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MAPR_integrated_population_model_v3.r
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MAPR_integrated_population_model_v3.r
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##########################################################################
#
# MACGILLIVRAY PRION POPULATION MODEL FOR GOUGH ISLAND
#
##########################################################################
# population model adapted from Jiguet, F., Robert, A., Micol, T. and Barbraud, C. (2007), Quantifying stochastic and deterministic threats to island seabirds: last endemic prions face extinction from falcon peregrinations. Animal Conservation, 10: 245-253. doi:10.1111/j.1469-1795.2007.00100.x
# implemented in JAGS based on Kery and Schaub 2012
# written by Steffen.oppel@rspb.org.uk in May 2020
# revised in June 2020: start projection in 1955 with 5 million pairs, 2001 had 1 million pairs, project to 2050 (100 years)
library(tidyverse)
library(jagsUI)
library(data.table)
library(lubridate)
library(popbio)
filter<-dplyr::filter
select<-dplyr::select
#########################################################################
# 1. LOAD AND PREPARE DATA FOR ADULT ANNUAL SURVIVAL ESTIMATION
#########################################################################
##### LOAD FORMATTED RINGING DATA ###########
setwd("C:/STEFFEN/RSPB/UKOT/Gough/ANALYSIS/SeabirdSurvival")
## run the RODBC import of CMR data in a 32-bit version of R
system(paste0("C:/PROGRA~1/R/R-35~1.1/bin/i386/Rscript.exe ", shQuote("C:\\STEFFEN\\RSPB\\UKOT\\Gough\\ANALYSIS\\SeabirdSurvival\\RODBC_CMR_import.R")), wait = TRUE, invisible = FALSE, intern = T)
try(setwd("C:\\STEFFEN\\RSPB\\UKOT\\Gough\\ANALYSIS\\SeabirdSurvival"), silent=T)
load("GOUGH_seabird_CMR_data.RData")
###### FILTER DATA FROM RAW CONTACTS ########
contacts<-contacts %>% filter(SpeciesCode %in% c("MAPR","BBPR","PRIO")) %>% filter(Location=="Prion Cave")
head(contacts) ## seabird count data
EncHist<-contacts %>% group_by(BirdID,Contact_Year) %>%
summarise(n=length(Date_Time)) %>%
spread(key=Contact_Year,value=n,fill=0)
#### FORMAT FOR SIMPLE CJS MODEL ############
CH<-as.matrix(EncHist[,2:ncol(EncHist)], dimnames=F)
CH<-ifelse(CH>0,1,0)
head(CH)
# ELIMINATE TRANSIENTS ONLY OBSERVED IN A SINGLE YEAR
del <- apply(CH[,1:ncol(CH)], 1, sum)
dim(CH)
rCH<-CH[!(del==1),]
dim(rCH)
# Compute vector with occasion of first capture
get.first <- function(x) min(which(x==1))
f <- apply(rCH, 1, get.first)
#########################################################################
# 2. LOAD AND PREPARE DATA FOR BREEDING SUCCESS SUMMARY
#########################################################################
## run the RODBC import in a 32-bit version of R
system(paste0("C:/PROGRA~1/R/R-35~1.1/bin/i386/Rscript.exe ", shQuote("C:\\STEFFEN\\RSPB\\UKOT\\Gough\\ANALYSIS\\SeabirdBreedingSuccess\\RODBC_nest_import.r")), wait = TRUE, invisible = FALSE, intern=T)
#system(paste0(Sys.getenv("R_HOME"), "/bin/i386/Rscript.exe ", shQuote("C:\\Users\\Gough Conservation\\Documents\\Gough Birders\\2018-2019\\12.Monthly reports 2018-19\\RODBC_imports.r")), wait = FALSE, invisible = FALSE)
try(setwd("C:\\STEFFEN\\RSPB\\UKOT\\Gough\\ANALYSIS\\SeabirdBreedingSuccess"), silent=T)
#try(setwd("C:\\Users\\Gough Conservation\\Documents\\Gough Birders\\2018-2019\\12.Monthly reports 2018-19"), silent=T)
load("GOUGH_nest_data.RData")
head(nestsDB) ## nest data
head(visDB) ## nest visit data
## SELECT DATA FOR TARGET SPECIES AND SUMMARISE NEST SUCCESS ####
head(nestsDB)
succ<-nestsDB %>% filter(Species=="MAPR") %>% filter(Year>2013) %>%
mutate(count=1) %>%
group_by(Species,Year) %>%
summarise(R=sum(count),J=sum(SUCCESS))
#########################################################################
# 3. Specify BASIC POPULATION MODEL WITH TWO SCENARIOS
#########################################################################
### DEMOGRAPHIC PARAMETERS
#Juvenile survival: 0.728 from Barbraud & Weimerskirch (2003), Oro et al. (2004)
#Immature survival: 0.894 fromBarbraud & Weimerskirch (2003)
#Adult survival: 0.894 from Barbraud & Weimerskirch (2003)
#Age at maturity: 4 from Warham (1990), Oro et al. (2004)
#Female breeding success: 0.519 from Nevoux & Barbraud (2005)
### Calculation of stable age distribution
### CREATING THE POPULATION MATRIX ###
seabird.matrix<-matrix(c(
0,0,0,0,0.519*0.5,
0.728,0,0,0,0,
0,0.894,0,0,0,
0,0,0.894,0,0,
0,0,0,0.894,0.894),ncol=5, byrow=T)
stable.stage(seabird.matrix)
setwd("C:\\STEFFEN\\RSPB\\UKOT\\Gough\\ANALYSIS\\PopulationModel\\MAPR")
sink("MAPR_IPM_v4.jags")
cat("
model {
#-------------------------------------------------
# integrated population model for the MacGillivray's Prion population
# - age structured model with 4 age classes
# - adult survival based on CMR ringing data
# - productivity based on Prion Cave nest monitoring data
# - simplified population process with informed prior for adults skipping breeding and uninformed immatures recruiting
# - TWO future scenarios to project population growth with and without eradication
# -------------------------------------------------
#-------------------------------------------------
# 1. PRIORS FOR ALL DATA SETS
#-------------------------------------------------
# -------------------------------------------------
# 1.1. Priors and constraints FOR FECUNDITY
# -------------------------------------------------
mean.fec ~ dunif(0,0.2) ## uninformative prior for CURRENT FECUNDITY
orig.fec ~ dunif(0.155,0.165) ## uninformative prior for ORIGINAL FECUNDITY
full.fec ~ dnorm(0.519,100) T(0.1,0.52) ## prior for full fecundity without predation from Nevoux & Barbraud (2005) - very high precision
fec.decrease <- (mean.fec-orig.fec)/(66-1)
# -------------------------------------------------
# 1.2. Priors and constraints FOR SURVIVAL
# -------------------------------------------------
phi ~ dunif(0.7, 1)
p ~ dunif(0, 1)
juv.surv <- juv.surv.prop*phi
juv.surv.prop ~ dnorm(mean.juv.surv.prop,1000) T(0,1)
#-------------------------------------------------
# 2. LIKELIHOODS AND ECOLOGICAL STATE MODEL
#-------------------------------------------------
# -------------------------------------------------
# 2.1. System process: female based matrix model
# -------------------------------------------------
for (scen in 1:2){
### INITIAL VALUES FOR COMPONENTS FOR YEAR 1 - based on stable stage distribution from previous model
JUV[1,scen]<-round(Ntot.breed[1,scen]*0.5*(orig.fec))
N1[1,scen]<-round(Ntot.breed[1,scen]*0.5*(orig.fec)*juv.surv)
N2[1,scen]<-round(Ntot.breed[1,scen]*0.5*(orig.fec)*juv.surv*phi)
N3[1,scen]<-round(Ntot.breed[1,scen]*0.5*(orig.fec)*juv.surv*phi*phi)
Ntot.breed[1,scen] ~ dunif(4000000,5000000) # initial value of population size
for (tt in 2:66){
## DECREASING PROBABILITY OF A GOOD YEAR FROM 1 in 1956 to 0.2 in 2015
fec.proj[scen,tt]<-orig.fec + fec.decrease*tt ## models linear decrease of fecundity
## THE PRE-BREEDERS ##
JUV[tt,scen] ~ dbin(fec.proj[scen,tt],round(0.5 * Ntot.breed[tt,scen])) ### number of locally produced FEMALE chicks
N1[tt,scen] ~ dbin(juv.surv, max(2,round(JUV[tt-1,scen]))) ### number of 1-year old survivors
N2[tt,scen] ~ dbin(phi, max(2,round(N1[tt-1,scen]))) ### number of 2-year old survivors
N3[tt,scen] ~ dbin(phi, max(2,round(N2[tt-1,scen]))) ### number of 3-year old survivors
## THE BREEDERS ##
Ntot.breed[tt,scen] ~ dbin(phi, max(2,round(N3[tt-1,scen]+Ntot.breed[tt-1,scen]))) ### the annual number of breeding birds is the sum of old breeders and recent recruits
} # tt
for (tt in 67:PROJ){
## SELECT CURRENT OR RODENT FREE FECUNDITY FOR FUTURE
fec.proj[scen,tt]<-max(mean.fec,(scen-1)*full.fec) ## takes current fecundity for scenario 1 and full fecundity for scenario 2
## THE PRE-BREEDERS ##
JUV[tt,scen] ~ dbin(fec.proj[scen,tt],round(0.5 * Ntot.breed[tt,scen])) ### need a discrete number otherwise dbin will fail, dpois must be >0
N1[tt,scen] ~ dbin(juv.surv, max(2,round(JUV[tt-1,scen]))) ### number of 1-year old survivors
N2[tt,scen] ~ dbin(phi, max(2,round(N1[tt-1,scen]))) ### number of 2-year old survivors
N3[tt,scen] ~ dbin(phi, max(2,round(N2[tt-1,scen]))) ### number of 3-year old survivors
## THE BREEDERS ##
Ntot.breed[tt,scen] ~ dbin(phi, max(2,round(N3[tt-1,scen]+Ntot.breed[tt-1,scen]))) ### the annual number of breeding birds is the sum of old breeders and recent recruits
} # tt
} # scen
# -------------------------------------------------
# 2.2. Likelihood for fecundity: Poisson regression from the number of surveyed broods
# -------------------------------------------------
for (t in 1:(T.fec)){ ### T-1 or not
J[t] ~ dpois(rho.fec[t])
rho.fec[t] <- R[t]*mean.fec
} # close loop over every year in which we have fecundity data
# -------------------------------------------------
# 2.3. Likelihood for adult and juvenile survival from CMR
# -------------------------------------------------
for (i in 1:nind){
# Define latent state at first capture
z[i,f[i]] <- 1
for (t in (f[i]+1):n.occasions){
# State process
z[i,t] ~ dbern(mu1[i,t])
mu1[i,t] <- phi * z[i,t-1]
# Observation process
y[i,t] ~ dbern(mu2[i,t])
mu2[i,t] <- p * z[i,t]
} #t
} #i
# -------------------------------------------------
# 4. DERIVED POPULATION GROWTH RATE
# -------------------------------------------------
## DERIVED POPULATION GROWTH RATE
for (scen in 1:2){
for (tt in 1:33){
lambda[tt,scen]<-Ntot.breed[tt+67,scen]/max(1,Ntot.breed[tt+66,scen])
loglam[tt,scen]<-log(lambda[tt,scen])
} ## end of tt
growth.rate[scen] <- exp((1/(33))*sum(loglam[1:(33),scen])) ### geometric mean growth rate
} ## end of scen
} ## END MODEL LOOP
",fill = TRUE)
sink()
#########################################################################
# 4. SET UP AND RUN INTEGRATED POPULATION MODEL
#########################################################################
# Bundle data
jags.data <- list(## survival
y = rCH,
f = f,
n.occasions = dim(rCH)[2],
nind = dim(rCH)[1],
mean.juv.surv.prop= 0.728/0.894, ## juvenile survival based on proportion of adult survival from Jiguet 2007
## fecundity
R =succ$R,
J=succ$J,
T.fec=length(succ$J),
## population process
#Ntot.breed=matrix(NA,nrow=100,ncol=2),
PROJ=100)
#jags.data$Ntot.breed[46,1:2]<-800000
#jags.data$Ntot.breed[1,1:2]<-4500000
# Initial values
inits <- function(){list(phi = runif(1, 0.7, 1),
p = runif(1, 0, 1))}
# Parameters monitored
parameters <- c("orig.fec","mean.fec","full.fec","fec.decrease","juv.surv","phi","p","growth.rate","lambda","Ntot.breed")
# MCMC settings
ni <- 10000
nt <- 2
nb <- 5000
nc <- 4
# Call JAGS from R (model created below)
MAPR_IPM <- autojags(jags.data, inits, parameters, "C:\\STEFFEN\\RSPB\\UKOT\\Gough\\ANALYSIS\\PopulationModel\\MAPR\\MAPR_IPM_v4.jags",
n.chains = nc, n.thin = nt, n.burnin = nb,parallel=T) # n.iter = ni,
#########################################################################
# 5. SUMMARISE OUTPUT AND PLOT POPULATION TRAJECTORY
#########################################################################
## compile output
out<-as.data.frame(MAPR_IPM$summary)
out$parameter<-row.names(MAPR_IPM$summary)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# CREATE OUTPUT TABLE FOR REPORT /MANUSCRIPT
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
head(out)
TABLE1<-out %>% filter(parameter %in% c('orig.fec','mean.fec','full.fec','fec.decrease','phi','juv.surv','growth.rate[1]','growth.rate[2]')) %>%
select(parameter,c(5,3,7))
names(TABLE1)<-c("Parameter","Median","lowerCL","upperCL")
TABLE1$Parameter<-c("original fecundity","current fecundity","mouse-free fecundity","fecundity decrease","first year survival","adult survival","population growth rate (no eradication)","population growth rate (with eradication)")
TABLE1
fwrite(TABLE1,"MAPR_demographic_parameter_estimates_v4.csv")
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# GRAPH 1: POPULATION TRAJECTORY UNDER BOTH SCENARIOS
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
## retrieve the past population estimates (2006-2019)
MAPRpop<-out[(grep("Ntot.breed\\[",out$parameter)),c(12,5,4,6)] %>%
mutate(Year=rep(seq(1956,2055),2)) %>%
mutate(scenario=as.numeric(str_extract_all(parameter,"\\(?[0-9]+\\)?", simplify=TRUE)[,2])) %>%
mutate(Scenario=ifelse(scenario==1,"no eradication","with eradication")) %>%
filter(!(Scenario=="with eradication" & Year<2025)) %>%
#filter((Scenario=="with eradication")) %>%
#rename(parm=parameter,median=`50%`,lcl=`2.5%`,ucl=`97.5%`) %>%
rename(parm=parameter,median=`50%`,lcl=`25%`,ucl=`75%`) %>%
dplyr::select(parm,Scenario,Year,median,lcl,ucl)
### CREATE PLOT FOR BASELINE TRAJECTORY
MAPRpop$ucl[MAPRpop$ucl>6000000]<-6000000
ggplot()+
geom_line(data=MAPRpop, aes(x=Year, y=median, color=Scenario), size=1)+
geom_ribbon(data=MAPRpop,aes(x=Year, ymin=lcl,ymax=ucl, fill=Scenario),alpha=0.2)+
## format axis ticks
scale_y_continuous(name="N MacGillivray's Prion on Gough (1000s)", limits=c(0,5000000),breaks=seq(0,5000000,500000),labels=seq(0,5000,500))+
scale_x_continuous(name="Year", limits=c(1956,2056), breaks=seq(1956,2056,20), labels=as.character(seq(1956,2056,20)))+
## add count data
geom_segment(aes(x=1956, xend=1956,y=0.4*10000000,yend=0.5*10000000),lineend = "round", size=2, colour="darkblue") +
geom_segment(aes(x=2000, xend=2000,y=0.4*1500000,yend=0.5*2000000),lineend = "round", size=2, colour="darkblue") +
## beautification of the axes
theme(panel.background=element_rect(fill="white", colour="black"), panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
axis.text.y=element_text(size=18, color="black"),
axis.text.x=element_text(size=14, color="black"),
axis.title=element_text(size=18),
legend.text=element_text(size=12, color="black"),
legend.title=element_text(size=14, color="black"),
legend.key = element_rect(fill = NA),
strip.text.x=element_text(size=18, color="black"),
strip.background=element_rect(fill="white", colour="black"))
ggsave("MAPR_population_projection_v4_CI50.jpg", width=9, height=6)