Supplement 2
Code for R and Bugs models

setwd("C:/Data/Documents/R")   #Working Directory
require(R2WinBUGS)
require(BRugs)
y0000=read.csv(file="C:/Data/Documents/R/TTI_Seagrass.csv", header = TRUE)
y000<-  subset(y00000,ZONE=="Gulf")  # Use only offshore data
y00<-   subset(y0000,SPP=="Sf")  # Choose Species
y0<-   subset(y000,SEASON=="Spring")  # Choose Season
y<-y0$DROPS # Number of camera drops

y.strata<-c(1,2,3,4,5,y0$Strata) # "unknown" data from each stratum to estimate histograms
y.observed<-c(NA,NA,NA,NA,NA,as.numeric(gsub(8,NA,y)))  # observations with 0-7 drops
y.censored<-c(0,0,0,0,0,((as.logical(y-8)-1)*(-8))) # observations with 8 positive drops

num.y<-length(y.observed)
num.strata = 5
nChains = 5
nThin = 7
nBurn = 140000
nUpdate = 140000

# model specification in WinBUGS
modelFilename = 'seagrass_bugs.txt'
cat('
model {
        for (i in 1:num.y) {
            y.observed[i]  ~ dpois(poisson.lambda.ind[i])I(y.censored[i],100) 
            poisson.lambda0.ind[i] ~ dgamma(gamma.r.ind[i],gamma.mu.ind[i])
            poisson.lambda.ind[i] <- max(.001,(poisson.lambda0.ind[i]*(1-u[i]) ))
            gamma.mu.ind[i]<-gamma.mu.strata[y.strata[i]]                                                  
            gamma.r.ind[i]<-gamma.r.strata[y.strata[i]]
            u[i]~ dbern(p0.strata[y.strata[i]])                
        }
        for (j in 1:num.strata) {
            gamma.mu0[j] ~ dunif(.001,1000)
            gamma.mu.strata[j]<-sqrt(gamma.mu0[j])
            gamma.r0[j] ~ dunif(.001,1000)
            gamma.r.strata[j] <-sqrt(gamma.r0[j])
            p0.strata[j] ~ dunif(0,1)
            nb.mu[j]  <- cut(gamma.r.strata[j])/ cut(gamma.mu.strata[j])
            nb.p[j] <- 1-pow((8/(nb.mu[j]+8)),8)
            expected[j] <- (nb.p[j]*(1-cut(p0.strata[j])))
            observed.strata[j] <- cut(y.observed[j])
        }
        #differences between adjacent strata 
        d54<-expected[5]-expected[4]  
        d43<-expected[4]-expected[3]
        d32<-expected[3]-expected[2]
        d21<-expected[2]-expected[1]
}
', fill=TRUE, file=modelFilename)


bugs.data(data=list( num.y=num.y, y.observed=y.observed,num.strata=num.strata, 
y.censored=y.censored,y.strata=y.strata), dir = getwd(), digits = 5)

inits = function() {
    p0.strata = c(.5,.5,.5,.5,.5)
    gamma.r0 = runif(5,.001,1000)
    gamma.mu0 = runif(5,.001,1000)
    list(p0.strata=p0.strata,gamma.r0=gamma.r0,gamma.mu0=gamma.mu0)
}

bugsInits(inits, numChains=nChains ,fileName = file.path(getwd(), 
    paste("inits", 1:nChains, ".txt", sep = "")))

modelCheck(modelFilename)
modelData("data.txt")
modelCompile(numChains=nChains)
modelGenInits()  
modelInits(fileName = file.path(getwd(), 
    paste("inits", 1:nChains, ".txt", sep = "")) )
  
modelUpdate(nBurn)
samplesSet(c('gamma.r.strata','gamma.mu.strata','p0.strata','nb.mu','nb.p','expected',
'd54','d43','d32','d21','observed.strata'))
modelUpdate(nUpdate)

samplesDensity("*", thin = nThin)
samplesHistory("*", thin = nThin) 
write.csv (samplesStats("*",thin = nThin),file="TTI_Seagrass_BugsOut_Sf_Spring.csv")