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samp_sims_figure6_7.R
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##########################################################################
##### CATCH MONITORING SIMULATION 1 - equal pop sizes and single sampling event
### for populations of even size (harvest rate is controlled below)
mean.pop<-8.5172
pop.var<-0
n.pops<-10
harvest.rate<-0.20 ### True harvest rate -
samp.yr<-c(60,120,240,360,600) ### a vector of the different sample numbers taken in yearly sampling
catch.true<-array(dim=c(1000,10,length(samp.yr))) ### true catch numbers for each model run
harv.rate<-array(dim=c(1000,10,length(samp.yr))) ### true harvest rates for each model run
annual.samp<-array(dim=c(1000,10,length(samp.yr)))
catch.est.yr<-array(dim=c(1000,10,length(samp.yr))) # est. catch proportions for each stock
total.est.yr<-array(dim=c(1000,10,length(samp.yr))) # est. catch totals for each stock
total.est.yr2<-array(dim=c(1000,10,length(samp.yr))) # est. catch totals for each stock w/uncertainty in catch CV=0.2
total.est.yr5<-array(dim=c(1000,10,length(samp.yr))) # est. catch totals for each stock w/uncertainty in catch CV=0.5
harv.rate.yr0<-array(dim=c(1000,10,length(samp.yr))) # estimated harvest rate CV = 0 for escape and total catch
harv.rate.yr1<-array(dim=c(1000,10,length(samp.yr)))
harv.rate.yr2<-array(dim=c(1000,10,length(samp.yr)))
harv.rate.yr3<-array(dim=c(1000,10,length(samp.yr)))
harv.rate.yr4<-array(dim=c(1000,10,length(samp.yr))) # estimated harvest rate CV = 0.5 for escape and total catch
##### Running the model ofr each sample number (s), and 1000 iterations (i)
for(s in 1:length(samp.yr)){
for (i in 1:1000){ #### running the models 1000 times
### weekly abundance for each population w/ differing levels of uncertainty
pop.sizes<-round(rlnorm(n.pops,mean.pop,pop.var))
pop.sizesCV.2<-round(pop.sizes*(rlnorm(length(pop.sizes),0,0.2)))
pop.sizesCV.5<-round(pop.sizes*(rlnorm(length(pop.sizes),0,0.5)))
pop.timing<-rmultinom(n.pops,100,c(0.1,0.2,0.3,0.2,0.15,0.05))/100 ## the 100 in the rmultinom statement controls the variance
###### these are all the fish coming through the fishing area for each week
run.weeks<-matrix(NA,nrow=6,ncol=n.pops)
for (n in 1:n.pops){
run.weeks[,n]<-round(pop.timing[,n]*pop.sizes[n])
}
week1<-c(rep(1,run.weeks[1,1]),rep(2,run.weeks[1,2]),rep(3,run.weeks[1,3]),rep(4,run.weeks[1,4]),
rep(5,run.weeks[1,5]),rep(6,run.weeks[1,6]),rep(7,run.weeks[1,7]),rep(8,run.weeks[1,8]),rep(9,run.weeks[1,9]),
rep(10,run.weeks[1,10]))
week2<-c(rep(1,run.weeks[2,1]),rep(2,run.weeks[2,2]),rep(3,run.weeks[2,3]),rep(4,run.weeks[2,4]),
rep(5,run.weeks[2,5]),rep(6,run.weeks[2,6]),rep(7,run.weeks[2,7]),rep(8,run.weeks[2,8]),rep(9,run.weeks[2,9]),
rep(10,run.weeks[2,10]))
week3<-c(rep(1,run.weeks[3,1]),rep(2,run.weeks[3,2]),rep(3,run.weeks[3,3]),rep(4,run.weeks[3,4]),
rep(5,run.weeks[3,5]),rep(6,run.weeks[3,6]),rep(7,run.weeks[3,7]),rep(8,run.weeks[3,8]),rep(9,run.weeks[3,9]),
rep(10,run.weeks[3,10]))
week4<-c(rep(1,run.weeks[4,1]),rep(2,run.weeks[4,2]),rep(3,run.weeks[4,3]),rep(4,run.weeks[4,4]),
rep(5,run.weeks[4,5]),rep(6,run.weeks[4,6]),rep(7,run.weeks[4,7]),rep(8,run.weeks[4,8]),rep(9,run.weeks[4,9]),
rep(10,run.weeks[4,10]))
week5<-c(rep(1,run.weeks[5,1]),rep(2,run.weeks[5,2]),rep(3,run.weeks[5,3]),rep(4,run.weeks[5,4]),
rep(5,run.weeks[5,5]),rep(6,run.weeks[5,6]),rep(7,run.weeks[5,7]),rep(8,run.weeks[5,8]),rep(9,run.weeks[5,9]),
rep(10,run.weeks[5,10]))
week6<-c(rep(1,run.weeks[6,1]),rep(2,run.weeks[6,2]),rep(3,run.weeks[6,3]),rep(4,run.weeks[6,4]),
rep(5,run.weeks[6,5]),rep(6,run.weeks[6,6]),rep(7,run.weeks[6,7]),rep(8,run.weeks[6,8]),rep(9,run.weeks[6,9]),
rep(10,run.weeks[6,10]))
###################################################
### PART 2a - simulating the catch process - total catch
CV.2<-rnorm(1,0,0.2) ### observation error CV = 0.2
CV.5<-rnorm(1,0,0.5) ### observation error CV = 0.5
catch<-rep(NA,6) # BC added this May 1, 2019
catch.estCV.2<-rep(NA,6)
catch.estCV.5<-rep(NA,6)
for (j in 1:6){
catch[j]<-sum(run.weeks[j,])*harvest.rate
catch.estCV.2[j]<-abs(round(catch[j]+(catch[j]*CV.2)))
catch.estCV.5[j]<-abs(round(catch[j]+(catch[j]*CV.5)))
}
total.catch<-sum(catch)
total.catch_CV.2<-sum(catch.estCV.2) ### this is the estimated total harvest - including obs error (CV = 0.2)
total.catch_CV.5<-sum(catch.estCV.5) ### this is the estimated total harvest - inlcuding obs error (CV = 0.5)
############################################################################
##### PART 2b - the weekly catch of individual fish (e.g. different stocks)
## the catch process - This is the true catch numbers.
catch1<-sample(week1,catch[1],replace=FALSE,prob=NULL)
catch.tab1<-table(catch1)
catch2<-sample(week2,catch[2],replace=FALSE,prob=NULL)
catch.tab2<-table(catch2)
catch3<-sample(week3,catch[3],replace=FALSE,prob=NULL)
catch.tab3<-table(catch3)
catch4<-sample(week4,catch[4],replace=FALSE,prob=NULL)
catch.tab4<-table(catch4)
catch5<-sample(week5,catch[5],replace=FALSE,prob=NULL)
catch.tab5<-table(catch5)
catch6<-sample(week6,catch[6],replace=FALSE,prob=NULL)
catch.tab6<-table(catch6)
### combining stock-ID for all the fish caught (5000 total)
catch.all<-c(catch1,catch2,catch3,catch4,catch5,catch6)
### Making a table of stock specific catch
catch.tab_all<-table(catch.all)
catch.true[i,,s]<-as.vector(catch.tab_all)
harv.rate[i,,s]<-catch.true[i,,s]/pop.sizes
##########################################
## PART 3 - the catch sampling process
catch.wks<-list(catch2,catch3,catch4)
samples.yr<-sample(catch.wks[[sample(1:3,1)]],samp.yr[s],replace=FALSE,prob=NULL)
annual.samp[i,1,s]<-length(which(samples.yr==1))
annual.samp[i,2,s]<-length(which(samples.yr==2))
annual.samp[i,3,s]<-length(which(samples.yr==3))
annual.samp[i,4,s]<-length(which(samples.yr==4))
annual.samp[i,5,s]<-length(which(samples.yr==5))
annual.samp[i,6,s]<-length(which(samples.yr==6))
annual.samp[i,7,s]<-length(which(samples.yr==7))
annual.samp[i,8,s]<-length(which(samples.yr==8))
annual.samp[i,9,s]<-length(which(samples.yr==9))
annual.samp[i,10,s]<-length(which(samples.yr==10))
## contribution of each population in the catch
catch.est.yr[i,,s]<-as.vector(annual.samp[i,,s]/sum(annual.samp[i,,s]))
# total estimated harvest for each pop.
total.est.yr[i,,s]<-round(catch.est.yr[i,,s]*total.catch)
total.est.yr2[i,,s]<-round(catch.est.yr[i,,s]*total.catch_CV.2)
total.est.yr5[i,,s]<-round(catch.est.yr[i,,s]*total.catch_CV.5)
# total estimated harvest rate for each pop.
harv.rate.yr0[i,,s]<-total.est.yr[i,,s]/pop.sizes
harv.rate.yr1[i,,s]<-total.est.yr2[i,,s]/pop.sizesCV.2 # catch CV = 0.2; escape CV = 0.2
harv.rate.yr2[i,,s]<-total.est.yr2[i,,s]/pop.sizesCV.5 # catch CV = 0.2; escape CV = 0.5
harv.rate.yr3[i,,s]<-total.est.yr5[i,,s]/pop.sizesCV.2 # catch CV = 0.5; escape CV = 0.2
harv.rate.yr4[i,,s]<-total.est.yr5[i,,s]/pop.sizesCV.5 # catch CV = 0.5; escape CV = 0.5
}
}
##### sweeet!!! we are now generating data
###############################################################################
##### estimating the mean & sd of catch contrib. - just reflects sample sizes not obs error
comp.yr1<-array(dim=c(n.pops,4,length(samp.yr))) ## catch composition for single sample and even pop sizes
for(j in 1:length(samp.yr)){
for(i in 1:10){
comp.yr1[i,1,j]<-mean(catch.est.yr[,i,j])
comp.yr1[i,2,j]<-mean(catch.est.yr[,i,j])-(1.96*sd(catch.est.yr[,i,j]))
comp.yr1[i,3,j]<-mean(catch.est.yr[,i,j])+(1.96*sd(catch.est.yr[,i,j]))
comp.yr1[i,4,j]<-sd(catch.est.yr[,i,j])/mean(catch.est.yr[,i,j])
}
}
##### estimating the mean and sd of harvest rate estimates for our model
rate.yr1.0<-array(dim=c(n.pops,4,length(samp.yr)))
rate.yr1.1<-array(dim=c(n.pops,4,length(samp.yr)))
rate.yr1.2<-array(dim=c(n.pops,4,length(samp.yr)))
rate.yr1.3<-array(dim=c(n.pops,4,length(samp.yr)))
rate.yr1.4<-array(dim=c(n.pops,4,length(samp.yr)))
### assuming perfect knowledge of total catch and escapement
for(j in 1:length(samp.yr)){
for(i in 1:10){
rate.yr1.0[i,1,j]<-mean(harv.rate.yr0[,i,j])
rate.yr1.0[i,2,j]<-mean(harv.rate.yr0[,i,j])-(1.96*sd(harv.rate.yr0[,i,j]))
rate.yr1.0[i,3,j]<-mean(harv.rate.yr0[,i,j])+(1.96*sd(harv.rate.yr0[,i,j]))
rate.yr1.0[i,4,j]<-sd(harv.rate.yr0[,i,j])/mean(harv.rate.yr0[,i,j])
}
}
### CV = 0.2 for catch and escapement
harv.rate.yr1[which(harv.rate.yr1>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(samp.yr)){
for(i in 1:10){
rate.yr1.1[i,1,j]<-mean(harv.rate.yr1[,i,j])
rate.yr1.1[i,2,j]<-mean(harv.rate.yr1[,i,j])-(1.96*sd(harv.rate.yr1[,i,j]))
rate.yr1.1[i,3,j]<-mean(harv.rate.yr1[,i,j])+(1.96*sd(harv.rate.yr1[,i,j]))
rate.yr1.1[i,4,j]<-sd(harv.rate.yr1[,i,j])/mean(harv.rate.yr1[,i,j])
}
}
### CV = 0.2 for catch; CV = 0.5 for escapement
harv.rate.yr2[which(harv.rate.yr2>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(samp.yr)){
for(i in 1:10){
rate.yr1.2[i,1,j]<-mean(harv.rate.yr2[,i,j])
rate.yr1.2[i,2,j]<-mean(harv.rate.yr2[,i,j])-(1.96*sd(harv.rate.yr2[,i,j]))
rate.yr1.2[i,3,j]<-mean(harv.rate.yr2[,i,j])+(1.96*sd(harv.rate.yr2[,i,j]))
rate.yr1.2[i,4,j]<-sd(harv.rate.yr2[,i,j])/mean(harv.rate.yr2[,i,j])
}
}
### CV = 0.5 for catch; CV = 0.2 for escapement
harv.rate.yr3[which(harv.rate.yr3>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(samp.yr)){
for(i in 1:10){
rate.yr1.3[i,1,j]<-mean(harv.rate.yr3[,i,j])
rate.yr1.3[i,2,j]<-mean(harv.rate.yr3[,i,j])-(1.96*sd(harv.rate.yr3[,i,j]))
rate.yr1.3[i,3,j]<-mean(harv.rate.yr3[,i,j])+(1.96*sd(harv.rate.yr3[,i,j]))
rate.yr1.3[i,4,j]<-sd(harv.rate.yr3[,i,j])/mean(harv.rate.yr3[,i,j])
}
}
### CV = 0.5 for catch; CV = 0.5 for escapement
harv.rate.yr4[which(harv.rate.yr4>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(samp.yr)){
for(i in 1:10){
rate.yr1.4[i,1,j]<-mean(harv.rate.yr4[,i,j])
rate.yr1.4[i,2,j]<-mean(harv.rate.yr4[,i,j])-(1.96*sd(harv.rate.yr4[,i,j]))
rate.yr1.4[i,3,j]<-mean(harv.rate.yr4[,i,j])+(1.96*sd(harv.rate.yr4[,i,j]))
rate.yr1.4[i,4,j]<-sd(harv.rate.yr4[,i,j])/mean(harv.rate.yr4[,i,j])
}
}
##########################################################################
##### CATCH MONITORING SIMULATION 2 - variable pop sizes and single sampling event
n.pops<-10
harvest.rate<-0.20 ### True harvest rate -
samp.yr<-c(60,120,240,360,600) ### a vector of the different sample numbers taken in yearly sampling
catch.true<-array(dim=c(1000,10,length(samp.yr))) ### true catch numbers for each model run
harv.rate<-array(dim=c(1000,10,length(samp.yr))) ### true harvest rates for each model run
annual.samp<-array(dim=c(1000,10,length(samp.yr)))
catch.est.yr<-array(dim=c(1000,10,length(samp.yr))) # est. catch proportions for each stock
total.est.yr<-array(dim=c(1000,10,length(samp.yr))) # est. catch totals for each stock
total.est.yr2<-array(dim=c(1000,10,length(samp.yr))) # est. catch totals for each stock w/uncertainty in catch CV=0.2
total.est.yr5<-array(dim=c(1000,10,length(samp.yr))) # est. catch totals for each stock w/uncertainty in catch CV=0.5
harv.rate.yr0<-array(dim=c(1000,10,length(samp.yr))) # estimated harvest rate CV = 0 for escape and total catch
harv.rate.yr1<-array(dim=c(1000,10,length(samp.yr)))
harv.rate.yr2<-array(dim=c(1000,10,length(samp.yr)))
harv.rate.yr3<-array(dim=c(1000,10,length(samp.yr)))
harv.rate.yr4<-array(dim=c(1000,10,length(samp.yr))) # estimated harvest rate CV = 0.5 for escape and total catch
##### Running the model ofr each sample number (s), and 1000 iterations (i)
for(s in 1:length(samp.yr)){
for (i in 1:1000){ #### running the models 1000 times
### weekly abundance for each population w/ differing levels of uncertainty
pop.sizes<-c(500,1000,2000,3000,4000,6000,8000,10000,15000,20000)
pop.sizesCV.2<-round(pop.sizes*(rlnorm(length(pop.sizes),0,0.2)))
pop.sizesCV.5<-round(pop.sizes*(rlnorm(length(pop.sizes),0,0.5)))
pop.timing<-rmultinom(n.pops,100,c(0.1,0.2,0.3,0.2,0.15,0.05))/100 ## the 100 in the rmultinom statement controls the variance
###### these are all the fish coming through the fishing area for each week
run.weeks<-matrix(NA,nrow=6,ncol=n.pops)
for (n in 1:n.pops){
run.weeks[,n]<-round(pop.timing[,n]*pop.sizes[n])
}
week1<-c(rep(1,run.weeks[1,1]),rep(2,run.weeks[1,2]),rep(3,run.weeks[1,3]),rep(4,run.weeks[1,4]),
rep(5,run.weeks[1,5]),rep(6,run.weeks[1,6]),rep(7,run.weeks[1,7]),rep(8,run.weeks[1,8]),rep(9,run.weeks[1,9]),
rep(10,run.weeks[1,10]))
week2<-c(rep(1,run.weeks[2,1]),rep(2,run.weeks[2,2]),rep(3,run.weeks[2,3]),rep(4,run.weeks[2,4]),
rep(5,run.weeks[2,5]),rep(6,run.weeks[2,6]),rep(7,run.weeks[2,7]),rep(8,run.weeks[2,8]),rep(9,run.weeks[2,9]),
rep(10,run.weeks[2,10]))
week3<-c(rep(1,run.weeks[3,1]),rep(2,run.weeks[3,2]),rep(3,run.weeks[3,3]),rep(4,run.weeks[3,4]),
rep(5,run.weeks[3,5]),rep(6,run.weeks[3,6]),rep(7,run.weeks[3,7]),rep(8,run.weeks[3,8]),rep(9,run.weeks[3,9]),
rep(10,run.weeks[3,10]))
week4<-c(rep(1,run.weeks[4,1]),rep(2,run.weeks[4,2]),rep(3,run.weeks[4,3]),rep(4,run.weeks[4,4]),
rep(5,run.weeks[4,5]),rep(6,run.weeks[4,6]),rep(7,run.weeks[4,7]),rep(8,run.weeks[4,8]),rep(9,run.weeks[4,9]),
rep(10,run.weeks[4,10]))
week5<-c(rep(1,run.weeks[5,1]),rep(2,run.weeks[5,2]),rep(3,run.weeks[5,3]),rep(4,run.weeks[5,4]),
rep(5,run.weeks[5,5]),rep(6,run.weeks[5,6]),rep(7,run.weeks[5,7]),rep(8,run.weeks[5,8]),rep(9,run.weeks[5,9]),
rep(10,run.weeks[5,10]))
week6<-c(rep(1,run.weeks[6,1]),rep(2,run.weeks[6,2]),rep(3,run.weeks[6,3]),rep(4,run.weeks[6,4]),
rep(5,run.weeks[6,5]),rep(6,run.weeks[6,6]),rep(7,run.weeks[6,7]),rep(8,run.weeks[6,8]),rep(9,run.weeks[6,9]),
rep(10,run.weeks[6,10]))
###################################################
### PART 2a - simulating the catch process - total catch
CV.2<-rnorm(1,0,0.2) ### observation error CV = 0.2
CV.5<-rnorm(1,0,0.5) ### observation error CV = 0.5
catch.estCV.2<-rep(NA,6)
catch.estCV.5<-rep(NA,6)
for (j in 1:6){
catch[j]<-sum(run.weeks[j,])*harvest.rate
catch.estCV.2[j]<-abs(round(catch[j]+(catch[j]*CV.2)))
catch.estCV.5[j]<-abs(round(catch[j]+(catch[j]*CV.5)))
}
total.catch<-sum(catch)
total.catch_CV.2<-sum(catch.estCV.2) ### this is the estimated total harvest - including obs error (CV = 0.2)
total.catch_CV.5<-sum(catch.estCV.5) ### this is the estimated total harvest - inlcuding obs error (CV = 0.5)
############################################################################
##### PART 2b - the weekly catch of individual fish (e.g. different stocks)
## the catch process - This is the true catch numbers.
catch1<-sample(week1,catch[1],replace=FALSE,prob=NULL)
catch.tab1<-table(catch1)
catch2<-sample(week2,catch[2],replace=FALSE,prob=NULL)
catch.tab2<-table(catch2)
catch3<-sample(week3,catch[3],replace=FALSE,prob=NULL)
catch.tab3<-table(catch3)
catch4<-sample(week4,catch[4],replace=FALSE,prob=NULL)
catch.tab4<-table(catch4)
catch5<-sample(week5,catch[5],replace=FALSE,prob=NULL)
catch.tab5<-table(catch5)
catch6<-sample(week6,catch[6],replace=FALSE,prob=NULL)
catch.tab6<-table(catch6)
### combining stock-ID for all the fish caught (5000 total)
catch.all<-c(catch1,catch2,catch3,catch4,catch5,catch6)
### Making a table of stock specific catch
catch.tab_all<-table(catch.all)
catch.true[i,,s]<-as.vector(catch.tab_all)
harv.rate[i,,s]<-catch.true[i,,s]/pop.sizes
##########################################
## PART 3 - the catch sampling process
catch.wks<-list(catch2,catch3,catch4)
samples.yr<-sample(catch.wks[[sample(1:3,1)]],samp.yr[s],replace=FALSE,prob=NULL)
annual.samp[i,1,s]<-length(which(samples.yr==1))
annual.samp[i,2,s]<-length(which(samples.yr==2))
annual.samp[i,3,s]<-length(which(samples.yr==3))
annual.samp[i,4,s]<-length(which(samples.yr==4))
annual.samp[i,5,s]<-length(which(samples.yr==5))
annual.samp[i,6,s]<-length(which(samples.yr==6))
annual.samp[i,7,s]<-length(which(samples.yr==7))
annual.samp[i,8,s]<-length(which(samples.yr==8))
annual.samp[i,9,s]<-length(which(samples.yr==9))
annual.samp[i,10,s]<-length(which(samples.yr==10))
## contribution of each population in the catch
catch.est.yr[i,,s]<-as.vector(annual.samp[i,,s]/sum(annual.samp[i,,s]))
# total estimated harvest for each pop.
total.est.yr[i,,s]<-round(catch.est.yr[i,,s]*total.catch)
total.est.yr2[i,,s]<-round(catch.est.yr[i,,s]*total.catch_CV.2)
total.est.yr5[i,,s]<-round(catch.est.yr[i,,s]*total.catch_CV.5)
# total estimated harvest rate for each pop.
harv.rate.yr0[i,,s]<-total.est.yr[i,,s]/pop.sizes
harv.rate.yr1[i,,s]<-total.est.yr2[i,,s]/pop.sizesCV.2 # catch CV = 0.2; escape CV = 0.2
harv.rate.yr2[i,,s]<-total.est.yr2[i,,s]/pop.sizesCV.5 # catch CV = 0.2; escape CV = 0.5
harv.rate.yr3[i,,s]<-total.est.yr5[i,,s]/pop.sizesCV.2 # catch CV = 0.5; escape CV = 0.2
harv.rate.yr4[i,,s]<-total.est.yr5[i,,s]/pop.sizesCV.5 # catch CV = 0.5; escape CV = 0.5
}
}
###############################################################################
##### estimating the mean & sd of catch contrib. - just reflects sample sizes not obs error
comp.yr2<-array(dim=c(n.pops,4,length(samp.yr))) ## catch composition for single sample and even pop sizes
for(j in 1:length(samp.yr)){
for(i in 1:10){
comp.yr2[i,1,j]<-mean(catch.est.yr[,i,j])
comp.yr2[i,2,j]<-mean(catch.est.yr[,i,j])-(1.96*sd(catch.est.yr[,i,j]))
comp.yr2[i,3,j]<-mean(catch.est.yr[,i,j])+(1.96*sd(catch.est.yr[,i,j]))
comp.yr2[i,4,j]<-sd(catch.est.yr[,i,j])/mean(catch.est.yr[,i,j])
}
}
##### estimating the mean and sd of harvest rate estimates for our model
rate.yr2.0<-array(dim=c(n.pops,4,length(samp.yr)))
rate.yr2.1<-array(dim=c(n.pops,4,length(samp.yr)))
rate.yr2.2<-array(dim=c(n.pops,4,length(samp.yr)))
rate.yr2.3<-array(dim=c(n.pops,4,length(samp.yr)))
rate.yr2.4<-array(dim=c(n.pops,4,length(samp.yr)))
### assuming perfect knowledge of total catch and escapement
for(j in 1:length(samp.yr)){
for(i in 1:10){
rate.yr2.0[i,1,j]<-mean(harv.rate.yr0[,i,j])
rate.yr2.0[i,2,j]<-mean(harv.rate.yr0[,i,j])-(1.96*sd(harv.rate.yr0[,i,j]))
rate.yr2.0[i,3,j]<-mean(harv.rate.yr0[,i,j])+(1.96*sd(harv.rate.yr0[,i,j]))
rate.yr2.0[i,4,j]<-sd(harv.rate.yr0[,i,j])/mean(harv.rate.yr0[,i,j])
}
}
### CV = 0.2 for catch and escapement
harv.rate.yr1[which(harv.rate.yr1>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(samp.yr)){
for(i in 1:10){
rate.yr2.1[i,1,j]<-mean(harv.rate.yr1[,i,j])
rate.yr2.1[i,2,j]<-mean(harv.rate.yr1[,i,j])-(1.96*sd(harv.rate.yr1[,i,j]))
rate.yr2.1[i,3,j]<-mean(harv.rate.yr1[,i,j])+(1.96*sd(harv.rate.yr1[,i,j]))
rate.yr2.1[i,4,j]<-sd(harv.rate.yr1[,i,j])/mean(harv.rate.yr1[,i,j])
}
}
### CV = 0.2 for catch; CV = 0.5 for escapement
harv.rate.yr2[which(harv.rate.yr2>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(samp.yr)){
for(i in 1:10){
rate.yr2.2[i,1,j]<-mean(harv.rate.yr2[,i,j])
rate.yr2.2[i,2,j]<-mean(harv.rate.yr2[,i,j])-(1.96*sd(harv.rate.yr2[,i,j]))
rate.yr2.2[i,3,j]<-mean(harv.rate.yr2[,i,j])+(1.96*sd(harv.rate.yr2[,i,j]))
rate.yr2.2[i,4,j]<-sd(harv.rate.yr2[,i,j])/mean(harv.rate.yr2[,i,j])
}
}
### CV = 0.5 for catch; CV = 0.2 for escapement
harv.rate.yr3[which(harv.rate.yr3>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(samp.yr)){
for(i in 1:10){
rate.yr2.3[i,1,j]<-mean(harv.rate.yr3[,i,j])
rate.yr2.3[i,2,j]<-mean(harv.rate.yr3[,i,j])-(1.96*sd(harv.rate.yr3[,i,j]))
rate.yr2.3[i,3,j]<-mean(harv.rate.yr3[,i,j])+(1.96*sd(harv.rate.yr3[,i,j]))
rate.yr2.3[i,4,j]<-sd(harv.rate.yr3[,i,j])/mean(harv.rate.yr3[,i,j])
}
}
### CV = 0.5 for catch; CV = 0.5 for escapement
harv.rate.yr4[which(harv.rate.yr4>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(samp.yr)){
for(i in 1:10){
rate.yr2.4[i,1,j]<-mean(harv.rate.yr4[,i,j])
rate.yr2.4[i,2,j]<-mean(harv.rate.yr4[,i,j])-(1.96*sd(harv.rate.yr4[,i,j]))
rate.yr2.4[i,3,j]<-mean(harv.rate.yr4[,i,j])+(1.96*sd(harv.rate.yr4[,i,j]))
rate.yr2.4[i,4,j]<-sd(harv.rate.yr4[,i,j])/mean(harv.rate.yr4[,i,j])
}
}
##########################################################################
###### Weekly sampling
##########
### for populations of constant size (harvest rate is controlled below)
mean.pop<-8.5172
pop.var<-0
n.pops<-10
harvest.rate<-0.20 ### True harvest rate -
no.wk<-c(10,20,40,60,100) ### a vector of the different sample numbers taken in yearly sampling
catch.true<-array(dim=c(1000,10,length(no.wk))) ### true catch numbers for each model run
harv.rate<-array(dim=c(1000,10,length(no.wk))) ### true harvest rates for each model run
weekly.samp<-array(dim=c(1000,10,length(no.wk)))
catch.est.yr<-array(dim=c(1000,10,length(no.wk))) # est. catch proportions for each stock
total.est.yr<-array(dim=c(1000,10,length(no.wk))) # est. catch totals for each stock
total.est.yr2<-array(dim=c(1000,10,length(no.wk))) # est. catch totals for each stock w/uncertainty in catch CV=0.2
total.est.yr5<-array(dim=c(1000,10,length(no.wk))) # est. catch totals for each stock w/uncertainty in catch CV=0.5
harv.rate.yr0<-array(dim=c(1000,10,length(no.wk))) # estimated harvest rate CV = 0 for escape and total catch
harv.rate.yr1<-array(dim=c(1000,10,length(no.wk)))
harv.rate.yr2<-array(dim=c(1000,10,length(no.wk)))
harv.rate.yr3<-array(dim=c(1000,10,length(no.wk)))
harv.rate.yr4<-array(dim=c(1000,10,length(no.wk))) # estimated harvest rate CV = 0.5 for escape and total catch
##### Running the model ofr each sample number (s), and 1000 iterations (i)
for(s in 1:length(no.wk)){
for (i in 1:1000){ #### running the models 1000 times
### weekly abundance for each population w/ differing levels of uncertainty
pop.sizes<-round(rlnorm(n.pops,mean.pop,pop.var))
pop.sizesCV.2<-round(pop.sizes*(rlnorm(length(pop.sizes),0,0.2)))
pop.sizesCV.5<-round(pop.sizes*(rlnorm(length(pop.sizes),0,0.5)))
pop.timing<-rmultinom(n.pops,100,c(0.1,0.2,0.3,0.2,0.15,0.05))/100 ## the 100 in the rmultinom statement controls the variance
###### these are all the fish coming through the fishing area for each week
run.weeks<-matrix(NA,nrow=6,ncol=n.pops)
for (n in 1:n.pops){
run.weeks[,n]<-round(pop.timing[,n]*pop.sizes[n])
}
week1<-c(rep(1,run.weeks[1,1]),rep(2,run.weeks[1,2]),rep(3,run.weeks[1,3]),rep(4,run.weeks[1,4]),
rep(5,run.weeks[1,5]),rep(6,run.weeks[1,6]),rep(7,run.weeks[1,7]),rep(8,run.weeks[1,8]),rep(9,run.weeks[1,9]),
rep(10,run.weeks[1,10]))
week2<-c(rep(1,run.weeks[2,1]),rep(2,run.weeks[2,2]),rep(3,run.weeks[2,3]),rep(4,run.weeks[2,4]),
rep(5,run.weeks[2,5]),rep(6,run.weeks[2,6]),rep(7,run.weeks[2,7]),rep(8,run.weeks[2,8]),rep(9,run.weeks[2,9]),
rep(10,run.weeks[2,10]))
week3<-c(rep(1,run.weeks[3,1]),rep(2,run.weeks[3,2]),rep(3,run.weeks[3,3]),rep(4,run.weeks[3,4]),
rep(5,run.weeks[3,5]),rep(6,run.weeks[3,6]),rep(7,run.weeks[3,7]),rep(8,run.weeks[3,8]),rep(9,run.weeks[3,9]),
rep(10,run.weeks[3,10]))
week4<-c(rep(1,run.weeks[4,1]),rep(2,run.weeks[4,2]),rep(3,run.weeks[4,3]),rep(4,run.weeks[4,4]),
rep(5,run.weeks[4,5]),rep(6,run.weeks[4,6]),rep(7,run.weeks[4,7]),rep(8,run.weeks[4,8]),rep(9,run.weeks[4,9]),
rep(10,run.weeks[4,10]))
week5<-c(rep(1,run.weeks[5,1]),rep(2,run.weeks[5,2]),rep(3,run.weeks[5,3]),rep(4,run.weeks[5,4]),
rep(5,run.weeks[5,5]),rep(6,run.weeks[5,6]),rep(7,run.weeks[5,7]),rep(8,run.weeks[5,8]),rep(9,run.weeks[5,9]),
rep(10,run.weeks[5,10]))
week6<-c(rep(1,run.weeks[6,1]),rep(2,run.weeks[6,2]),rep(3,run.weeks[6,3]),rep(4,run.weeks[6,4]),
rep(5,run.weeks[6,5]),rep(6,run.weeks[6,6]),rep(7,run.weeks[6,7]),rep(8,run.weeks[6,8]),rep(9,run.weeks[6,9]),
rep(10,run.weeks[6,10]))
###################################################
### PART 2a - simulating the catch process - total catch
CV.2<-rnorm(1,0,0.2) ### observation error CV = 0.2
CV.5<-rnorm(1,0,0.5) ### observation error CV = 0.5
catch.estCV.2<-rep(NA,6)
catch.estCV.5<-rep(NA,6)
for (j in 1:6){
catch[j]<-sum(run.weeks[j,])*harvest.rate
catch.estCV.2[j]<-abs(round(catch[j]+(catch[j]*CV.2)))
catch.estCV.5[j]<-abs(round(catch[j]+(catch[j]*CV.5)))
}
total.catch<-sum(catch)
total.catch_CV.2<-sum(catch.estCV.2) ### this is the estimated total harvest - including obs error (CV = 0.2)
total.catch_CV.5<-sum(catch.estCV.5) ### this is the estimated total harvest - inlcuding obs error (CV = 0.5)
############################################################################
##### PART 2b - the weekly catch of individual fish (e.g. different stocks)
## the catch process - This is the true catch numbers.
catch1<-sample(week1,catch[1],replace=FALSE,prob=NULL)
catch.tab1<-table(catch1)
catch2<-sample(week2,catch[2],replace=FALSE,prob=NULL)
catch.tab2<-table(catch2)
catch3<-sample(week3,catch[3],replace=FALSE,prob=NULL)
catch.tab3<-table(catch3)
catch4<-sample(week4,catch[4],replace=FALSE,prob=NULL)
catch.tab4<-table(catch4)
catch5<-sample(week5,catch[5],replace=FALSE,prob=NULL)
catch.tab5<-table(catch5)
catch6<-sample(week6,catch[6],replace=FALSE,prob=NULL)
catch.tab6<-table(catch6)
### combining stock-ID for all the fish caught (5000 total)
catch.all<-c(catch1,catch2,catch3,catch4,catch5,catch6)
### Making a table of stock specific catch
catch.tab_all<-table(catch.all)
catch.true[i,,s]<-as.vector(catch.tab_all)
harv.rate[i,,s]<-catch.true[i,,s]/pop.sizes
##########################################
## PART 3 - the catch sampling process
samples.wk<-matrix(nrow=6,ncol=no.wk[s])
catch.wks<-list(catch1,catch2,catch3,catch4,catch5,catch6)
### this is our weekly sampling process with 6 weeks and sample numbers = no.wk[s]
for(w in 1:length(catch.wks)){
samples.wk[w,]<-sample(catch.wks[[w]],no.wk[s],replace=FALSE,prob=NULL)
}
weekly.samp[i,1,s]<-length(which(samples.wk==1))
weekly.samp[i,2,s]<-length(which(samples.wk==2))
weekly.samp[i,3,s]<-length(which(samples.wk==3))
weekly.samp[i,4,s]<-length(which(samples.wk==4))
weekly.samp[i,5,s]<-length(which(samples.wk==5))
weekly.samp[i,6,s]<-length(which(samples.wk==6))
weekly.samp[i,7,s]<-length(which(samples.wk==7))
weekly.samp[i,8,s]<-length(which(samples.wk==8))
weekly.samp[i,9,s]<-length(which(samples.wk==9))
weekly.samp[i,10,s]<-length(which(samples.wk==10))
## contribution of each population in the catch
catch.est.yr[i,,s]<-as.vector(weekly.samp[i,,s]/sum(weekly.samp[i,,s]))
# total estimated harvest for each pop.
total.est.yr[i,,s]<-round(catch.est.yr[i,,s]*total.catch)
total.est.yr2[i,,s]<-round(catch.est.yr[i,,s]*total.catch_CV.2)
total.est.yr5[i,,s]<-round(catch.est.yr[i,,s]*total.catch_CV.5)
# total estimated harvest rate for each pop.
harv.rate.yr0[i,,s]<-total.est.yr[i,,s]/pop.sizes
harv.rate.yr1[i,,s]<-total.est.yr2[i,,s]/pop.sizesCV.2 # catch CV = 0.2; escape CV = 0.2
harv.rate.yr2[i,,s]<-total.est.yr2[i,,s]/pop.sizesCV.5 # catch CV = 0.2; escape CV = 0.5
harv.rate.yr3[i,,s]<-total.est.yr5[i,,s]/pop.sizesCV.2 # catch CV = 0.5; escape CV = 0.2
harv.rate.yr4[i,,s]<-total.est.yr5[i,,s]/pop.sizesCV.5 # catch CV = 0.5; escape CV = 0.5
}
}
###############################################################################
##### estimating the mean & sd of catch contrib. - just reflects sample sizes not obs error
comp.yr3<-array(dim=c(n.pops,4,length(no.wk))) ## catch composition for single sample and even pop sizes
for(j in 1:length(no.wk)){
for(i in 1:10){
comp.yr3[i,1,j]<-mean(catch.est.yr[,i,j])
comp.yr3[i,2,j]<-mean(catch.est.yr[,i,j])-(1.96*sd(catch.est.yr[,i,j]))
comp.yr3[i,3,j]<-mean(catch.est.yr[,i,j])+(1.96*sd(catch.est.yr[,i,j]))
comp.yr3[i,4,j]<-sd(catch.est.yr[,i,j])/mean(catch.est.yr[,i,j])
}
}
comp.yr3[,,5]
##### estimating the mean and sd of harvest rate estimates for our model
rate.yr3.0<-array(dim=c(n.pops,4,length(no.wk)))
rate.yr3.1<-array(dim=c(n.pops,4,length(no.wk)))
rate.yr3.2<-array(dim=c(n.pops,4,length(no.wk)))
rate.yr3.3<-array(dim=c(n.pops,4,length(no.wk)))
rate.yr3.4<-array(dim=c(n.pops,4,length(no.wk)))
### assuming perfect knowledge of total catch and escapement
for(j in 1:length(no.wk)){
for(i in 1:10){
rate.yr3.0[i,1,j]<-mean(harv.rate.yr0[,i,j])
rate.yr3.0[i,2,j]<-mean(harv.rate.yr0[,i,j])-(1.96*sd(harv.rate.yr0[,i,j]))
rate.yr3.0[i,3,j]<-mean(harv.rate.yr0[,i,j])+(1.96*sd(harv.rate.yr0[,i,j]))
rate.yr3.0[i,4,j]<-sd(harv.rate.yr0[,i,j])/mean(harv.rate.yr0[,i,j])
}
}
### CV = 0.2 for catch and escapement
harv.rate.yr1[which(harv.rate.yr1>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(no.wk)){
for(i in 1:10){
rate.yr3.1[i,1,j]<-mean(harv.rate.yr1[,i,j])
rate.yr3.1[i,2,j]<-mean(harv.rate.yr1[,i,j])-(1.96*sd(harv.rate.yr1[,i,j]))
rate.yr3.1[i,3,j]<-mean(harv.rate.yr1[,i,j])+(1.96*sd(harv.rate.yr1[,i,j]))
rate.yr3.1[i,4,j]<-sd(harv.rate.yr1[,i,j])/mean(harv.rate.yr1[,i,j])
}
}
### CV = 0.2 for catch; CV = 0.5 for escapement
harv.rate.yr2[which(harv.rate.yr2>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(no.wk)){
for(i in 1:10){
rate.yr3.2[i,1,j]<-mean(harv.rate.yr2[,i,j])
rate.yr3.2[i,2,j]<-mean(harv.rate.yr2[,i,j])-(1.96*sd(harv.rate.yr2[,i,j]))
rate.yr3.2[i,3,j]<-mean(harv.rate.yr2[,i,j])+(1.96*sd(harv.rate.yr2[,i,j]))
rate.yr3.2[i,4,j]<-sd(harv.rate.yr2[,i,j])/mean(harv.rate.yr2[,i,j])
}
}
### CV = 0.5 for catch; CV = 0.2 for escapement
harv.rate.yr3[which(harv.rate.yr3>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(no.wk)){
for(i in 1:10){
rate.yr3.3[i,1,j]<-mean(harv.rate.yr3[,i,j])
rate.yr3.3[i,2,j]<-mean(harv.rate.yr3[,i,j])-(1.96*sd(harv.rate.yr3[,i,j]))
rate.yr3.3[i,3,j]<-mean(harv.rate.yr3[,i,j])+(1.96*sd(harv.rate.yr3[,i,j]))
rate.yr3.3[i,4,j]<-sd(harv.rate.yr3[,i,j])/mean(harv.rate.yr3[,i,j])
}
}
### CV = 0.5 for catch; CV = 0.5 for escapement
harv.rate.yr4[which(harv.rate.yr4>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(no.wk)){
for(i in 1:10){
rate.yr3.4[i,1,j]<-mean(harv.rate.yr4[,i,j])
rate.yr3.4[i,2,j]<-mean(harv.rate.yr4[,i,j])-(1.96*sd(harv.rate.yr4[,i,j]))
rate.yr3.4[i,3,j]<-mean(harv.rate.yr4[,i,j])+(1.96*sd(harv.rate.yr4[,i,j]))
rate.yr3.4[i,4,j]<-sd(harv.rate.yr4[,i,j])/mean(harv.rate.yr4[,i,j])
}
}
##########################################################################
###### Weekly sampling
######
##### for populations of variable size (harvest rate is controlled below)
n.pops<-10
harvest.rate<-0.20 ### True harvest rate -
no.wk<-c(10,20,40,60,100) ### a vector of the different sample numbers taken in yearly sampling
catch.true<-array(dim=c(1000,10,length(no.wk))) ### true catch numbers for each model run
harv.rate<-array(dim=c(1000,10,length(no.wk))) ### true harvest rates for each model run
weekly.samp<-array(dim=c(1000,10,length(no.wk)))
catch.est.yr<-array(dim=c(1000,10,length(no.wk))) # est. catch proportions for each stock
total.est.yr<-array(dim=c(1000,10,length(no.wk))) # est. catch totals for each stock
total.est.yr2<-array(dim=c(1000,10,length(no.wk))) # est. catch totals for each stock w/uncertainty in catch CV=0.2
total.est.yr5<-array(dim=c(1000,10,length(no.wk))) # est. catch totals for each stock w/uncertainty in catch CV=0.5
harv.rate.yr0<-array(dim=c(1000,10,length(no.wk))) # estimated harvest rate CV = 0 for escape and total catch
harv.rate.yr1<-array(dim=c(1000,10,length(no.wk)))
harv.rate.yr2<-array(dim=c(1000,10,length(no.wk)))
harv.rate.yr3<-array(dim=c(1000,10,length(no.wk)))
harv.rate.yr4<-array(dim=c(1000,10,length(no.wk))) # estimated harvest rate CV = 0.5 for escape and total catch
##### Running the model ofr each sample number (s), and 1000 iterations (i)
for(s in 1:length(no.wk)){
for (i in 1:1000){ #### running the models 1000 times
### weekly abundance for each population w/ differing levels of uncertainty
pop.sizes<-c(500,1000,2000,3000,4000,6000,8000,10000,15000,20000)
pop.sizesCV.2<-round(pop.sizes*(rlnorm(length(pop.sizes),0,0.2)))
pop.sizesCV.5<-round(pop.sizes*(rlnorm(length(pop.sizes),0,0.5)))
pop.timing<-rmultinom(n.pops,100,c(0.1,0.2,0.3,0.2,0.15,0.05))/100 ## the 100 in the rmultinom statement controls the variance
###### these are all the fish coming through the fishing area for each week
run.weeks<-matrix(NA,nrow=6,ncol=n.pops)
for (n in 1:n.pops){
run.weeks[,n]<-round(pop.timing[,n]*pop.sizes[n])
}
week1<-c(rep(1,run.weeks[1,1]),rep(2,run.weeks[1,2]),rep(3,run.weeks[1,3]),rep(4,run.weeks[1,4]),
rep(5,run.weeks[1,5]),rep(6,run.weeks[1,6]),rep(7,run.weeks[1,7]),rep(8,run.weeks[1,8]),rep(9,run.weeks[1,9]),
rep(10,run.weeks[1,10]))
week2<-c(rep(1,run.weeks[2,1]),rep(2,run.weeks[2,2]),rep(3,run.weeks[2,3]),rep(4,run.weeks[2,4]),
rep(5,run.weeks[2,5]),rep(6,run.weeks[2,6]),rep(7,run.weeks[2,7]),rep(8,run.weeks[2,8]),rep(9,run.weeks[2,9]),
rep(10,run.weeks[2,10]))
week3<-c(rep(1,run.weeks[3,1]),rep(2,run.weeks[3,2]),rep(3,run.weeks[3,3]),rep(4,run.weeks[3,4]),
rep(5,run.weeks[3,5]),rep(6,run.weeks[3,6]),rep(7,run.weeks[3,7]),rep(8,run.weeks[3,8]),rep(9,run.weeks[3,9]),
rep(10,run.weeks[3,10]))
week4<-c(rep(1,run.weeks[4,1]),rep(2,run.weeks[4,2]),rep(3,run.weeks[4,3]),rep(4,run.weeks[4,4]),
rep(5,run.weeks[4,5]),rep(6,run.weeks[4,6]),rep(7,run.weeks[4,7]),rep(8,run.weeks[4,8]),rep(9,run.weeks[4,9]),
rep(10,run.weeks[4,10]))
week5<-c(rep(1,run.weeks[5,1]),rep(2,run.weeks[5,2]),rep(3,run.weeks[5,3]),rep(4,run.weeks[5,4]),
rep(5,run.weeks[5,5]),rep(6,run.weeks[5,6]),rep(7,run.weeks[5,7]),rep(8,run.weeks[5,8]),rep(9,run.weeks[5,9]),
rep(10,run.weeks[5,10]))
week6<-c(rep(1,run.weeks[6,1]),rep(2,run.weeks[6,2]),rep(3,run.weeks[6,3]),rep(4,run.weeks[6,4]),
rep(5,run.weeks[6,5]),rep(6,run.weeks[6,6]),rep(7,run.weeks[6,7]),rep(8,run.weeks[6,8]),rep(9,run.weeks[6,9]),
rep(10,run.weeks[6,10]))
###################################################
### PART 2a - simulating the catch process - total catch
CV.2<-rnorm(1,0,0.2) ### observation error CV = 0.2
CV.5<-rnorm(1,0,0.5) ### observation error CV = 0.5
catch.estCV.2<-rep(NA,6)
catch.estCV.5<-rep(NA,6)
for (j in 1:6){
catch[j]<-sum(run.weeks[j,])*harvest.rate
catch.estCV.2[j]<-abs(round(catch[j]+(catch[j]*CV.2)))
catch.estCV.5[j]<-abs(round(catch[j]+(catch[j]*CV.5)))
}
total.catch<-sum(catch)
total.catch_CV.2<-sum(catch.estCV.2) ### this is the estimated total harvest - including obs error (CV = 0.2)
total.catch_CV.5<-sum(catch.estCV.5) ### this is the estimated total harvest - inlcuding obs error (CV = 0.5)
############################################################################
##### PART 2b - the weekly catch of individual fish (e.g. different stocks)
## the catch process - This is the true catch numbers.
catch1<-sample(week1,catch[1],replace=FALSE,prob=NULL)
catch.tab1<-table(catch1)
catch2<-sample(week2,catch[2],replace=FALSE,prob=NULL)
catch.tab2<-table(catch2)
catch3<-sample(week3,catch[3],replace=FALSE,prob=NULL)
catch.tab3<-table(catch3)
catch4<-sample(week4,catch[4],replace=FALSE,prob=NULL)
catch.tab4<-table(catch4)
catch5<-sample(week5,catch[5],replace=FALSE,prob=NULL)
catch.tab5<-table(catch5)
catch6<-sample(week6,catch[6],replace=FALSE,prob=NULL)
catch.tab6<-table(catch6)
### combining stock-ID for all the fish caught (5000 total)
catch.all<-c(catch1,catch2,catch3,catch4,catch5,catch6)
### Making a table of stock specific catch
catch.tab_all<-table(catch.all)
catch.true[i,,s]<-as.vector(catch.tab_all)
harv.rate[i,,s]<-catch.true[i,,s]/pop.sizes
##########################################
## PART 3 - the catch sampling process
samples.wk<-matrix(nrow=6,ncol=no.wk[s])
catch.wks<-list(catch1,catch2,catch3,catch4,catch5,catch6)
### this is our weekly sampling process with 6 weeks and sample numbers = no.wk[s]
for(w in 1:length(catch.wks)){
samples.wk[w,]<-sample(catch.wks[[w]],no.wk[s],replace=FALSE,prob=NULL)
}
weekly.samp[i,1,s]<-length(which(samples.wk==1))
weekly.samp[i,2,s]<-length(which(samples.wk==2))
weekly.samp[i,3,s]<-length(which(samples.wk==3))
weekly.samp[i,4,s]<-length(which(samples.wk==4))
weekly.samp[i,5,s]<-length(which(samples.wk==5))
weekly.samp[i,6,s]<-length(which(samples.wk==6))
weekly.samp[i,7,s]<-length(which(samples.wk==7))
weekly.samp[i,8,s]<-length(which(samples.wk==8))
weekly.samp[i,9,s]<-length(which(samples.wk==9))
weekly.samp[i,10,s]<-length(which(samples.wk==10))
## contribution of each population in the catch
catch.est.yr[i,,s]<-as.vector(weekly.samp[i,,s]/sum(weekly.samp[i,,s]))
# total estimated harvest for each pop.
total.est.yr[i,,s]<-round(catch.est.yr[i,,s]*total.catch)
total.est.yr2[i,,s]<-round(catch.est.yr[i,,s]*total.catch_CV.2)
total.est.yr5[i,,s]<-round(catch.est.yr[i,,s]*total.catch_CV.5)
# total estimated harvest rate for each pop.
harv.rate.yr0[i,,s]<-total.est.yr[i,,s]/pop.sizes
harv.rate.yr1[i,,s]<-total.est.yr2[i,,s]/pop.sizesCV.2 # catch CV = 0.2; escape CV = 0.2
harv.rate.yr2[i,,s]<-total.est.yr2[i,,s]/pop.sizesCV.5 # catch CV = 0.2; escape CV = 0.5
harv.rate.yr3[i,,s]<-total.est.yr5[i,,s]/pop.sizesCV.2 # catch CV = 0.5; escape CV = 0.2
harv.rate.yr4[i,,s]<-total.est.yr5[i,,s]/pop.sizesCV.5 # catch CV = 0.5; escape CV = 0.5
}
}
###############################################################################
##### estimating the mean & sd of catch contrib. - just reflects sample sizes not obs error
comp.yr4<-array(dim=c(n.pops,4,length(no.wk))) ## catch composition for single sample and even pop sizes
for(j in 1:length(no.wk)){
for(i in 1:10){
comp.yr4[i,1,j]<-mean(catch.est.yr[,i,j])
comp.yr4[i,2,j]<-mean(catch.est.yr[,i,j])-(1.96*sd(catch.est.yr[,i,j]))
comp.yr4[i,3,j]<-mean(catch.est.yr[,i,j])+(1.96*sd(catch.est.yr[,i,j]))
comp.yr4[i,4,j]<-sd(catch.est.yr[,i,j])/mean(catch.est.yr[,i,j])
}
}
comp.yr4[,,5]
##### estimating the mean and sd of harvest rate estimates for our model
rate.yr4.0<-array(dim=c(n.pops,4,length(no.wk)))
rate.yr4.1<-array(dim=c(n.pops,4,length(no.wk)))
rate.yr4.2<-array(dim=c(n.pops,4,length(no.wk)))
rate.yr4.3<-array(dim=c(n.pops,4,length(no.wk)))
rate.yr4.4<-array(dim=c(n.pops,4,length(no.wk)))
### assuming perfect knowledge of total catch and escapement
for(j in 1:length(no.wk)){
for(i in 1:10){
rate.yr4.0[i,1,j]<-mean(harv.rate.yr0[,i,j])
rate.yr4.0[i,2,j]<-mean(harv.rate.yr0[,i,j])-(1.96*sd(harv.rate.yr0[,i,j]))
rate.yr4.0[i,3,j]<-mean(harv.rate.yr0[,i,j])+(1.96*sd(harv.rate.yr0[,i,j]))
rate.yr4.0[i,4,j]<-sd(harv.rate.yr0[,i,j])/mean(harv.rate.yr0[,i,j])
}
}
### CV = 0.2 for catch and escapement
harv.rate.yr1[which(harv.rate.yr1>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(no.wk)){
for(i in 1:10){
rate.yr4.1[i,1,j]<-mean(harv.rate.yr1[,i,j])
rate.yr4.1[i,2,j]<-mean(harv.rate.yr1[,i,j])-(1.96*sd(harv.rate.yr1[,i,j]))
rate.yr4.1[i,3,j]<-mean(harv.rate.yr1[,i,j])+(1.96*sd(harv.rate.yr1[,i,j]))
rate.yr4.1[i,4,j]<-sd(harv.rate.yr1[,i,j])/mean(harv.rate.yr1[,i,j])
}
}
### CV = 0.2 for catch; CV = 0.5 for escapement
harv.rate.yr2[which(harv.rate.yr2>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(no.wk)){
for(i in 1:10){
rate.yr4.2[i,1,j]<-mean(harv.rate.yr2[,i,j])
rate.yr4.2[i,2,j]<-mean(harv.rate.yr2[,i,j])-(1.96*sd(harv.rate.yr2[,i,j]))
rate.yr4.2[i,3,j]<-mean(harv.rate.yr2[,i,j])+(1.96*sd(harv.rate.yr2[,i,j]))
rate.yr4.2[i,4,j]<-sd(harv.rate.yr2[,i,j])/mean(harv.rate.yr2[,i,j])
}
}
### CV = 0.5 for catch; CV = 0.2 for escapement
harv.rate.yr3[which(harv.rate.yr3>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(no.wk)){
for(i in 1:10){
rate.yr4.3[i,1,j]<-mean(harv.rate.yr3[,i,j])
rate.yr4.3[i,2,j]<-mean(harv.rate.yr3[,i,j])-(1.96*sd(harv.rate.yr3[,i,j]))
rate.yr4.3[i,3,j]<-mean(harv.rate.yr3[,i,j])+(1.96*sd(harv.rate.yr3[,i,j]))
rate.yr4.3[i,4,j]<-sd(harv.rate.yr3[,i,j])/mean(harv.rate.yr3[,i,j])
}
}
### CV = 0.5 for catch; CV = 0.5 for escapement
harv.rate.yr4[which(harv.rate.yr4>1)]<-0.95 ## setting harvest rates above 1 to 0.95
for(j in 1:length(no.wk)){
for(i in 1:10){
rate.yr4.4[i,1,j]<-mean(harv.rate.yr4[,i,j])
rate.yr4.4[i,2,j]<-mean(harv.rate.yr4[,i,j])-(1.96*sd(harv.rate.yr4[,i,j]))
rate.yr4.4[i,3,j]<-mean(harv.rate.yr4[,i,j])+(1.96*sd(harv.rate.yr4[,i,j]))
rate.yr4.4[i,4,j]<-sd(harv.rate.yr4[,i,j])/mean(harv.rate.yr4[,i,j])
}
}
####################################################################
##### Plotting uncertainty in catch composition
### fixed population size (5000)
comp.equal<-matrix(nrow=5,ncol=2)
comp.yr1[,,1]
for (i in 1:5){
comp.equal[i,1]<-mean(comp.yr1[,4,i]) ## single sample
comp.equal[i,2]<-mean(comp.yr3[,4,i]) ## weekly sample
}
### variable population size
comp.var<-matrix(nrow=10,ncol=10)
for (i in 1:5){
comp.var[,i]<-comp.yr2[,4,i]
comp.var[,i+5]<-comp.yr4[,4,i]
}
max(comp.var)
library(viridis)
colors <- rev(viridis(10))
jpeg(filename = "figures/figure_6.jpeg",
width = 2600, height = 1500, units = "px", pointsize = 9,
bg = "white", res = 600)
samples<-c(60,120,240,360,600)
par(mfrow=c(1,2))
par(mar=c(2,1,1,0),oma=c(2,4,1,1))