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MonarchPopulationForecasts.R
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MonarchPopulationForecasts.R
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#####################################################################################################
#Combining results from a retrospective population model for monarch butterflies in eastern
#North America (2004-2018) with projections of climate on the spring and summer breeding grounds
#to forecast the population's response to future climate change
#####################################################################################################
#-----------------------------------------------------------------------------------------------------#
# Set working directory and load packages
#-----------------------------------------------------------------------------------------------------#
# setwd()
library(plyr)
library(reshape2)
library(rstan)
rstan_options(auto_write = TRUE)
rstan_options(javascript = FALSE)
# rm(list=ls())
#-----------------------------------------------------------------------------------------------------#
# Read in data for the retrospective population model (assuming these files are in a "Data" subfolder)
#-----------------------------------------------------------------------------------------------------#
#Summer monarch data
summer <- read.csv('Data/Monarchs_summer.csv',header=TRUE,stringsAsFactors=FALSE)
#Winter monarch data and annual covariate data
dat.y <- read.csv('Data/YearlyData.csv',header=TRUE,stringsAsFactors=FALSE)
#Covariates: county
cov.c <- read.table('Data/Covariates_County.txt',sep='\t',header=TRUE,quote='\"',
colClasses=c(rep('numeric',2),rep('character',4),rep('numeric',8)))
#Covariates: county * year
cov.cy <- read.csv('Data/Covariates_CountyYear.csv',header=TRUE)
#Covariates: county * year * week
cov.cw <- read.csv('Data/Covariates_CountyWeek.csv',header=TRUE)
#-----------------------------------------------------------------------------------------------------#
# Retrospective population model: format summer survey data (2004-2018)
#-----------------------------------------------------------------------------------------------------#
#Specify number of weeks, years, counties, sites, etc.
uyears <- sort(unique(summer$yr))
n_years <- length(uyears)
uweeks <- sort(unique(summer$wk))
n_weeks <- length(uweeks)
ucounties <- cov.c$county.ind
n_counties <- length(ucounties)
usites <- sort(unique(summer$site.ind))
n_sites <- length(usites)
#Add indicators for state monitoring programs (using NABA as a reference level)
summer$ia.ind <- ifelse(summer$program=='Iowa',1,0)
summer$il.ind <- ifelse(summer$program=='Illinois',1,0)
summer$mi.ind <- ifelse(summer$program=='Michigan',1,0)
summer$oh.ind <- ifelse(summer$program=='Ohio',1,0)
#Standardize estimates of %open (ie, %unforested within 2.5 or 12.5 km of a NABA or BMN survey, respectively)
openS.m <- mean(summer$perc.open)
openS.sd <- sd(summer$perc.open)
summer$openS.st <- (summer$perc.open - openS.m)/openS.sd
#-----------------------------------------------------------------------------------------------------#
# Retrospective population model: standardize annual covariates
#-----------------------------------------------------------------------------------------------------#
#GDD in spring, eastern Texas
spGDD.m <- mean(dat.y$spGDD.east)
spGDD.sd <- sd(dat.y$spGDD.east)
dat.y$spGDD.st <- (dat.y$spGDD.east - spGDD.m)/spGDD.sd
#Quadratic
dat.y$spGDD.st2 <- dat.y$spGDD.st*dat.y$spGDD.st
#Precipitation in spring (FMA), eastern Texas
spPCP.m <- mean(dat.y$spPCP.east)
spPCP.sd <- sd(dat.y$spPCP.east)
dat.y$spPCP.st <- (dat.y$spPCP.east - spPCP.m)/spPCP.sd
#Quadratic
dat.y$spPCP.st2 <- dat.y$spPCP.st*dat.y$spPCP.st
#Autumn nectar availability (NDVI, along first half of migration route)
nectar.m <- mean(dat.y$NDVI)
nectar.sd <- sd(dat.y$NDVI)
dat.y$nectar.st <- (dat.y$NDVI - nectar.m)/nectar.sd
#Dense forest cover at overwintering sites
forest.m <- mean(dat.y$denseforest)
forest.sd <- sd(dat.y$denseforest)
dat.y$forest.st <- (dat.y$denseforest-forest.m)/forest.sd
#-----------------------------------------------------------------------------------------------------#
# Retrospective population model: standardize county covariates
#-----------------------------------------------------------------------------------------------------#
#Sort by county index
cov.c <- cov.c[with(cov.c,order(county.ind)),]
#Average GDD for weeks 10-24, 2004-2018
avgGDD.m <- mean(cov.c$avgGDD)
avgGDD.sd <- sd(cov.c$avgGDD)
cov.c$avgGDD.st <- (cov.c$avgGDD - avgGDD.m)/avgGDD.sd
#Average summer precipitation (AMJJA), 2004-2018
avgPCP.m <- mean(cov.c$avgPCP)
avgPCP.sd <- sd(cov.c$avgPCP)
cov.c$avgPCP.st <- (cov.c$avgPCP - avgPCP.m)/avgPCP.sd
#%open (ie, %unforested in each county)
openC.m <- mean(cov.c$perc.open)
openC.sd <- sd(cov.c$perc.open)
cov.c$openC.st <- (cov.c$perc.open - openC.m)/openC.sd
#%crop
cropC.m <- mean(cov.c$perc.crop)
cropC.sd <- sd(cov.c$perc.crop)
cov.c$cropC.st <- (cov.c$perc.crop - cropC.m)/cropC.sd
#-----------------------------------------------------------------------------------------------------#
# Retrospective population model: standardize county*year covariates
#-----------------------------------------------------------------------------------------------------#
#Sort by county and year index
cov.cy <- cov.cy[with(cov.cy,order(yr,county.ind)),]
#Glyphosate use (proportion of corn and soy crops sprayed)
#First, calculate county averages over 2004-2018
gly.c <- ddply(cov.cy,.(county.ind,state.county),summarize,gly.avg=mean(glyphosate),gly.min=min(glyphosate))
# sum(gly.c$gly.avg==0) #28 counties
# summary(cov.c$perc.crop[cov.c$county.ind %in% c(gly.c$county.ind[gly.c$gly.avg==0])]) #all with <9% crop cover
#Calculate minimum (non-zero) county average
gly.c.min <- min(gly.c$gly.avg[gly.c$gly.avg!=0])
#Impute the minimum county average in all years for those counties with glyphosate use = 0
cov.cy$glyphosate[cov.cy$state.county %in% gly.c$state.county[gly.c$gly.avg==0]] <- gly.c.min
gly.m <- mean(cov.cy$glyphosate)
gly.sd <- sd(cov.cy$glyphosate)
cov.cy$gly.st <- (cov.cy$glyphosate-gly.m)/gly.sd
#Summer precipitation (annual deviations from 2004-2018 means for AMJJA)
diffPCP.m <- mean(cov.cy$diffPCP)
diffPCP.sd <- sd(cov.cy$diffPCP)
cov.cy$diffPCP.st <- (cov.cy$diffPCP - diffPCP.m)/diffPCP.sd
#-----------------------------------------------------------------------------------------------------#
# Retrospective population model: standardize county*week covariates
#-----------------------------------------------------------------------------------------------------#
#Sort by county, week, and year index
cov.cw <- cov.cw[with(cov.cw,order(yr,wk,county.ind)),]
#Difference between GDD and average GDD for that week and county across all years of the study
diffGDD.m <- mean(cov.cw$diffGDD)
diffGDD.sd <- sd(cov.cw$diffGDD)
cov.cw$diffGDD.st <- (cov.cw$diffGDD-diffGDD.m)/diffGDD.sd
#-----------------------------------------------------------------------------------------------------#
# Retrospective population model: bundle covariates for the summer submodel
#-----------------------------------------------------------------------------------------------------#
cyw <- expand.grid(wk=uweeks,county.ind=ucounties,yr=uyears)
cyw$yr.ind <- cyw$yr-2003
#Standarize week
wk.m <- mean(cyw$wk)
wk.sd <- sd(cyw$wk)
cyw$wk.st <- (cyw$wk-wk.m)/wk.sd
cyw <- join(cyw,dat.y[,c('yr','spGDD.st','spGDD.st2','spPCP.st','spPCP.st2')],by='yr',type='left')
cyw <- join(cyw,cov.c[,c('county.ind','avgGDD.st','avgPCP.st','cropC.st')],by='county.ind',type='left')
cyw <- join(cyw,cov.cy[,c('county.ind','yr','diffPCP.st','gly.st')],by=c('county.ind','yr'),type='left')
cyw <- join(cyw,cov.cw[,c('county.ind','yr','wk','diffGDD.st')],by=c('county.ind','yr','wk'),type='left')
cyw$diffavgGDD <- cyw$diffGDD.st*cyw$avgGDD.st
cyw$diffGDD2 <- cyw$diffGDD.st*cyw$diffGDD.st
cyw$diffavgPCP <- cyw$diffPCP.st*cyw$avgPCP.st
cyw$diffPCP2 <- cyw$diffPCP.st*cyw$diffPCP.st
cyw$glycrop <- cyw$gly.st*cyw$cropC.st
cyw <- cyw[,c('county.ind','yr','yr.ind','wk','wk.st','spGDD.st','spGDD.st2','spPCP.st','spPCP.st2',
'avgGDD.st','diffGDD.st','diffGDD2','diffavgGDD',
'avgPCP.st','diffPCP.st','diffPCP2','diffavgPCP',
'gly.st','cropC.st','glycrop')]
names(cyw)[6:20] <- c('spGDD','spGDD2','spPCP','spPCP2',
'avgGDD','diffGDD','diffGDD2','diffavgGDD',
'avgPCP','diffPCP','diffPCP2','diffavgPCP',
'gly','crop','glycrop')
#Need to sort in a particular way to create the model-based annual index of peak summer population size in STAN
#Put first 5 weeks (16-20) on top
#Then sort week-fastest, year-slowest: first 4 rows would be county=1, yr=2004, wk=21-24, next 4 rows = county=2, yr=2004, wk=21-24
cyw15 <- cyw[cyw$wk %in% 16:20,]
cyw69 <- cyw[cyw$wk %in% 21:24,]
# head(cyw69); tail(cyw69)
cyw <- rbind(cyw15,cyw69)
#Finally, create an index for unique combinations of county, year, and week
cyw$cyw.ind <- 1:nrow(cyw)
#And attach these indices to the survey data
summer <- join(summer,cyw[,c('county.ind','wk','yr','cyw.ind')],by=c('county.ind','wk','yr'),type='left')
#-----------------------------------------------------------------------------------------------------#
# Retrospective population model: county weights based on area unforested land
#-----------------------------------------------------------------------------------------------------#
area.open <- as.vector(cov.c$area.land.sqmi*cov.c$perc.open/100)
weights.open <- area.open/sum(area.open)
#-----------------------------------------------------------------------------------------------------#
# Retrospective population model: package data, initial values, and parameters for Stan
#-----------------------------------------------------------------------------------------------------#
#Survey-level covariates in matrix
X_survey <- as.matrix(summer[,c('ia.ind','il.ind','mi.ind','oh.ind','openS.st')])
#County-year-week covariates
X_county <- as.matrix(cyw[,c('spGDD','spGDD2','spPCP','spPCP2',
'avgGDD','diffGDD','diffGDD2','diffavgGDD',
'avgPCP','diffPCP','diffPCP2','diffavgPCP',
'gly','crop','glycrop')])
#Covariates in winter submodel
X_winter <- as.matrix(dat.y[,c('forest.st','nectar.st')])
#Bundle data
standata <- list(n_years=n_years,
n_counties=n_counties,
n_cyw=nrow(cyw),
n_sites=n_sites,
n_surveys=nrow(summer),
year_id=cyw$yr.ind,
county_id=cyw$county.ind,
site_id=summer$site.ind,
cyw_id=summer$cyw.ind,
n_cov_alpha=ncol(X_county),
n_cov_beta=ncol(X_survey),
n_cov_gamma=ncol(X_winter),
X_county=X_county,
week_st=cyw$wk.st,
X_survey=X_survey,
effort=summer$duration,
X_winter=X_winter,
y_count=summer$monarch,
area=dat.y$area.dec,
weights=weights.open,
ind1=seq(1,n_counties*n_years*4,by=4),
ind2=seq(1,n_counties*n_years,by=n_counties),
start_peak=which(cyw$wk %in% 21:24)[1],
n_peak=sum(cyw$wk %in% 21:24),
n_cy=n_counties*n_years)
#MCMC parameters
ni <- 4000 # No. iterations (including warmup)
nb <- 3000 # No. burn-in iterations to discard (ie, warmup)
nt <- 1 # Thin rate
nc <- 3 # No. chains
#Initial values
set.seed(126)
inits <- lapply(1:nc, function(i)
list(alpha0=runif(1,2,3),
alphaFE=runif(ncol(X_county),-0.5,0.5),
alphaRE_week=runif(1,-0.5,0.5),
alphaRE_week2=runif(1,-0.5,0.5),
betaFE=runif(ncol(X_survey),-0.5,0.5),
gamma0=runif(1,0,2),
gamma_sum=runif(1,-0.5,0.5),
gammaFE=runif(ncol(X_winter),-0.5,0.5),
sd_county=runif(1,0,1),
sd_week=runif(1,0,1),
sd_week2=runif(1,0,1),
sd_site=runif(1,0,1),
sd_year=runif(1,0,1),
r_count=runif(1,0,2),
shape=runif(1,0,2)))
#Parameters to monitor
params <- c('alpha0','alphaFE','alphaRE_week','alphaRE_week2','betaFE',
'gamma0','gamma_sum','gammaFE','sd_county','sd_week','sd_week2',
'sd_site','sd_year','r_count','shape','pred_orig_log','pred_orig_exp','pred_sum','mu_win',
'randweek','randweek2','randyear','randcounty')
#-----------------------------------------------------------------------------------------------------#
# Retrospective population model: Run model in Stan using rstan package and save posterior samples
#-----------------------------------------------------------------------------------------------------#
out <- stan('FACM_2004-2018.stan',
control=list(adapt_delta=0.8),
data=standata, init=inits, pars=params,
chains=nc, iter=ni, warmup=nb, thin=nt,
seed=1,cores=3,open_progress=FALSE)
#If run previously, load workspace with stanfit object
load('...Rdata')
posterior <- as.matrix(out)
#Extract 1000 samples from posterior distribution (thin by 3)
iter <- seq(1,3000,by=3)
posterior <- posterior[iter,]
#Rename matrix of covariate values used in retrospective model
cyw.obs <- cyw
#Remove objects from workspace that aren't needed anymore
rm(standata)
rm(out)
rm(X_survey)
rm(X_county)
rm(X_winter)
#-----------------------------------------------------------------------------------------------------#
# Climate projections: import and format climate data
#-----------------------------------------------------------------------------------------------------#
#Import spring data
springclim <- read.csv('Data/SpringClimateProjections.csv',header=TRUE)
names(springclim)[1:3] <- c('scenarioname','yr','modelname')
#Import summer data
summerclim1a <- read.csv('Data/SummerClimateProjections1a.csv',header=TRUE)
summerclim1b <- read.csv('Data/SummerClimateProjections1b.csv',header=TRUE)
summerclim2a <- read.csv('Data/SummerClimateProjections2a.csv',header=TRUE)
summerclim2b <- read.csv('Data/SummerClimateProjections2b.csv',header=TRUE)
summerclim3a <- read.csv('Data/SummerClimateProjections3a.csv',header=TRUE)
summerclim3b <- read.csv('Data/SummerClimateProjections3b.csv',header=TRUE)
summerclim <- rbind(summerclim1a,summerclim1b,summerclim2a,summerclim2b,
summerclim3a,summerclim3b)
names(summerclim)[1:3] <- c('scenarioname','yr','modelname')
rm(list=c('summerclim1a','summerclim1b','summerclim2a','summerclim2b',
'summerclim3a','summerclim3b'))
#Time periods
periods <- 1:3
#Years
years1 <- 2023:2043
years2 <- 2050:2070
years3 <- 2080:2100
#Emissions scenarios:
#1 = low, SSP1-2.6 (SSP126); 2 = moderate, SSP2-4.5 (SSP245); 3 = high, SSP3-7.0 (SSP370); 4 = worst-case, SSP5-8.5 (SSP585)
sc <- data.frame(scenario=1:4,scenarioname=c('SSP126','SSP245','SSP370','SSP585'))
#GCMs
mod <- data.frame(model=1:6,modelname=sort(unique(springclim$modelname)))
#Adding time period, model number, and scenario number to spring and summer data
springclim$period <- ifelse(springclim$yr %in% years1,1,ifelse(springclim$yr %in% years2,2,3))
summerclim$period <- ifelse(summerclim$yr %in% years1,1,ifelse(summerclim$yr %in% years2,2,3))
springclim$model <- mod$model[match(springclim$modelname,mod$modelname)]
summerclim$model <- mod$model[match(summerclim$modelname,mod$modelname)]
springclim$scenario <- sc$scenario[match(springclim$scenarioname,sc$scenarioname)]
summerclim$scenario <- sc$scenario[match(summerclim$scenarioname,sc$scenarioname)]
#Adding county index (1:545) to summer data
summerclim$county.ind <- cov.c$county.ind[match(summerclim$state.county,cov.c$state.county)]
#Sort dataframes
springclim <- springclim[with(springclim,order(scenario,model,yr)),]
summerclim <- summerclim[with(summerclim,order(scenario,model,yr,county.ind)),]
#-----------------------------------------------------------------------------------------------------#
# Climate projections: create climate covariates and standardize
#-----------------------------------------------------------------------------------------------------#
#Standardizing all covariates using the mean/SD of 2004-2018 data
#Spring GDD (spGDD)
springclim$spGDD.st <- (springclim$spGDD - spGDD.m)/spGDD.sd
#Quadratic
springclim$spGDD.st2 <- springclim$spGDD.st*springclim$spGDD.st
#Spring precipitation (spPCP)
springclim$spPCP <- rowSums(springclim[,c('pcp.Feb','pcp.Mar','pcp.Apr')])
springclim$spPCP.st <- (springclim$spPCP - spPCP.m)/spPCP.sd
#Quadratic
springclim$spPCP.st2 <- springclim$spPCP.st*springclim$spPCP.st
#Summer GDD (avgGDD and diffGDD)
avgGDD <- ddply(summerclim,.(scenario,model,period,county.ind,state.county),summarize,avgGDD=mean(gdd.wk10.24))
avgGDD$avgGDD.st <- (avgGDD$avgGDD - avgGDD.m)/avgGDD.sd
#Calculate difference from average for that time period, for each county, year, and week
GDDlong <- melt(summerclim,id.vars=c('scenario','model','period','yr','county.ind','state.county'),
measure.vars=paste('gdd.wk10',21:24,sep='.'),variable.name='wk',value.name='GDD')
GDDlong$wk <- as.numeric(substr(GDDlong$wk,10,11))
wkGDDavg <- ddply(GDDlong,.(scenario,model,period,county.ind,state.county,wk),summarize,
GDD.mn=mean(GDD))
diffGDD <- join(GDDlong,wkGDDavg,by=c('scenario','model','period','wk','county.ind','state.county'),type='left')
diffGDD$diffGDD <- diffGDD$GDD - diffGDD$GDD.mn
diffGDD$diffGDD.st <- (diffGDD$diffGDD - diffGDD.m)/diffGDD.sd
#Quadratic
diffGDD$diffGDD.st2 <- diffGDD$diffGDD.st*diffGDD$diffGDD.st
#Summer PCP (avgPCP and diffGDD)
summerclim$suPCP <- rowSums(summerclim[,c('pcp.Apr','pcp.May','pcp.Jun','pcp.Jul','pcp.Aug')])
avgPCP <- ddply(summerclim,.(scenario,model,period,county.ind,state.county),summarize,avgPCP=mean(suPCP))
avgPCP$avgPCP.st <- (avgPCP$avgPCP - avgPCP.m)/avgPCP.sd
#Calculate difference from average for that time period, for each county and year
diffPCP <- join(summerclim[,c('scenario','model','period','yr','county.ind','state.county','suPCP')],
avgPCP[,c('scenario','model','period','county.ind','state.county','avgPCP')],
by=c('scenario','model','period','county.ind','state.county'),type='left')
diffPCP$diffPCP <- diffPCP$suPCP - diffPCP$avgPCP
diffPCP$diffPCP.st <- (diffPCP$diffPCP - diffPCP.m)/diffPCP.sd
#Quadratic
diffPCP$diffPCP.st2 <- diffPCP$diffPCP.st*diffPCP$diffPCP.st
#-----------------------------------------------------------------------------------------------------#
# Population forecasts: format and standardize other (non-climate) covariates
#----------------------------------------------------------------------------------------------------#
#Forest cover (forest) assuming value equal to 2004-2018 mean; standardized = 0
#Nectar availability (nectar) assuming value equal to 2004-2018 mean; standardized = 0
#Crop cover: using 2004-2018 county-level values, which were time-invariant (cov.c$cropC.st)
#Glyphosate: using 2004-2018 county-level means (gly.c)
#Impute the minimum non-zero value (0.62) for counties with no data
gly.c$gly.avg[gly.c$gly.avg==0] <- gly.c.min
gly.c$gly.st <- (gly.c$gly.avg - gly.m)/gly.sd
#-----------------------------------------------------------------------------------------------------#
# Population forecasts: create vectors/matrices with all posterior samples or the median posterior value from retrospective model
#----------------------------------------------------------------------------------------------------#
ucounties <- cov.c$county.ind
n_counties <- length(ucounties)
uweeks <- sort(unique(diffGDD$wk))
n_weeks <- length(uweeks)
n_years <- length(years1)
n_iter <- nrow(posterior)
#Matrix with posterior samples for fixed effects in summer submodel
alpha <- as.matrix(posterior[,grep('alpha0|alphaFE',colnames(posterior))])
#Median values from posterior distribution
alpha.md <- apply(alpha,2,median)
#Vectors with posterior samples for week effects
alpha.wk <- posterior[,'alphaRE_week']
alpha.wk2 <- posterior[,'alphaRE_week2']
sd.wk <- posterior[,'sd_week']
sd.wk2 <- posterior[,'sd_week2']
#Median values of week effects
alpha.wk.md <- median(alpha.wk)
alpha.wk2.md <- median(alpha.wk2)
#Matrix with posterior samples for county random effects
RE.counties <- as.matrix(posterior[,grep('randcounty',colnames(posterior))])
RE.counties <- t(RE.counties)
RE.county1yr <- RE.counties[rep(1:nrow(RE.counties),each=n_weeks),]
#Median values from posterior samples
RE.county1yr.md <- apply(RE.county1yr,1,median)
RE.countyallyr.md <- rep(RE.county1yr.md,n_years)
#Matrix with posterior samples from intercept in winter submodel
gamma0 <- as.matrix(posterior[,'gamma0'])
WinInt <- as.matrix(rep(1,n_years),nrow=n_years)
Wgamma0 <- WinInt %*% t(gamma0)
#Median of those values
Wgamma0.md <- apply(Wgamma0,1,median)
#Matrix with posterior samples from summer effect in winter submodel
gamma.sum <- as.matrix(posterior[,'gamma_sum'])
#Median value
gamma.sum.md <- apply(gamma.sum,2,median)
#Vector with posterior samples from SD parameter associated with random yearly effects in winter submodel
sd.yr <- posterior[,'sd_year']
#Matrix with posterior samples from shape parameter (for gamma distribution of winter areas)
shape <- as.matrix(posterior[,'shape'])
#-----------------------------------------------------------------------------------------------------#
# Population forecasts: forecasting summer counts and winter population size for each scenario, GCM, year
# Accounting for parameter uncertainty, climate uncertainty, environmental stochasticity
#-----------------------------------------------------------------------------------------------------#
#Forecasts will be compiled into lists:
win.list <- list()
sum.list <- list()
i <- 0
set.seed(44)
#Loop through emissions scenarios, GCMs, and time periods:
for(ss in 1:nrow(sc)){ #scenario
for(mm in 1:nrow(mod)){ #GCM
for(pp in 1:3){ #time period
uyears <- get(paste0('years',pp))
i <- i+1
#Combine ecological covariates in summer submodel in dataframe
cyw <- expand.grid(wk=uweeks,county.ind=ucounties,yr=uyears)
cyw$yr.ind <- cyw$yr - min(cyw$yr) + 1
#Standardize week (want same values as those used in 2004-2018 analysis)
cyw$wk.st <- (cyw$wk-wk.m)/wk.sd
cyw <- join(cyw,springclim[springclim$scenario==ss & springclim$model==mm & springclim$period==pp,
c('yr','spGDD.st','spGDD.st2','spPCP.st','spPCP.st2')],by='yr',type='left')
cyw <- join_all(list(cyw,cov.c[,c('county.ind','cropC.st')],gly.c[,c('county.ind','gly.st')],
avgGDD[avgGDD$scenario==ss & avgGDD$model==mm & avgGDD$period==pp,c('county.ind','avgGDD.st')],
avgPCP[avgPCP$scenario==ss & avgPCP$model==mm & avgPCP$period==pp,c('county.ind','avgPCP.st')]),
by='county.ind',type='left')
cyw <- join(cyw,diffPCP[diffPCP$scenario==ss & diffPCP$model==mm & diffPCP$period==pp,c('county.ind','yr','diffPCP.st','diffPCP.st2')],
by=c('county.ind','yr'),type='left')
cyw <- join(cyw,diffGDD[diffGDD$scenario==ss & diffGDD$model==mm & diffGDD$period==pp,c('county.ind','yr','wk','diffGDD.st','diffGDD.st2')],
by=c('county.ind','yr','wk'),type='left')
cyw$diffavgGDD <- cyw$diffGDD.st*cyw$avgGDD.st
cyw$diffavgPCP <- cyw$diffPCP.st*cyw$avgPCP.st
cyw$glycrop <- cyw$gly.st*cyw$cropC.st
cyw <- cyw[,c('county.ind','yr','yr.ind','wk','wk.st','spGDD.st','spGDD.st2','spPCP.st','spPCP.st2',
'avgGDD.st','diffGDD.st','diffGDD.st2','diffavgGDD',
'avgPCP.st','diffPCP.st','diffPCP.st2','diffavgPCP',
'gly.st','cropC.st','glycrop')]
names(cyw)[6:ncol(cyw)] <- c('spGDD','spGDD2','spPCP','spPCP2',
'avgGDD','diffGDD','diffGDD2','diffavgGDD',
'avgPCP','diffPCP','diffPCP2','diffavgPCP',
'gly','crop','glycrop')
#Calculate summer expected counts from posterior samples
#Fixed effects
Xcounty <- as.matrix(cbind(rep(1,nrow(cyw)),
cyw[,c('spGDD','spGDD2','spPCP','spPCP2',
'avgGDD','diffGDD','diffGDD2','diffavgGDD',
'avgPCP','diffPCP','diffPCP2','diffavgPCP',
'gly','crop','glycrop')]))
Xalpha <- Xcounty %*% t(alpha)
#Effect of week
Xweeks <- matrix(c(cyw$wk.st,cyw$wk.st*cyw$wk.st),ncol=2,nrow=nrow(cyw),byrow=FALSE)
alphaRE.wk <- alphaRE.wk2 <- matrix(NA,nrow=n_years,ncol=n_iter)
for(s in 1:n_years){
alphaRE.wk[s,] <- alpha.wk + rnorm(n_iter,0,sd.wk)
alphaRE.wk2[s,] <- alpha.wk2 + rnorm(n_iter,0,sd.wk2)
} #s
Xalpha.wk <- Xalpha.wk2 <- matrix(NA,nrow=nrow(Xweeks),ncol=n_iter)
for(s in 1:nrow(cyw)){
Xalpha.wk[s,] <- Xweeks[s,1]*alphaRE.wk[cyw$yr.ind[s],]
Xalpha.wk2[s,] <- Xweeks[s,2]*alphaRE.wk2[cyw$yr.ind[s],]
} #s
#Random county effects
eps.county <- RE.county1yr[rep(1:nrow(RE.county1yr),times=n_years),]
#Combine components in summer submodel
mu.county.log <- Xalpha + Xalpha.wk + Xalpha.wk2 + eps.county
#Calculate means for each county-year combination
split.muc <- lapply(split(mu.county.log,rep(1:(n_counties*n_years),each=n_weeks)),matrix,ncol=ncol(mu.county.log))
mu.cy.log <- t(sapply(split.muc,colMeans))
#Add matrix of forecasted counts (in each county and year) to sum.list
mu.cy <- exp(mu.cy.log)
params.cy <- matrix(as.numeric(c(ss,mm,pp)),nrow=n_years*n_counties,ncol=3,byrow=TRUE)
params.cy <- cbind(params.cy,unique(cyw[,c('county.ind','yr')]))
sum.list[[i]] <- cbind(params.cy,mu.cy)
colnames(sum.list[[i]]) <- c('scenario','model','period','county.ind','yr',paste0('i',1:n_iter))
#Calculate weighted mean of expected counts in each year (mean across counties)
weights.mat <- matrix(weights.open,nrow=nrow(mu.cy.log),ncol=ncol(mu.cy.log),byrow=FALSE)
mu.cy.weights <- mu.cy.log*weights.mat
split.mucy <- lapply(split(mu.cy.weights,rep(1:n_years,each=n_counties)),matrix,ncol=ncol(mu.cy.weights))
mu.y.log <- t(sapply(split.mucy,colSums))
#Standardize annual population index by fixed mean, SD
mu.y.z <- (mu.y.log - 1.14)/0.58
#Calculate expected area occupied from posterior samples
Wsum <- matrix(NA,nrow=n_years,ncol=n_iter)
Wyr <- matrix(NA,nrow=n_years,ncol=n_iter)
#Summer effect
for(ii in 1:n_iter){
Wsum[,ii] <- mu.y.z[,ii]*gamma.sum[ii,1]
#Random yearly effects
Wyr[,ii] <- rnorm(n_years,0,sd.yr[ii])
} #ii
#Combine components and exponentiate
mu.win <- exp(Wgamma0 + Wsum + Wyr)
#Calculate rate parameter
rate <- matrix(NA,nrow=n_years,ncol=n_iter)
pred.win <- matrix(NA,nrow=n_years,ncol=n_iter)
for(ii in 1:n_iter){
rate[,ii] <- shape[ii,1]*(1/mu.win[,ii])
#Generate value from gamma distribution with specified shape, rate parameters
pred.win[,ii] <- rgamma(n_years,shape=shape[ii,1],rate=rate[,ii])
} #ii
#Add matrix of annual forecasted values of the area occupied to win.list
params.y <- matrix(as.numeric(c(ss,mm,pp)),nrow=n_years,ncol=3,byrow=TRUE)
params.y <- cbind(params.y,uyears)
win.list[[i]] <- cbind(params.y,pred.win)
colnames(win.list[[i]]) <- c('scenario','model','period','yr',paste0('i',1:n_iter))
#See progress
print(i)
} #pp
} #mm
} #ss
preds.sum <- do.call(rbind,sum.list)
#-----------------------------------------------------------------------------------------------------#
# Summarize forecasted monarch counts on the summer breeding grounds during each future time period
#-----------------------------------------------------------------------------------------------------#
#-----------------------------------------------------------------------------#
#For comparison, first calculate the expected means in each county and year between 2004-2018
cyw.obs <- cyw.obs[cyw.obs$wk %in% 21:24,]
Xcounty <- as.matrix(cbind(rep(1,nrow(cyw.obs)),
cyw.obs[,c('spGDD','spGDD2','spPCP','spPCP2',
'avgGDD','diffGDD','diffGDD2','diffavgGDD',
'avgPCP','diffPCP','diffPCP2','diffavgPCP',
'gly','crop','glycrop')]))
alpha.full <- as.matrix(posterior[,grep('alpha0|alphaFE',colnames(posterior))])
Xalpha <- Xcounty %*% t(alpha.full)
Xweeks <- matrix(c(cyw.obs$wk.st,cyw.obs$wk.st*cyw.obs$wk.st),ncol=2,byrow=FALSE)
randweekboth <- posterior[,grep('randweek',colnames(posterior))]
randweek <- randweekboth[,1:15]
randweek2 <- randweekboth[,16:30]
alphaRE.wk <- alphaRE.wk2 <- matrix(NA,nrow=15,ncol=n_iter)
for(s in 1:15){
alphaRE.wk[s,] <- alpha.wk + randweek[,s]
alphaRE.wk2[s,] <- alpha.wk2 + randweek2[,s]
}
Xalpha.wk <- Xalpha.wk2 <- matrix(NA,nrow=nrow(Xweeks),ncol=n_iter)
for(s in 1:nrow(cyw.obs)){
Xalpha.wk[s,] <- Xweeks[s,1]*alphaRE.wk[cyw.obs$yr.ind[s],]
Xalpha.wk2[s,] <- Xweeks[s,2]*alphaRE.wk2[cyw.obs$yr.ind[s],]
}
eps.county <- RE.county1yr[rep(1:nrow(RE.county1yr),times=15),]
#Combine components
obs.log <- Xalpha + Xalpha.wk + Xalpha.wk2 + eps.county
#Calculate means (across weeks) for each county-year-iteration combination
split.cy <- lapply(split(obs.log,rep(1:(n_counties*15),each=4)),matrix,ncol=ncol(obs.log))
cy.log <- t(sapply(split.cy,colMeans))
cy.real <- as.data.frame(exp(cy.log))
#For each county, calculate the 15-year mean (for each iteration)
cy.obs <- data.frame(unique(cyw.obs[,c('yr','county.ind')]))
c.obs.list <- split(cy.real,f=cy.obs$county.ind)
c.obs.byperiod <- lapply(c.obs.list,colMeans)
c.obs.byperiod <- do.call(rbind,c.obs.byperiod)
#Then summarize across iterations for each county
c.obs.summary <- data.frame(county.ind=unique(cy.obs$county.ind))
c.obs.summary$obs.mn <- apply(c.obs.byperiod,1,mean)
c.obs.summary$obs.sd <- apply(c.obs.byperiod,1,sd)
c.obs.summary$obs.q0.05 <- apply(c.obs.byperiod,1,quantile,0.05)
c.obs.summary$obs.q0.5 <- apply(c.obs.byperiod,1,quantile,0.5)
c.obs.summary$obs.q0.95 <- apply(c.obs.byperiod,1,quantile,0.95)
c.obs.summary$state.county <- cov.c$state.county[match(c.obs.summary$county.ind,cov.c$county.ind)]
#Summary of median counts
summary(c.obs.summary$obs.q0.5)
#-----------------------------------------------------------------------------#
#Summarizing forecasts for a low emissions scenario, SSP126 (across GCMs)
preds.sum1 <- preds.sum[preds.sum$scenario==1,]
index.cpm <- paste(preds.sum1$county.ind,preds.sum1$period,preds.sum1$model,sep='-')
preds.list.cpm1 <- split(preds.sum1,f=index.cpm)
#For each county and GCM, calculate the 21-year mean (for each iteration)
preds.bycpm1 <- lapply(preds.list.cpm1,colMeans)
preds.bycpm1a <- do.call(rbind,preds.bycpm1)
preds.bycpm1a <- as.data.frame(preds.bycpm1a)
#Summarize period means across 6000 iteration-GCM combinations
index.cp <- paste(preds.bycpm1a$county.ind,preds.bycpm1a$period,sep='-')
preds.bycp1 <- split(preds.bycpm1a,f=index.cp)
preds.summary.cp1 <- unique(preds.bycpm1a[,c('period','county.ind')])
preds.summary.cp1$mn <- sapply(preds.bycp1,function(x) mean(as.matrix(x[,6:(n_iter+5)])))
preds.summary.cp1$sd <- sapply(preds.bycp1,function(x) sd(as.matrix(x[,6:(n_iter+5)])))
preds.summary.cp1$q0.05 <- sapply(preds.bycp1,function(x) quantile(as.matrix(x[,6:(n_iter+5)]),0.05))
preds.summary.cp1$q0.5 <- sapply(preds.bycp1,function(x) quantile(as.matrix(x[,6:(n_iter+5)]),0.5))
preds.summary.cp1$q0.95 <- sapply(preds.bycp1,function(x) quantile(as.matrix(x[,6:(n_iter+5)]),0.95))
#Attach 2004-2018 mean/median, and county covariates
preds.summary.cp1 <- join(preds.summary.cp1,c.obs.summary[,c('county.ind','obs.mn','obs.q0.5')],
by='county.ind',type='left')
preds.summary.cp1 <- join(preds.summary.cp1,cov.c[,c('county.ind','state.county')],
by='county.ind',type='left')
#Calculate absolute and percent difference from 2004-2018 means
#Using median of distributions of means
preds.summary.cp1$diff <- preds.summary.cp1$q0.5 - preds.summary.cp1$obs.q0.5
preds.summary.cp1$perc.diff <- preds.summary.cp1$diff/preds.summary.cp1$obs.q0.5*100
#-----------------------------------------------------------------------------#
#Summarizing forecasts for a high emissions scenario, SSP585 (across GCMs)
preds.sum4 <- preds.sum[preds.sum$scenario==4,]
index.cpm <- paste(preds.sum4$county.ind,preds.sum4$period,preds.sum4$model,sep='-')
preds.list.cpm4 <- split(preds.sum4,f=index.cpm)
#For each county and GCM, calculate the 21-year mean (for each iteration)
preds.bycpm4 <- lapply(preds.list.cpm4,colMeans)
preds.bycpm4a <- do.call(rbind,preds.bycpm4)
preds.bycpm4a <- as.data.frame(preds.bycpm4a)
#Summarize period means across 6000 iteration-GCM combinations
index.cp <- paste(preds.bycpm4a$county.ind,preds.bycpm4a$period,sep='-')
preds.bycp4 <- split(preds.bycpm4a,f=index.cp)
preds.summary.cp4 <- unique(preds.bycpm4a[,c('period','county.ind')])
preds.summary.cp4$mn <- sapply(preds.bycp4,function(x) mean(as.matrix(x[,6:(n_iter+5)])))
preds.summary.cp4$sd <- sapply(preds.bycp4,function(x) sd(as.matrix(x[,6:(n_iter+5)])))
preds.summary.cp4$q0.05 <- sapply(preds.bycp4,function(x) quantile(as.matrix(x[,6:(n_iter+5)]),0.05))
preds.summary.cp4$q0.5 <- sapply(preds.bycp4,function(x) quantile(as.matrix(x[,6:(n_iter+5)]),0.5))
preds.summary.cp4$q0.95 <- sapply(preds.bycp4,function(x) quantile(as.matrix(x[,6:(n_iter+5)]),0.95))
#Attach 2004-2018 mean/median, and county covariates
preds.summary.cp4 <- join(preds.summary.cp4,c.obs.summary[,c('county.ind','obs.mn','obs.q0.5')],
by='county.ind',type='left')
preds.summary.cp4 <- join(preds.summary.cp4,cov.c[,c('county.ind','state.county')],
by='county.ind',type='left')
#Calculate absolute and percent difference from 2004-2018 means
#Using median of distributions of means
preds.summary.cp4$diff <- preds.summary.cp4$q0.5 - preds.summary.cp4$obs.q0.5
preds.summary.cp4$perc.diff <- preds.summary.cp4$diff/preds.summary.cp4$obs.q0.5*100
#-----------------------------------------------------------------------------------------------------#
# Summarize forecasted area occupied on the overwintering grounds during each future time period
#-----------------------------------------------------------------------------------------------------#
#-----------------------------------------------------------------------------#
#For comparison, summarize observed data, 2004-2018
obsmn.0418 <- mean(dat.y$area.dec)
#Standard error and 90% CI
se.obs0418 <- sd(dat.y$area.dec)/sqrt(15)
ci90.obs0418 <- obsmn.0418 + c(-1,1)*1.761*se.obs0418 #(t-stat for 90% CI, 14 df is 1.761)
#-----------------------------------------------------------------------------#
#Summarize forecasts for each GCM-emission scenario combination
#First, average forecasts over years for each iteration-period-GCM-scenario
preds.byperiod <- lapply(win.list,colMeans)
#Then summarize period means (mean, sd, quants) over iterations for each GCM-scenario combination
preds.byperiod2 <- do.call(rbind,preds.byperiod)
preds.summary <- as.data.frame(preds.byperiod2[,1:3])
preds.summary$mn <- apply(preds.byperiod2[,5:(n_iter+4)],1,mean)
preds.summary$sd <- apply(preds.byperiod2[,5:(n_iter+4)],1,sd)
preds.summary$q0.05 <- apply(preds.byperiod2[,5:(n_iter+4)],1,quantile,0.05)
preds.summary$q0.25 <- apply(preds.byperiod2[,5:(n_iter+4)],1,quantile,0.25)
preds.summary$q0.5 <- apply(preds.byperiod2[,5:(n_iter+4)],1,quantile,0.5)
preds.summary$q0.75 <- apply(preds.byperiod2[,5:(n_iter+4)],1,quantile,0.75)
preds.summary$q0.95 <- apply(preds.byperiod2[,5:(n_iter+4)],1,quantile,0.95)
#-----------------------------------------------------------------------------#
#Summarize forecasts for each emission scenario (across GCMs)
#Summarize period means (mean, sd, quants) across (6000) iteration-GCM combinations for each scenario
preds.byperiod.df <- as.data.frame(preds.byperiod2)
index.s <- paste(preds.byperiod.df$scenario,preds.byperiod.df$period,sep='-')
preds.list.s <- split(preds.byperiod.df,f=index.s)
preds.summary.s <- unique(preds.byperiod.df[,c('scenario','period')])
preds.summary.s$mn <- sapply(preds.list.s,function(x) mean(as.matrix(x[,5:(n_iter+4)])))
preds.summary.s$sd <- sapply(preds.list.s,function(x) sd(as.matrix(x[,5:(n_iter+4)])))
preds.summary.s$q0.05 <- sapply(preds.list.s,function(x) quantile(as.matrix(x[,5:(n_iter+4)]),0.05))
preds.summary.s$q0.25 <- sapply(preds.list.s,function(x) quantile(as.matrix(x[,5:(n_iter+4)]),0.25))
preds.summary.s$q0.5 <- sapply(preds.list.s,function(x) quantile(as.matrix(x[,5:(n_iter+4)]),0.5))
preds.summary.s$q0.75 <- sapply(preds.list.s,function(x) quantile(as.matrix(x[,5:(n_iter+4)]),0.75))
preds.summary.s$q0.95 <- sapply(preds.list.s,function(x) quantile(as.matrix(x[,5:(n_iter+4)]),0.95))
pss <- preds.summary.s
#-----------------------------------------------------------------------------#
#Plot with forecasts (medians, 50 & 90% CIs), averaged across GCMs for each emission scenario
#(Figs. 5a-c in paper)
figcol4 <- c('dodgerblue4','darkseagreen4','lightsalmon2','tomato4')
par(mfrow=c(1,3),mar=c(0,0,0.3,0),oma=c(1.4,3.5,0.2,0.5),cex=0.9)
plot(0,0,type='n',xlim=c(0,max(pss$scenario)+1),ylim=c(0,9.6),axes=FALSE,xlab='',ylab='')
polygon(x=c(par('usr')[1],par('usr')[2],par('usr')[2],par('usr')[1],par('usr')[1]),
y=c(ci90.obs0418[1],ci90.obs0418[1],ci90.obs0418[2],ci90.obs0418[2],ci90.obs0418[1]),
col='gray95',border=NA)
arrows(x0=par('usr')[1],x1=par('usr')[2],y0=obsmn.0418,y1=obsmn.0418,length=0,col='gray40',lty=2)
axis(1,at=par('usr')[1:2],tcl=0,labels=FALSE)
axis(2,at=par('usr')[3:4],tcl=0,labels=FALSE)
axis(2,at=seq(0,9,by=2),tcl=-0.25,labels=seq(0,9,by=2),las=1,mgp=c(1.5,0.5,0))
axis(3,at=par('usr')[1:2],tcl=0,labels=FALSE)
axis(4,at=par('usr')[3:4],tcl=0,labels=FALSE)
arrows(x0=pss$scenario[pss$period==1],x1=pss$scenario[pss$period==1],y0=pss$q0.05[pss$period==1],y1=pss$q0.95[pss$period==1],
length=0,col=figcol4,lwd=1.2)
arrows(x0=pss$scenario[pss$period==1],x1=pss$scenario[pss$period==1],y0=pss$q0.25[pss$period==1],y1=pss$q0.75[pss$period==1],
length=0,col=figcol4,lwd=2.5)
arrows(x0=par('usr')[1],x1=par('usr')[2],y0=obsmn.0418,y1=obsmn.0418,length=0,col='gray40',lty=2)
points(q0.5~scenario,data=pss[pss$period==1,],pch=21,col=figcol4,bg=figcol4)
legend(x=-0.2,y=10.1,c('Low','Mod-Low','Mod-High','High'),col=figcol4,lwd=2.5,bty='n',cex=0.8,x.intersp=0.7)
mtext('2023-2043',side=1,line=0.2,cex=0.9)
plot(0,0,type='n',xlim=c(0,max(pss$scenario)+1),ylim=c(0,9.6),axes=FALSE,xlab='',ylab='')
polygon(x=c(par('usr')[1],par('usr')[2],par('usr')[2],par('usr')[1],par('usr')[1]),
y=c(ci90.obs0418[1],ci90.obs0418[1],ci90.obs0418[2],ci90.obs0418[2],ci90.obs0418[1]),
col='gray95',border=NA)
arrows(x0=par('usr')[1],x1=par('usr')[2],y0=obsmn.0418,y1=obsmn.0418,length=0,col='gray40',lty=2)
axis(1,at=par('usr')[1:2],tcl=0,labels=FALSE)
axis(2,at=par('usr')[3:4],tcl=0,labels=FALSE)
axis(3,at=par('usr')[1:2],tcl=0,labels=FALSE)
axis(4,at=par('usr')[3:4],tcl=0,labels=FALSE)
arrows(x0=pss$scenario[pss$period==2],x1=pss$scenario[pss$period==2],y0=pss$q0.05[pss$period==2],y1=pss$q0.95[pss$period==2],
length=0,col=figcol4,lwd=1.2)
arrows(x0=pss$scenario[pss$period==2],x1=pss$scenario[pss$period==2],y0=pss$q0.25[pss$period==2],y1=pss$q0.75[pss$period==2],
length=0,col=figcol4,lwd=2.5)
points(q0.5~scenario,data=pss[pss$period==2,],pch=21,col=figcol4,bg=figcol4)
mtext('2050-2070',side=1,line=0.2,cex=0.9)
plot(0,0,type='n',xlim=c(0,max(pss$scenario)+1),ylim=c(0,9.6),axes=FALSE,xlab='',ylab='')
polygon(x=c(par('usr')[1],par('usr')[2],par('usr')[2],par('usr')[1],par('usr')[1]),
y=c(ci90.obs0418[1],ci90.obs0418[1],ci90.obs0418[2],ci90.obs0418[2],ci90.obs0418[1]),
col='gray95',border=NA)
arrows(x0=par('usr')[1],x1=par('usr')[2],y0=obsmn.0418,y1=obsmn.0418,length=0,col='gray40',lty=2)
axis(1,at=par('usr')[1:2],tcl=0,labels=FALSE)
axis(2,at=par('usr')[3:4],tcl=0,labels=FALSE)
axis(3,at=par('usr')[1:2],tcl=0,labels=FALSE)
axis(4,at=par('usr')[3:4],tcl=0,labels=FALSE)
arrows(x0=pss$scenario[pss$period==3],x1=pss$scenario[pss$period==3],y0=pss$q0.05[pss$period==3],y1=pss$q0.95[pss$period==3],
length=0,col=figcol4,lwd=1.2)
arrows(x0=pss$scenario[pss$period==3],x1=pss$scenario[pss$period==3],y0=pss$q0.25[pss$period==3],y1=pss$q0.75[pss$period==3],
length=0,col=figcol4,lwd=2.5)
points(q0.5~scenario,data=pss[pss$period==3,],pch=21,col=figcol4,bg=figcol4)
mtext('2080-2100',side=1,line=0.2,cex=0.9)
mtext('Total area occupied (ha)',side=2,line=2.0,outer=TRUE,cex=0.9)
#-----------------------------------------------------------------------------#
#Summarizing annual variation in the forecasted area occupied
match <- data.frame(summary=c('min','max','mn','md','sd'),summary.no=1:5,stringsAsFactors=FALSE)
preds.annmin <- lapply(win.list,function(x) c(x[1,1:3],apply(x[,5:(n_iter+4)],2,min)))
preds.annmax <- lapply(win.list,function(x) c(x[1,1:3],apply(x[,5:(n_iter+4)],2,max)))
preds.annmn <- lapply(win.list,function(x) c(x[1,1:3],apply(x[,5:(n_iter+4)],2,mean)))
preds.annmd <- lapply(win.list,function(x) c(x[1,1:3],apply(x[,5:(n_iter+4)],2,median)))
preds.annsd <- lapply(win.list,function(x) c(x[1,1:3],apply(x[,5:(n_iter+4)],2,sd)))
preds.annmin <- lapply(1:length(preds.annmin), function(x) c(summary.no=1,preds.annmin[[x]]))
preds.annmax <- lapply(1:length(preds.annmax), function(x) c(summary.no=2,preds.annmax[[x]]))
preds.annmn <- lapply(1:length(preds.annmn), function(x) c(summary.no=3,preds.annmn[[x]]))
preds.annmd <- lapply(1:length(preds.annmd), function(x) c(summary.no=4,preds.annmd[[x]]))
preds.annsd <- lapply(1:length(preds.annsd), function(x) c(summary.no=5,preds.annsd[[x]]))
#Dataframe with the min/max/mn/md/sd of the forecasted annual area occupied (preds.ann)
#(min/max/mn/md/sd among years for each scenario, GCM, period and iteration)
preds.ann <- rbind(do.call(rbind,preds.annmin),
do.call(rbind,preds.annmax),
do.call(rbind,preds.annmn),
do.call(rbind,preds.annmd),
do.call(rbind,preds.annsd))
preds.ann <- as.data.frame(preds.ann)
preds.ann <- join(preds.ann,match,by='summary.no',type='left')
preds.ann <- preds.ann[,c(2:4,ncol(preds.ann),5:(ncol(preds.ann)-1))]
#Then, calculate the median of those values across iterations
#(ie, on average, the minimum/maximum/mean/median/sd of annual forecasted values across 21 years for each scenario, GCM, period)
preds.annvar.l <- preds.ann[,1:4]
preds.annvar.l$md <- apply(preds.ann[,5:ncol(preds.ann)],1,median)
preds.annvar <- dcast(preds.annvar.l,scenario + model + period ~ summary,value.var='md')
preds.annvar <- preds.annvar[,c(1:3,6,4,7,5,8)]
#-----------------------------------------------------------------------------#
#Calculate the probability that one or more years in each period falls below a given threshold
th <- 0.67 #0.67 = minimum observed value
#Extracting minimum areas for each scenario, GCM, period, and iteration
mins <- preds.ann[preds.ann$summary=='min',]
#Create table with median probability that at least one year per period is below threshold
#with min and max probabilities among GCMs
mins$pbelow <- apply(mins[,5:1004],1,function(x) sum(x<th)/length(x))
probbelow <- ddply(mins,.(period,scenario),summarize,prob.md=round(median(pbelow),2),
prob.min=round(min(pbelow),2),prob.max=round(max(pbelow),2))
probbelow$scenarioname <- sc$scenarioname[match(probbelow$scenario,sc$scenario)]
#-----------------------------------------------------------------------------#
#Forecast the number of years per period that fall below a given threshold
#First, create dataframe with number of years below threshold for each scenario, GCM, period, and iteration
preds.low <- lapply(win.list,function(x) c(x[1,1:3],apply(x[,5:(n_iter+4)],2,function(xx) sum(xx<th))))
preds.lowyrs <- as.data.frame(do.call(rbind,preds.low))
#Then calculate the probable number of years for each scenario and period (averaged across GCMs)
index.s <- paste(preds.lowyrs$scenario,preds.lowyrs$period,sep='-')
lowyrs.list.s <- split(preds.lowyrs,f=index.s)
lowyrs.summary.s <- unique(preds.lowyrs[,c('scenario','period')])
lowyrs.matlist.s <- lapply(lowyrs.list.s,'[',4:(n_iter+3))
lowyrs.veclist.s <- lapply(lowyrs.matlist.s,unlist)
lowyrs.summary.s$q0.5 <- sapply(lowyrs.veclist.s,median)
lowyrs.summary.s$q0.05 <- sapply(lowyrs.veclist.s,quantile,0.05)
lowyrs.summary.s$q0.25 <- sapply(lowyrs.veclist.s,quantile,0.25)
lowyrs.summary.s$q0.75 <- sapply(lowyrs.veclist.s,quantile,0.75)
lowyrs.summary.s$q0.95 <- sapply(lowyrs.veclist.s,quantile,0.95)
pls <- lowyrs.summary.s
#-----------------------------------------------------------------------------#
#Plot with forecasted number of years below threshold (medians, 50 & 90% CIs), averaged across GCMs for each emission scenario
#(Figs. 5d-f in paper)
par(mfrow=c(1,3),mar=c(0,0,0.3,0),oma=c(1.4,3.5,0.2,0.5),cex=0.9)
plot(0,0,type='n',xlim=c(0,max(pls$scenario)+1),ylim=c(0,21),axes=FALSE,xlab='',ylab='')
axis(1,at=par('usr')[1:2],tcl=0,labels=FALSE)
axis(2,at=par('usr')[3:4],tcl=0,labels=FALSE)
axis(2,at=seq(0,20,by=5),tcl=-0.25,labels=seq(0,20,by=5),las=1,mgp=c(1.5,0.5,0))
axis(3,at=par('usr')[1:2],tcl=0,labels=FALSE)
axis(4,at=par('usr')[3:4],tcl=0,labels=FALSE)
arrows(x0=pls$scenario[pls$period==1],x1=pls$scenario[pls$period==1],y0=pls$q0.05[pls$period==1],y1=pls$q0.95[pls$period==1],
length=0,col=figcol4,lwd=1.2)
arrows(x0=pls$scenario[pls$period==1],x1=pls$scenario[pls$period==1],y0=pls$q0.25[pls$period==1],y1=pls$q0.75[pls$period==1],
length=0,col=figcol4,lwd=2.5)
points(q0.5~scenario,data=pls[pls$period==1,],pch=21,col=figcol4,bg=figcol4)
mtext('2023-2043',side=1,line=0.2,cex=0.9)
legend(x=0,y=21,c('Low','Mod-Low','Mod-High','High'),pch=21,col=figcol4,pt.bg=figcol4,bty='n',cex=0.8,)
plot(0,0,type='n',xlim=c(0,max(pls$scenario)+1),ylim=c(0,21),axes=FALSE,xlab='',ylab='')
axis(1,at=par('usr')[1:2],tcl=0,labels=FALSE)
axis(2,at=par('usr')[3:4],tcl=0,labels=FALSE)
axis(3,at=par('usr')[1:2],tcl=0,labels=FALSE)
axis(4,at=par('usr')[3:4],tcl=0,labels=FALSE)
arrows(x0=pls$scenario[pls$period==2],x1=pls$scenario[pls$period==2],y0=pls$q0.05[pls$period==2],y1=pls$q0.95[pls$period==2],
length=0,col=figcol4,lwd=1.2)
arrows(x0=pls$scenario[pls$period==2],x1=pls$scenario[pls$period==2],y0=pls$q0.25[pls$period==2],y1=pls$q0.75[pls$period==2],
length=0,col=figcol4,lwd=2.5)
points(q0.5~scenario,data=pls[pls$period==2,],pch=21,col=figcol4,bg=figcol4)
mtext('2050-2070',side=1,line=0.2,cex=0.9)
plot(0,0,type='n',xlim=c(0,max(pls$scenario)+1),ylim=c(0,21),axes=FALSE,xlab='',ylab='')
axis(1,at=par('usr')[1:2],tcl=0,labels=FALSE)
axis(2,at=par('usr')[3:4],tcl=0,labels=FALSE)
axis(3,at=par('usr')[1:2],tcl=0,labels=FALSE)
axis(4,at=par('usr')[3:4],tcl=0,labels=FALSE)
arrows(x0=pls$scenario[pls$period==3],x1=pls$scenario[pls$period==3],y0=pls$q0.05[pls$period==3],y1=pls$q0.95[pls$period==3],
length=0,col=figcol4,lwd=1.2)
arrows(x0=pls$scenario[pls$period==3],x1=pls$scenario[pls$period==3],y0=pls$q0.25[pls$period==3],y1=pls$q0.75[pls$period==3],
length=0,col=figcol4,lwd=2.5)
points(q0.5~scenario,data=pls[pls$period==3,],pch=21,col=figcol4,bg=figcol4)
mtext('2080-2100',side=1,line=0.2,cex=0.9)
mtext('Number of years below 0.67 ha',side=2,line=2.0,outer=TRUE,cex=0.9)
#---------------------------------------------------------------------------------------------------------#
# Partitioning uncertainty
#---------------------------------------------------------------------------------------------------------#
#First remove big objects
rm(preds.annmax,preds.annmd,preds.annmin,preds.annmn,preds.annsd,preds.bycp1,preds.bycp4,
preds.bycpm1,preds.bycpm4,c.obs.byperiod,c.obs.list,obs.log,preds.byperiod,preds.byperiod2,
preds.list.cpm1,preds.list.cpm4,preds.list.s,preds.low,split.cy,split.muc,split.mucy)
#-----------------------------------------------------------------------------#
#Forecasts that don't incorporate environmental stochasticity
#(but do account for parameter uncertainty and climate uncertainty)
win.list.noes <- list()
i <- 0
set.seed(44)
for(ss in 1:nrow(sc)){ #scenario
for(mm in 1:nrow(mod)){ #GCM
for(pp in 1:3){ #time period
uyears <- get(paste0('years',pp))
i <- i+1
#Combine ecological covariates in summer submodel in dataframe
cyw <- expand.grid(wk=uweeks,county.ind=ucounties,yr=uyears)
cyw$yr.ind <- cyw$yr - min(cyw$yr) + 1
#Standardize week (want same values as those used in 2004-2018 analysis)
cyw$wk.st <- (cyw$wk-wk.m)/wk.sd
cyw <- join(cyw,springclim[springclim$scenario==ss & springclim$model==mm & springclim$period==pp,
c('yr','spGDD.st','spGDD.st2','spPCP.st','spPCP.st2')],by='yr',type='left')
cyw <- join_all(list(cyw,cov.c[,c('county.ind','cropC.st')],gly.c[,c('county.ind','gly.st')],
avgGDD[avgGDD$scenario==ss & avgGDD$model==mm & avgGDD$period==pp,c('county.ind','avgGDD.st')],
avgPCP[avgPCP$scenario==ss & avgPCP$model==mm & avgPCP$period==pp,c('county.ind','avgPCP.st')]),
by='county.ind',type='left')
cyw <- join(cyw,diffPCP[diffPCP$scenario==ss & diffPCP$model==mm & diffPCP$period==pp,c('county.ind','yr','diffPCP.st','diffPCP.st2')],
by=c('county.ind','yr'),type='left')
cyw <- join(cyw,diffGDD[diffGDD$scenario==ss & diffGDD$model==mm & diffGDD$period==pp,c('county.ind','yr','wk','diffGDD.st','diffGDD.st2')],
by=c('county.ind','yr','wk'),type='left')
cyw$diffavgGDD <- cyw$diffGDD.st*cyw$avgGDD.st
cyw$diffavgPCP <- cyw$diffPCP.st*cyw$avgPCP.st
cyw$glycrop <- cyw$gly.st*cyw$cropC.st
cyw <- cyw[,c('county.ind','yr','yr.ind','wk','wk.st','spGDD.st','spGDD.st2','spPCP.st','spPCP.st2',
'avgGDD.st','diffGDD.st','diffGDD.st2','diffavgGDD',
'avgPCP.st','diffPCP.st','diffPCP.st2','diffavgPCP',
'gly.st','cropC.st','glycrop')]
names(cyw)[6:ncol(cyw)] <- c('spGDD','spGDD2','spPCP','spPCP2',
'avgGDD','diffGDD','diffGDD2','diffavgGDD',
'avgPCP','diffPCP','diffPCP2','diffavgPCP',
'gly','crop','glycrop')
#Calculate summer population index from posterior samples
#Fixed effects
Xcounty <- as.matrix(cbind(rep(1,nrow(cyw)),
cyw[,c('spGDD','spGDD2','spPCP','spPCP2',
'avgGDD','diffGDD','diffGDD2','diffavgGDD',
'avgPCP','diffPCP','diffPCP2','diffavgPCP',
'gly','crop','glycrop')]))
Xalpha <- Xcounty %*% t(alpha)
#Effect of week
Xweeks <- matrix(c(cyw$wk.st,cyw$wk.st*cyw$wk.st),ncol=2,nrow=nrow(cyw),byrow=FALSE)
alphaREweeks <- cbind(alpha.wk,alpha.wk2)