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01-analysis_basic-models-pois-ZIP.R
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01-analysis_basic-models-pois-ZIP.R
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############################
# Supplemental materials for:
# B. W. Rolek, D. J. Harrison, D. W. Linden, C. S. Loftin,
# P. B. Wood. 2021. Associations among breeding
# conifer-associated birds, forestry treatments,
# years-since-harvest, and vegetation characteristics in
# regenerating stands.
#############################
## ---- basic Poisson --------
#############################################
# This file is not needed to replicate analyses.
# We provide the simplest version of the model used
# as a template for other studies
#############################################
# software used
# JAGS 4.3.0
# R version 4.0.2 (2020-06-22) -- "Taking Off Again"
library (jagsUI) # v1.5.1
load ("./DATA.Rdata")
# set up data
datalfoc$SPP <- length(spp.list.foc)
yr <- array(NA, dim=c(dim (ab)[1], 9) )
yr[,1:3] <- 1; yr[,4:6] <- 2; yr[,7:9] <- 3
datalfoc$yr <- yr
s.year <- array(NA, dim=c(114, 9))
s.year[,1:3] <- 1; s.year[,4:6] <- 2; s.year[,7:9] <- 3
datalfoc$s.year <- s.year
datalfoc$ba <- datalfoc$CovsLam[, "ba"]
nobs <- datalfoc$nobs
dclass <- datalfoc$dclass
int <- datalfoc$int
site <- datalfoc$site
yr_rot <- datalfoc$yr_rot
# print sample sizes
apply(ab2[,1:2,,,dimnames(ab2)[[5]] %in% spp.list.foc], c(5), sum, na.rm=T)
####################################
# (1) basic Poisson model
####################################
cat("
model {
##### PRIORS ###############################################
pa.beta <- logit(p.pa.beta0)
p.pa.beta0 ~ dunif(0,1)
pp.beta ~ dunif(0, 250)
lam.beta ~ dnorm(0, 0.01)
##### DISTANCE AND REMOVAL #####################################
for (l in 1:L) {
int[l] ~ dcat(pi.pa.c[site[l], yr_rot[l], ]) # removal class frequencies
dclass[l] ~ dcat(pi.pd.c[site[l], yr_rot[l], ]) # distance class frequencies
} # L
# Distance
for(b in 1:nD){
f[b] <- (2*midpt[b]*delta)/(B*B) # radial density function for point counts, change for line transects
}
for (i in 1:nsites){
for(t in 1:YR){
for(b in 1:nD){
g[i,t,b] <- exp(-midpt[b]*midpt[b]/(2*dist.sigma[i,t]*dist.sigma[i,t])) # half-normal distance function
pi.pd[i,t,b] <- g[i,t,b]*f[b]
pi.pd.c[i,t,b] <- pi.pd[i,t,b]/pdet[i,t]
} #nD
pdet[i,t] <- sum(pi.pd[i,t,1:nD]) # Distance class probabilities
# Removal
for (r in 1:R){
pi.pa[i,t,r] <- p.a[i,t]*pow(1-p.a[i,t], (r-1))
pi.pa.c[i,t,r] <- pi.pa[i,t,r] / pcap[i,t]
} #R
pcap[i,t] <- sum(pi.pa[i,t,1:R])
# Detection models
pmarg[i,t] <- pcap[i,t] * pdet[i,t]
logit(p.a[i,t]) <- pa.beta # add covariates for availability (time-removal) here
log(dist.sigma[i,t]) <- log(pp.beta) # add covariates for perceptibility (distance) here
##### POINT-LEVEL ABUNDANCE ###########################
nobs[i,t] ~ dbin(pmarg[i,t], N[i,t])
N[i,t] ~ dpois(lambda[i,t])
log(lambda[i,t]) <- lam.beta # add covariates for abundance here
##### GOODNESS OF FIT #######################################
nobs.fit[i,t] ~ dbin(pmarg[i,t], N[i,t]) # create new realization of model
e.p[i,t] <- pmarg[i,t] * N[i,t] # original model prediction
E.p[i,t] <- pow((nobs[i,t]- e.p[i,t]),2)/(e.p[i,t]+0.5)
E.New.p[i,t]<- pow((nobs.fit[i,t]-e.p[i,t]),2)/(e.p[i,t]+0.5)
}} #YR #nsites
fit.p <- sum(E.p[1:nsites,1:YR])
fit.new.p <- sum(E.New.p[1:nsites,1:YR])
bayesp<-step(fit.new.p-fit.p) # Bayesian p-value for availability model. =0.5 is good fit, near 0 or 1 is poor fit
##### DERIVED QUANTITIES ####################################
for(t in 1:YR){
Ntot[t] <- sum(N[1:nsites,t])
D[t] <- Ntot[t] / ((3.14*B*B*nsites)/10000) # dens per ha
} #YR
} # End model
",file="./model-basic-Poisson.txt")
for (i in 1:19){
spp <- spp.list.foc[i]
spp.num<- which(dimnames(nobs)[[3]]==spp)
datalfoc$nobs <- Nav <- apply(ab2[,1:2,,,spp], c(1,4),sum, na.rm=T)
Mst <- apply(Nav, c(1), max, na.rm=T) +1
inits <- function(){ list(
N = Nav,
p.pa.beta0= runif(1, 0.01, 0.99),
pp.beta= runif(1, 5, 100)
) }
params <- c("pa.beta", "p.pa.beta", "pp.beta",
"lam.beta",
"Ntot", "D", "bayesp"
)
# MCMC settings
ni <- 200000 ; nb <- 100000 ; nt <- 10 ; nc <- 6 ; na=10000
# Run JAGS
out <- jags(datalfoc, inits=inits, params,
"./model-basic-Poisson.txt",
n.thin=nt, n.chains=nc,
n.burnin=nb, n.iter=ni, n.adapt=na,
parallel = T, modules=c("glm")
)
fn<- paste( "./", spp, "_basic-pois.RData", sep="" )
save(list= c("out"), file=fn)
}
## ---- basic ZIP --------
# software used
# JAGS 4.3.0
# R version 4.0.2 (2020-06-22) -- "Taking Off Again"
library (jagsUI) # v1.5.1
load ("./DATA.Rdata")
# set up data
datalfoc$SPP <- length(spp.list.foc)
yr <- array(NA, dim=c(dim (ab)[1], 9) )
yr[,1:3] <- 1; yr[,4:6] <- 2; yr[,7:9] <- 3
datalfoc$yr <- yr
s.year <- array(NA, dim=c(114, 9))
s.year[,1:3] <- 1; s.year[,4:6] <- 2; s.year[,7:9] <- 3
datalfoc$s.year <- s.year
datalfoc$ba <- datalfoc$CovsLam[, "ba"]
nobs <- datalfoc$nobs
dclass <- datalfoc$dclass
int <- datalfoc$int
site <- datalfoc$site
yr_rot <- datalfoc$yr_rot
# print sample sizes
apply(ab2[,1:2,,,dimnames(ab2)[[5]] %in% spp.list.foc], c(5), sum, na.rm=T)
###################################
# (2) basic zero-inflated Poisson model
###################################
cat("
model {
##### PRIORS ###############################################
pa.beta <- logit(p.pa.beta)
p.pa.beta ~ dunif(0,1)
pp.beta ~ dunif(0, 250)
lam.beta ~ dnorm(0, 0.01)
psi.beta <- logit(p.psi.beta)
p.psi.beta ~ dunif(0,1)
##### DISTANCE AND REMOVAL #####################################
for (l in 1:L) {
int[l] ~ dcat(pi.pa.c[site[l], yr_rot[l], ]) # removal class frequencies
dclass[l] ~ dcat(pi.pd.c[site[l], yr_rot[l], ]) # distance class frequencies
} # L
# Distance
for(b in 1:nD){
f[b] <- (2*midpt[b]*delta)/(B*B) # radial density function for point counts, change for line transects
}
for (i in 1:nsites){
for(t in 1:YR){
for(b in 1:nD){
g[i,t,b] <- exp(-midpt[b]*midpt[b]/(2*dist.sigma[i,t]*dist.sigma[i,t])) # half-normal distance function
pi.pd[i,t,b] <- g[i,t,b]*f[b]
pi.pd.c[i,t,b] <- pi.pd[i,t,b]/pdet[i,t]
} #nD
pdet[i,t] <- sum(pi.pd[i,t,1:nD]) # Distance class probabilities
# Removal
for (r in 1:R){
pi.pa[i,t,r] <- p.a[i,t]*pow(1-p.a[i,t], (r-1))
pi.pa.c[i,t,r] <- pi.pa[i,t,r] / pcap[i,t]
} #R
pcap[i,t] <- sum(pi.pa[i,t,1:R])
# Detection models
pmarg[i,t] <- pcap[i,t] * pdet[i,t]
logit(p.a[i,t]) <- pa.beta # add covariates for availability (time-removal) here
log(dist.sigma[i,t]) <- log(pp.beta) # add covariates for perceptibility (distance) here
##### POINT-LEVEL ABUNDANCE ###########################
nobs[i,t] ~ dbin(pmarg[i,t], N[i,t])
N[i,t] ~ dpois(lambda.eff[i,t])
lambda.eff[i,t] <- lambda[i,t] * w.lam[i,t]
w.lam[i,t] ~ dbern(psi[i,t])
log(lambda[i,t]) <- lam.beta # add covariates for abundance
logit(psi[i,t]) <- psi.beta # add covariates for habitat suitability
# If not running set inits near psi=1 on logit scale. For example psi.beta=10
##### GOODNESS OF FIT #######################################
nobs.fit[i,t] ~ dbin(pmarg[i,t], N[i,t]) # create new realization of model
e.p[i,t] <- pmarg[i,t] * N[i,t] # original model prediction
E.p[i,t] <- pow((nobs[i,t]- e.p[i,t]),2)/(e.p[i,t]+0.5)
E.New.p[i,t]<- pow((nobs.fit[i,t]-e.p[i,t]),2)/(e.p[i,t]+0.5)
}} #YR #nsites
fit.p <- sum(E.p[1:nsites,1:YR])
fit.new.p <- sum(E.New.p[1:nsites,1:YR])
bayesp<-step(fit.new.p-fit.p) # Bayesian p-value for availability model. =0.5 is good fit, near 0 or 1 is poor fit
##### DERIVED QUANTITIES ####################################
for(t in 1:YR){
Ntot[t] <- sum(N[1:nsites,t])
D[t] <- Ntot[t] / ((3.14*B*B*nsites)/10000) # dens per ha
} #YR
} # End model
",file="./model-basic-ZIP.txt")
for (i in 1:19){
spp <- spp.list.foc[i]
spp.num<- which(dimnames(nobs)[[3]]==spp)
datalfoc$nobs <- Nav <- apply(ab2[,1:2,,,spp], c(1,4),sum, na.rm=T)
Mst <- apply(Nav, c(1), max, na.rm=T) +1
inits <- function(){ list(
N = Nav, p.psi.beta= 0.99, # setting psi near 1 helps model run
p.pa.beta0= runif(1, 0.1, 0.9),
pp.beta= runif(1, 5, 100)
) }
params <- c("pa.beta", "p.pa.beta", "pp.beta",
"lam.beta", "psi.beta", "p.psi.beta",
"Ntot", "D", "bayesp"
)
# MCMC settings
ni <- 200000 ; nb <- 100000 ; nt <- 10 ; nc <- 6 ; na=10000
# Run JAGS
out <- jags(datalfoc, inits=inits, params,
"./model-basic-ZIP.txt",
n.thin=nt, n.chains=nc,
n.burnin=nb, n.iter=ni, n.adapt=na,
parallel = T, modules=c("glm")
)
fn<- paste( "./", spp, "_basic-ZIP.RData", sep="" )
save(list= c("out"), file=fn)
}