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03-analysis_treatment-zip-global.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.
#############################
## ---- treatment ZIP global --------
# 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")
# data manipulation
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)
# create data frame of stand covariates
dd <- data.frame(treat=factor(datalfoc$treat),tsh=datalfoc$tsh,tsh2=datalfoc$tsh^2)
# model matrix of stand effects (contr.sum is critical here)
mm <- model.matrix(~treat*tsh+treat*tsh2,dd,contrasts=list(treat="contr.sum"))
# position of the beta coefficients associated with bernoulli indicator variable (i.e., treat has 7 terms w/ intercept)
pos <- as.numeric(attr(mm,"assign")+1)
n.betas <- length(pos)
pos.pa <- c(1:6)
n.betas.pa <- length(pos.pa)
pos.pp <- c(1:4)
n.betas.pp <- length(pos.pp)
# Define model in BUGS
cat("
model {
##### Variables ##########################################
## indices: i=site, k=visit, t=year, spp=species
## pa.beta = availability/removal parameters
## pp.beta = perceptibility/distance scale parameters
## dist.sigma = distance scale parameter
## N = detection corrected abundance
## Ntot = population size of total area surveyed
## D = density
## bayesp = Bayesian p-value for model fit
##### PRIORS ###############################################
pa.beta[1] <- logit(p.pa.beta0)
p.pa.beta0 ~ dunif(0,1)
pp.beta[1] ~ dunif(0, 250)
# priors for the w model inclusion terms
# this ensures that each of the 8 model combos has equal probability: Pr(m)= 1/8
w[6] ~ dbern(0.125)
p.w5 <- (1-w[6])*0.143 + w[6]
w[5] ~ dbern(p.w5)
p.w4 <- (1-w[6])*0.286 + w[6]
w[4] ~ dbern(p.w4)
w456 <- w[4]+w[5]+w[6]
p.w3 <- equals(w456,0)*0.5 + (1-equals(w456,0))
w[3] ~ dbern(p.w3)
w56 <- w[5]+w[6]
p.w2 <- equals(w56,0)*0.5 + (1-equals(w56,0))
w[2] ~ dbern(p.w2)
w[1] ~ dbern(1)
# priors for wzi for zero-inflation param
wzi[6] ~ dbern(0.125)
p.wzi5 <- (1-wzi[6])*0.143 + wzi[6]
wzi[5] ~ dbern(p.wzi5)
p.wzi4 <- (1-wzi[6])*0.286 + wzi[6]
wzi[4] ~ dbern(p.wzi4)
wzi456 <- wzi[4]+wzi[5]+wzi[6]
p.wzi3 <- equals(wzi456,0)*0.5 + (1-equals(wzi456,0))
wzi[3] ~ dbern(p.wzi3)
wzi56 <- wzi[5]+wzi[6]
p.wzi2 <- equals(wzi56,0)*0.5 + (1-equals(wzi56,0))
wzi[2] ~ dbern(p.wzi2)
wzi[1] ~ dbern(1)
# priors for wpa for availability
wpa[6] ~ dbern(0.125)
p.wpa5 <- (1-wpa[6])*0.143 + wpa[6]
wpa[5] ~ dbern(p.wpa5)
p.wpa4 <- (1-wpa[6])*0.286 + wpa[6]
wpa[4] ~ dbern(p.wpa4)
wpa456 <- wpa[4]+wpa[5]+wpa[6]
p.wpa3 <- equals(wpa456,0)*0.5 + (1-equals(wpa456,0))
wpa[3] ~ dbern(p.wpa3)
wpa56 <- wpa[5]+wpa[6]
p.wpa2 <- equals(wpa56,0)*0.5 + (1-equals(wpa56,0))
wpa[2] ~ dbern(p.wpa2)
wpa[1] ~ dbern(1)
# priors for wpp for perceptibility
wpp[1] ~ dbern(1) #intercept
for (n in 2:4){ wpp[n] ~ dbern(0.5) }
# set up the vectors/matrices for beta estimation, abundance
for(b1 in 1:n.betas){
# wtemp[b1] <- w[pos[b1]] # this uses GVS
wtemp[b1] <- 1 # this forces you to fit the full model (all terms included)
mean.b[b1] <- post.b[b1]*(1-wtemp[b1]) # prior is either 0 or full-model posterior mean
for(b2 in 1:n.betas){ # set up the precision matrix (inverse variance) # allows for betas to be multivariate, if desired
tau.b[b1,b2] <- equals(b1,b2)*((1/sd.b[b1]^2)*(1-wtemp[b1])) + (wtemp[b1]*b.tau)
} # b2
s.beta[b1] ~ dnorm(mean.b[b1],tau.b[b1,b1]) # all beta coefficients
} # b1
# set up the vectors/matrices for beta estimation, zero-inflation
for(b1 in 1:n.betas){
# wzi.temp[b1] <- wzi[pos[b1]] # this uses GVS
wzi.temp[b1] <- 1 # this forces you to fit the full model (all terms included)
mean.b.zi[b1] <- post.b.zi[b1]*(1-wzi.temp[b1]) # prior is either 0 or full-model posterior mean
for(b2 in 1:n.betas){ # set up the precision matrix (inverse variance) # allows for betas to be multivariate, if desired
tau.b.zi[b1,b2] <- equals(b1,b2)*((1/sd.b.zi[b1]^2)*(1-wzi.temp[b1])) + (wzi.temp[b1]*b.tau.zi)
} # b2
s.beta.psi[b1] ~ dnorm(mean.b.zi[b1],tau.b.zi[b1,b1]) # all beta coefficients
} # b1
# set up the vectors/matrices for beta estimation, availability
for(b1 in 2:n.betas.pa){ # starts at 2 because intercept always requires a diff prior and w=1
# wpa.temp[b1] <- wpa[pos.pa[b1]]
wpa.temp[b1] <- 1
mean.b.pa[b1] <- post.b.pa[b1]*(1-wpa.temp[b1])
for(b2 in 2:n.betas.pa){ # starts at 2 because intercept always requires a diff prior and w=1
tau.b.pa[b1,b2] <- equals(b1,b2)*((1/sd.b.pa[b1]^2)*(1-wpa.temp[b1])) + (wpa.temp[b1]*b.tau.pa)
} # b2
pa.beta[b1] ~ dnorm(mean.b.pa[b1],tau.b.pa[b1,b1]) # all beta coefficients
} # b1
# set up the vectors/matrices for beta estimation, perceptility
for(b1 in 2:n.betas.pp){ # starts at 2 because intercept always requires a diff prior and w=1
#wpp.temp[b1] <- wpp[pos.pp[b1]]
wpp.temp[b1] <- 1
mean.b.pp[b1] <- post.b.pp[b1]*(1-wpp.temp[b1])
for(b2 in 2:n.betas.pp){ # starts at 2 because intercept always requires a diff prior and w=1
tau.b.pp[b1,b2] <- equals(b1,b2)*((1/sd.b.pp[b1]^2)*(1-wpp.temp[b1])) + (wpp.temp[b1]*b.tau.pp)
} # b2
pp.beta[b1] ~ dnorm(mean.b.pp[b1],tau.b.pp[b1,b1]) # all beta coefficients
} # b1
# vector of stand-specific predictors
stand.mu <- mm[,] %*% (s.beta[]*wtemp[])
stand.mu.psi <- mm[,] %*% (s.beta.psi[]*wzi.temp[])
stand.tau.psi <- 1/ (stand.sig.psi*stand.sig.psi)
stand.sig.psi ~ dunif(0,10)
stand.tau <- 1/ (stand.sig*stand.sig)
stand.sig ~ dunif(0,10)
yr.tau <- 1/ (yr.sig*yr.sig)
yr.sig ~ dunif(0,20)
#yr.tau.psi <- 1/ (yr.sig.psi*yr.sig.psi)
#yr.sig.psi ~ dunif(0,20)
obs.tau <- 1/ (obs.sig*obs.sig)
obs.sig ~ dunif(0,20)
b.tau <- 0.01
b.tau.zi <- 0.01
b.tau.pa <- 0.01
b.tau.pp <- 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]) <- wpa[1]*pa.beta[1] + wpa.temp[2]*pa.beta[2]*hr[i,t] + wpa.temp[3]*pa.beta[3]*date[i,t] +
wpa.temp[4]*pa.beta[4]*date2[i,t] +
wpa.temp[5]*pa.beta[5]*date[i,t]*hr[i,t] + wpa.temp[6]*pa.beta[6]*date[i,t]*date2[i,t]*hr[i,t]
log(dist.sigma[i,t]) <- wpp[1]*log(pp.beta[1]) + wpp.temp[2]*pp.beta[2]*densiom[i,t] + wpp.temp[3]*pp.beta[3]*noise[i,t] + wpp.temp[4]*pp.beta[4]*ba[i] + obs.eps[obs[i,t]]
##### 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])
logit(psi[i,t]) <- psi.beta.s[stand.id[i]] #+ yr.eps.psi[t]
log(lambda[i,t]) <- lam.beta.s[stand.id[i]] + yr.eps[t]
##### 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
# Random effects
for (s in 1:S){ psi.beta.s[s] ~ dnorm(stand.mu.psi[s], stand.tau.psi)
lam.beta.s[s] ~ dnorm(stand.mu[s], stand.tau) } #S
for (y in 1:9){ yr.eps[y] ~ dnorm(0, yr.tau) }
#yr.eps.psi[y] ~ dnorm(0, yr.tau.psi) } # y
for (o in 1:28){ obs.eps[o] ~ dnorm(0, obs.tau)} # o
##### 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
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
} # End model
" ,file="./T-zip-global.txt")
# CAUTION: These next lines run the model and
# take a VERY long time to run
# (>1 week, each species took 4 days)
# We ran these on an HPC and specified the
# loop to run 4-5 species sequentially.
# poor model fit for these species
# BOCH, GCKI, GRAJ, MAWA, YBFL, YPWA
spp.zi <- c(10, 11, 3, 5, 2, 8)
for (i in spp.zi){ #Create 5 files: 1:4, 5:8, 9:12, 13:16, 17:19
try(rm("out"))
spp <- spp.list.foc[i]
spp.num<- which(dimnames(nobs)[[3]]==spp)
# Inits and parameters to save
# Crunch the numbers, reformat
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
# remove comments to add covariates
inits <- function(){ list(
N = Nav,
p.pa.beta0= runif(1, 0.3, 0.8),
pp.beta= c(runif(1, 20, 65), rep(0, datalfoc$nCovsPP-2)),
s.beta= runif(21, -0.1, 0.1),
s.beta.psi= c(5,runif(20, -0.1, 0.1)),
stand.sig.psi= runif(1, 0, 0.1),
stand.sig= runif(1, 0, 0.1),
obs.sig= runif(1, 0, 0.1),
yr.sig= runif(1, 0, 0.1)
) }
params <- c("pa.beta", "pp.beta",
"Ntot", "D",
"stand.sig", "stand.sig.psi", "s.beta", "s.beta.psi",
"bayesp", "w", "wzi", "wpa", "wpp",
"yr.eps", "yr.sig", "yr.eps.psi", "yr.sig.psi", "obs.eps", "obs.sig"
)
datalfoc$nobs <- nobs[,,spp]
datalfoc$dclass <- dclass[datalfoc$species==spp.num]
datalfoc$int <- int[datalfoc$species==spp.num]
datalfoc$site <- site[datalfoc$species==spp.num]
datalfoc$yr_rot <- yr_rot[datalfoc$species==spp.num]
datalfoc$L <- length(datalfoc$species[datalfoc$species==spp.num])
# new objects for beta estimation
datalfoc$mm <- mm
datalfoc$pos <- pos
datalfoc$pos.pa <- pos.pa
datalfoc$pos.pp <- pos.pp
datalfoc$n.betas <- n.betas
datalfoc$n.betas.pa <- n.betas.pa
datalfoc$n.betas.pp <- n.betas.pp
# these should be replaced with actual posterior means & sds from a global model run to implement GVS
datalfoc$post.b <- rep(0, 21) # out$mean$post.b
datalfoc$sd.b <- rep(100, 21)
datalfoc$post.b.zi <- rep(0, 21) # out$mean$post.b
datalfoc$sd.b.zi <-rep(100, 21)
datalfoc$post.b.pa <- rep(0, 6) # out$mean$post.b
datalfoc$sd.b.pa <- rep(100, 6)
datalfoc$post.b.pp <- rep(0, 4) # out$mean$post.b
datalfoc$sd.b.pp <- rep(100, 4)
# MCMC settings
ni <- 200000 ; nb <- 100000 ; nt <- 10 ; nc <- 6 ; na=10000
#ni <- 100 ; nb <- 50 ; nt <- 1 ; nc <- 1 ; na <- 100
# Run JAGS
out <- jags(datalfoc, inits=inits,
params, "./T-zip-global.txt",
n.thin=nt, n.chains=nc,
n.burnin=nb, n.iter=ni, n.adapt=na
, parallel = T, modules=c("glm"),
codaOnly= "N")
fn<- paste( "./", spp, "_T-zip-global.RData", sep="" )
save(list= c("out", "datalfoc"), file=fn)
}