options(scipen=999)
# EIQ simulation code
### Function to calculate the EIQ value from a list of risk factors:
eiq<-function(dt=1, ca=1, sy=1, f=1, l=1, r=1, d=1, s=1, z=1, b=1, p=1){
              EIQ<-(ca*((dt*5)+(dt*p))+
                    ((ca*((s+p)/2)*sy)+(l))+
                    ((f*r)+(d*((s+p)/2)*3)+(z*p*3)+(b*p*5)))/3
              invisible(round(EIQ,1))
          }
### Calculate the minimum and maximum possible EIQ values:
eiq.min<-eiq(1,1,1,1,1,1,1,1,1,1,1)
eiq.max<-eiq(5,5,5,5,5,5,5,5,5,5,5)
### Calculate the maximum possible EIQ value for a herbicide:
eiq.maxHerb<-eiq(5,5,1,5,5,5,5,5,5,5,3)
data.frame(eiq.min, eiq.max, eiq.maxHerb)
### Create 100,000 iterations of each risk factor where possible values = (1,3,5)
### except for SY, which is always = 1 for herbicides, and for P, which is 1 for
### preemergence herbicides and 3 for postemergence herbicides
val<-c(1,3,5)
dt<-sample(val, 100000, replace=T)
ca<-sample(val, 100000, replace=T)
sy<-1
f<-sample(val, 100000, replace=T)
l<-sample(val, 100000, replace=T)
r<-sample(val, 100000, replace=T)
d<-sample(val, 100000, replace=T)
s<-sample(val, 100000, replace=T)
z<-sample(val, 100000, replace=T)
b<-sample(val, 100000, replace=T)
p<-sample(c(1,3), 100000, replace=T)
### Run each of the 100,000 iterations through the EIQ formula to calculate
### the EIQ value for each combination of values, then create a data frame with
### the simulation results.
eiq.calc<-eiq(dt, ca, sy, f, l, r ,d, s, z, b, p)
eiq.sim<-data.frame(dt, ca, sy, f, l, r, d, s, z, b, p, eiq.calc)
median(eiq.calc)
### Run a linear regression with EIQ value as the dependent variable against each
### risk factor as independent variables. The slope coefficient then gives a
### "Relative influence" values (slope) and explained variance (using sums of
### squares) for the calculated EIQ.
lm(eiq.calc~dt+ca+f+l+r+d+s+z+b+p, data=eiq.sim)->RI.lm
RI<-round(coef(RI.lm),1)[2:11]
RI
barplot(sort(RI, decreasing=TRUE))
data.frame(SumSq=round(anova(RI.lm)[2],0),
           PctMeanSq=round(anova(RI.lm)[2]/sum(anova(RI.lm)[2]),3))->ssRI
colnames(ssRI)<-c("SumSquares","PropOfTotalSS")
ssRI
### Calculate the median EIQ for each value of each risk factor
dts<-tapply(eiq.sim$eiq.calc, eiq.sim$dt, median)
cas<-tapply(eiq.sim$eiq.calc, eiq.sim$ca, median)
fs<-tapply(eiq.sim$eiq.calc, eiq.sim$f, median)
ls<-tapply(eiq.sim$eiq.calc, eiq.sim$l, median)
rs<-tapply(eiq.sim$eiq.calc, eiq.sim$r, median)
ds<-tapply(eiq.sim$eiq.calc, eiq.sim$d, median)
ss<-tapply(eiq.sim$eiq.calc, eiq.sim$s, median)
zs<-tapply(eiq.sim$eiq.calc, eiq.sim$z, median)
bs<-tapply(eiq.sim$eiq.calc, eiq.sim$b, median)
ps<-tapply(eiq.sim$eiq.calc, eiq.sim$p, median)
ps<-c(ps,NA)
data.frame(dts, cas, fs, ls, rs, ds, ss, zs, bs, ps)->eiq.simsens
colnames(eiq.simsens)<-c("DT","C","F","L","R","D","S","Z","B","P")
rownames(eiq.simsens)<-c("Min.1","Med.3","Max.5")
round(t(eiq.simsens),1)
### Calculate Spearman's rho between EIQ and each risk factor
simcor<-data.frame(Risk=colnames(eiq.sim),
                   Spearman=round(cor(eiq.sim,method="spearman")[,12],2))
print(simcor, row.names=FALSE)
### Subset into PRE and POST datasets
pre.sim<-subset(eiq.sim, p==1)
post.sim<-subset(eiq.sim, p==3)
### Relative influence for PRE herbicides
pre.RI<-round(coef(lm(eiq.calc~dt+ca+f+l+r+d+s+z+b, data=pre.sim)),1)[2:10]
### Relative influence for POST herbicides
post.RI<-round(coef(lm(eiq.calc~dt+ca+f+l+r+d+s+z+b, data=post.sim)),1)[2:10]
### Summary table
data.frame(pre.RI, post.RI, diff=post.RI-pre.RI)
### Relative influence of P interactions
rfs<-c("dt","ca","sy","f","l","r","d","s","z","b")
rfdf<-data.frame(rfs, P=NA, var=NA, pintx=NA)
for(i in 1:10){
    round(coef(lm(eiq.sim[,12]~eiq.sim[,11]*eiq.sim[,i]))[2:4],1)->rfdf[i,2:4]
}
rfdf
################# End simulation code ###########################

library(extrafont) # get Arial font due to PLOS request
loadfonts(device="postscript")

### Multi-panel box plot figure
g1<-gray(0.95)
g2<-gray(0.85)
g3<-gray(0.75)
gcol<-c(g1,g2,g3)
risks<-c("Low","Medium","High")
postscript("Fig1_EIQ-SimBoxplotsBW.eps", width=6, height=7, #units="in", res=300,
           pointsize=12, family="Arial",
           paper="special", horizontal=FALSE, onefile=FALSE)
par(mfrow=c(3,3), mar=c(4.2, 2.2, 2.0, 0.5), mgp=c(2.2, 1, 0), oma=c(0, 2, 0, 0))
boxplot(eiq.sim$eiq.calc~eiq.sim$dt, range=0, xlab="Dermal toxicity (DT)",
        ylab="", ylim=c(0,140), col=c(g1,g2,g3), names=risks, frame.plot=FALSE)
mtext("A", side=2, line=2, las=2, at=155)
boxplot(eiq.sim$eiq.calc~eiq.sim$ca, range=0, xlab="Chronic toxicity (C)",
        ylab="", ylim=c(0,140), col=gcol, names=risks, frame.plot=FALSE)
mtext("B", side=2, line=2, las=2, at=155)
boxplot(eiq.sim$eiq.calc~eiq.sim$f, range=0, xlab="Fish toxicity (F)",
        ylab="", ylim=c(0,140), col=gcol, names=risks, frame.plot=FALSE)
mtext("C", side=2, line=2, las=2, at=155)
boxplot(eiq.sim$eiq.calc~eiq.sim$l, range=0, xlab="Leaching potential (L)",
        ylab="", ylim=c(0,140), col=gcol, names=risks, frame.plot=FALSE)
mtext("D", side=2, line=2, las=2, at=155)
boxplot(eiq.sim$eiq.calc~eiq.sim$r, range=0, xlab="Surface loss potential (R)",
        ylab="", ylim=c(0,140), col=gcol, names=risks, frame.plot=FALSE)
mtext("E", side=2, line=2, las=2, at=155)
boxplot(eiq.sim$eiq.calc~eiq.sim$d, range=0, xlab="Bird toxicity (D)",
        ylab="", ylim=c(0,140), col=gcol, names=risks, frame.plot=FALSE)
mtext("F", side=2, line=2, las=2, at=155)
boxplot(eiq.sim$eiq.calc~eiq.sim$s, range=0, xlab="Soil half-life (S)",
        ylab="", ylim=c(0,140), col=gcol, names=risks, frame.plot=FALSE)
mtext("G", side=2, line=2, las=2, at=155)
boxplot(eiq.sim$eiq.calc~eiq.sim$z, range=0, xlab="Bee toxicity (Z)",
        ylab="", ylim=c(0,140), col=gcol, names=risks, frame.plot=FALSE)
mtext("H", side=2, line=2, las=2, at=155)
boxplot(eiq.sim$eiq.calc~eiq.sim$b, range=0, xlab="Beneficial arthropod toxicity (B)",
        ylab="", ylim=c(0,140), col=gcol, names=risks, frame.plot=FALSE)
mtext("I", side=2, line=2, las=2, at=155)
mtext("EIQ", 2, outer=T, line=0.5, at=0.856)
mtext("EIQ", 2, outer=T, line=0.5, at=0.525)
mtext("EIQ", 2, outer=T, line=0.5, at=0.19)
dev.off()

### Histogram of EIQ values, disaggregated by PRE vs POST
median(pre.sim$eiq)
median(post.sim$eiq)
postscript("Fig2_PREvPOSThistogram.eps", width=5, height=6, #units="in", res=300,
           pointsize=12, family="Arial",
           paper="special", horizontal=FALSE, onefile=FALSE)
par(mar=c(0, 4.2, 0, 0.5), oma=c(4,1,1,0))
layout(matrix(c(2,1,0,4,3), ncol=1), heights=c(2,0.5,1,2,0.5))
boxplot(pre.sim$eiq.calc, horizontal=TRUE, ylim=c(0,150), frame.plot=FALSE,
        axes=TRUE, col=gray(0.95), range=0)
hist(pre.sim$eiq.calc,  col=gray(0.95),xlim=c(0,150),
     breaks=0:15*10, main="", xlab="", ylim=c(0,15000), axes=FALSE)
  axis(2)
  text(34,12000, "median = 34", pos=4, cex=1.2)
legend("topright", legend=c("PRE (P=1)"), 
       cex=1.3, bty="n")
mtext("A", side=2, line=0, las=1, outer=TRUE, at=1)
boxplot(post.sim$eiq.calc, horizontal=TRUE, ylim=c(0,150), frame.plot=FALSE,
        axes=TRUE, col=gray(0.65), range=0)
hist(post.sim$eiq.calc, col=gray(0.65), xlim=c(0,150),
     breaks=0:15*10,main="", xlab="", ylim=c(0,15000), axes=FALSE)
  axis(2)
  text(34,12000, "median = 60", pos=4, cex=1.2)
legend("topright", legend=c("POST (P=3)"), 
       cex=1.3, bty="n")
mtext("B", side=2, line=0, las=1, outer=TRUE, at=0.415)
mtext("Simulated EIQ Values", side=1, line=2.8, at=0.57, outer=TRUE)
dev.off()
 
### Repeating the eiq function in case we don't want to run all of the above code...
eiq<-function(dt=1, ca=1, sy=1, f=1, l=1, r=1, d=1, s=1, z=1, b=1, p=1){
              EIQ<-(ca*((dt*5)+(dt*p))+
                    ((ca*((s+p)/2)*sy)+(l))+
                    ((f*r)+(d*((s+p)/2)*3)+(z*p*3)+(b*p*5)))/3
              invisible(round(EIQ,1))
          }
#### Atrazine EIQ
atrazine.eiq<-eiq(dt=1, ca=1, sy=1, f=3, l=3, r=3, d=1, s=5, z=1, b=1.57, p=3)
atrazine.L1<-eiq(dt=1, ca=1, sy=1, f=3, l=1, r=3, d=1, s=5, z=1, b=1.57, p=3)
atrazine.R1<-eiq(dt=1, ca=1, sy=1, f=3, l=3, r=1, d=1, s=5, z=1, b=1.57, p=3)
atrazine.pre<-eiq(dt=1, ca=1, sy=1, f=3, l=3, r=3, d=1, s=5, z=1, b=1.57, p=1)
atrazine.vals<-data.frame("Atrazine EIQ"=atrazine.eiq, "Low Leaching Atrazine"=atrazine.L1,
           "Atrazine PRE"=atrazine.pre, "Low Runoff Atrazine"=atrazine.R1)
atrazine.vals

### Histogram of EIQ values
### Not presented in manuscript
median(eiq.sim$eiq)
postscript("EIQ-simulation.eps", width=4.2, height=3, #units="in", res=300,
           pointsize=12, family="Times",
           paper="special", horizontal=FALSE, onefile=FALSE)
par(mfrow=c(1,1), mar=c(4.2, 4.2, 0.0, 0.5), oma=c(0,0,2.5,0))
hist(eiq.sim$eiq.calc, col=gray(0.8), xlab="EIQ",main="")
  abline(v=47.3, lty=2)
  text(47.3,15000, "median = 47.3", pos=4, cex=0.8)
mtext("EIQ simulation results", 3, 1.5, outer=T, cex=1.1)
mtext("(N=100,000)", 3, 0.5, outer=T, cex=0.9)
dev.off()

### ggplot side-by-side bar plots, instead of a 2-panel plot (Figure 2)
### Not used in manuscript
pre.hist<-hist(pre.sim$eiq.calc, breaks=0:15*10, plot=FALSE)
post.hist<-hist(post.sim$eiq.calc, breaks=0:15*10, plot=FALSE)
library(ggplot2)
pvp<-data.frame(Timing=c(rep("PRE",15),rep("POST",15)),
                Frequency=c(pre.hist$counts,post.hist$counts),
                SimulatedEIQ=c(pre.hist$mids,post.hist$mids))
postscript("EIQ-PREvPOST.eps", width=4.2, height=2.5, #units="in", res=300,
           pointsize=12, family="Times",
           paper="special", horizontal=FALSE, onefile=FALSE)
ggplot(pvp, aes(x=SimulatedEIQ, y=Frequency, fill=Timing)) +
    geom_bar(stat="identity", position="dodge") + theme_bw()
dev.off()

### Get mean values instead of medians, if interested
dts<-tapply(eiq.sim$eiq.calc, eiq.sim$dt, mean)
cas<-tapply(eiq.sim$eiq.calc, eiq.sim$ca, mean)
fs<-tapply(eiq.sim$eiq.calc, eiq.sim$f, mean)
ls<-tapply(eiq.sim$eiq.calc, eiq.sim$l, mean)
rs<-tapply(eiq.sim$eiq.calc, eiq.sim$r, mean)
ds<-tapply(eiq.sim$eiq.calc, eiq.sim$d, mean)
ss<-tapply(eiq.sim$eiq.calc, eiq.sim$s, mean)
zs<-tapply(eiq.sim$eiq.calc, eiq.sim$z, mean)
bs<-tapply(eiq.sim$eiq.calc, eiq.sim$b, mean)
ps<-tapply(eiq.sim$eiq.calc, eiq.sim$p, mean)
ps<-c(ps,NA)
data.frame(dts, cas, fs, ls, rs, ds, ss, zs, bs, ps)->eiq.simsens
colnames(eiq.simsens)<-c("DT","C","F","L","R","D","S","Z","B","P")
rownames(eiq.simsens)<-c("Min.1","Med.3","Max.5")
round(t(eiq.simsens),1)