize = FALSE)
save(ProbSpExtinct_PrePinatubo, ProbSpExtinct_PostPinatubo,
unitcircle_plot_PrePinatubo,
unitcircle_plot_PostPinatubo,
plot_feasibility_PrePinatubo,
plot_feasibility_PostPinatubo, file='output/SSRDLVR_model/plots.Rdata')