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Fig.4 code.R
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Fig.4 code.R
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###updated by JJ on 6-7-18: changed color direction and took off cell number
rm(list=ls())
setwd("C:\\Users\\jiaojin1\\Downloads\\PhD work")
library(deSolve)
library(reshape)
library(ggplot2)
library(scales)
library(pheatmap)
library(tidyverse)
################test
#####L is fishing ground while T is MPAs, total area is S
JAP08<-function(t, inits,parameters) {
with(as.list(c(inits, parameters)),{
x<-inits[1:L]
y<-inits[(L+1):(L+T)]
A<-array(NA,dim=c(1,(L+T)))
if(L==1)
{
A[1]<-R-(mu+F)*x[1]-D1*x[1]+D2/2*y[1]+D2/2*y[T]
}
else
{
A[1]<-R-(mu+F)*x[1]-D1*x[1]+D1/2*x[2]+D2/2*y[1]
A[L]<-R-(mu+F)*x[L]-D1*x[L]+D1/2*x[L-1]+D2/2*y[T]
}
if(L-1>=2)
{
for(i in 2:(L-1))
{
A[i]<-R-(mu+F)*x[i]-D1*x[i]+D1/2*(x[i-1]+x[i+1])
}
}
if(T==1)
{
A[(L+1)]<-R-mu*y[1]-D2*y[1]+D1/2*x[L]+D1/2*x[1]
}
else
{
A[(L+1)]<-R-mu*y[1]-D2*y[1]+D2/2*y[2]+D1/2*x[1]
A[(T+L)]<-R-mu*y[T]-D2*y[T]+D2/2*y[T-1]+D1/2*x[L]
}
if(T-1>=2)
{
for(i in (L+2):(T+L-1))
{
A[i]<-R-mu*y[i-L]-D2*y[i-L]+D2/2*(y[i-L-1]+y[i-L+1])
}
}
list(c(A))
})
}
#################
Timesteps=500
times <- seq(0, Timesteps, by = 1)
S=10
inits <- rep(1,S)
beta<-seq(1,4.1,0.25)
h<-seq(1,9,1)
F=0.25
##h is for MPA size, r is for differential movement
eqn<-array(NA,dim=c(length(beta),length(h),S))
eqn_before<-array(NA,dim=c(length(beta),length(h),S))
for(i in 1:length(beta))
{
for(j in 1:length(h))
{
for(z in 1:S)
{
parameters <- c(T=h[j],L=S-h[j],R=2,mu=0.5,D1=0.5*beta[i],D2=0.5,F=0.25)
out= ode(y = inits, times = times, func = JAP08, parms = parameters)
eqn[i,j,z]<-out[Timesteps+1,z+1]
###before data for each cell
parameters_before <- c(T=h[j],L=S-h[j],R=2,mu=0.5,D1=0*beta[i],D2=0,F=0.25)
out_before= ode(y = inits, times = times, func = JAP08, parms = parameters_before)
eqn_before[i,j,z]<-out_before[Timesteps+1,z+1]
}
}
}
###before-after
###using after density at each cell in MPA / before density at each cell
####after mean/before mean indicates the before-after effect
eqnmean_ba<-array(NA,dim=c(length(beta),length(h),2))
before_after<-array(NA,dim=c(length(beta),length(h)))
for(i in 1:length(beta))
{
for(j in 1:length(h))
{
eqnmean_ba[i,j,1]<-mean(eqn_before[i,j,1:(S-h[j])]) # mean density before MPA
eqnmean_ba[i,j,2]<-mean(eqn[i,j,(S-h[j]+1):S]) # mean density in MPA
before_after[i,j]<-eqnmean_ba[i,j,2]/eqnmean_ba[i,j,1]
}
}
###before status
###local effect: =1 since there is no MPA
loc_before=1
###regional abundance:eqnmean_ba[1,1,1]=2.666667
reg_before<-eqnmean_ba[1,1,1]*10
###fishing yield
fis_before<-F*reg_before
#local effect
yield<-array(NA,dim=c(length(beta),length(h)))
for(i in 1:length(beta))
{
for(j in 1:length(h))
{
yield[i,j]<-sum(eqn[i,j,1:(S-h[j])])*F
}
}
##local effect
eqnmean<-array(NA,dim=c(length(beta),length(h),2))
loceff<-array(NA,dim=c(length(beta),length(h)))
for(i in 1:length(beta))
{
for(j in 1:length(h))
{
eqnmean[i,j,1]<-mean(eqn[i,j,1:(S-h[j])])
eqnmean[i,j,2]<-mean(eqn[i,j,(S-h[j]+1):S])
loceff[i,j]<-eqnmean[i,j,2]/eqnmean[i,j,1]
}
}
##regional effect
regeff<-array(NA,dim=c(length(beta),length(h)))
for(i in 1:length(beta))
{
for(j in 1:length(h))
{
regeff[i,j]<-sum(eqn[i,j,1:S])
}
}
before_after1<-melt(before_after)
yield1<-melt(yield)
loceff1<-melt(loceff)
regeff1<-melt(regeff)
##at 50% MPA and FG
#rho<-loceff[,5]
#plot(rho,lwd=2,xlim=c(0,100),ylim=c(0,100),ylab="rho",xlab="beta",type="l")
#y<-function(x) {y=x}
#curve(y,0,100,lwd=2,add=T,col="red",type="l")
#y1<-function(x1) {y1=0.5*x1}
#curve(y1,0,100,lwd=2,add=T,col="red",lty=2)
theme_set(theme_bw(20))
#tiff("density in FG and MPA 5-2.tiff", width=5,height=5, units='in',res=600)
#par(mfrow=c(2,1))
#par(mar=c(1.98,4,1,0.8))
#plot(eqnmean[,5,1],type="l",lwd=2,xlab="beta",ylab="density in FG")
#plot(eqnmean[,5,2],type="l",lwd=2,xlab="beta",ylab="density in MPA")
#abline(h=100,col="red",lwd=2)
#dev.off()
##61 is the value MPA=0.5 and beta=1
#61=length(beta)*4+1
before_after2<-before_after1
#before_after2$value<-before_after1$value/before_after1$value[61]
before_after2$value<-before_after1$value/1
yield2<-yield1
#yield2$value<-yield1$value/yield1$value[61]
yield2$value<-yield1$value/fis_before
loceff2<-loceff1
#loceff2$value<-loceff1$value/loceff1$value[61]
loceff2$value<-loceff1$value/1
regeff2<-regeff1
#regeff2$value<-regeff1$value/regeff1$value[61]
regeff2$value<-regeff1$value/reg_before
#tiff("Fig.4_before_after-5-8-18.tiff", width=5,height=5, units='in',res=600)
#p1 <- ggplot(before_after2, aes(beta[X1], h[X2]/10)) + geom_tile(aes(fill = value))+ geom_text(aes(label=round(value,2)),position = position_dodge(width=0.05), size=1.5)+guides(fill = guide_colorbar(title=""))
#p1+xlab("")+ylab('')+ scale_fill_gradient2(low = 'steelblue', mid='white',high = 'red' ,
#
# midpoint=1, space = "rgb", na.value = "grey50", guide =
# "colourbar")+scale_x_continuous(expand #= c(0, 0)) + scale_y_continuous(expand
# = c(0, 0))
#dev.off()
tiff("5-11-18-Fig.4_fishing yield-0.25.tiff", width=5,height=5, units='in',res=600)
#p1 <- ggplot(yield2, aes(beta[X1], h[X2]/10)) + geom_tile(aes(fill = value)) + geom_text(aes(label=round(value,2)),position = position_dodge(width=0.05), size=1.5)+guides(fill = guide_colorbar(title=""))
p1 <- ggplot(yield2, aes(beta[X1], h[X2]/10)) + geom_tile(aes(fill = value))+guides(fill = guide_colorbar(title=""))
p1+xlab("")+ylab('')+ scale_fill_gradient2(low = 'red', mid='white',high = 'steelblue' ,
midpoint=1, space = "rgb", na.value = "grey50", guide =
"colourbar")+scale_x_continuous(expand = c(0, 0)) + scale_y_continuous(expand
= c(0, 0))
dev.off()
tiff("5-11-18-Fig.4_local-effect-0.25.tiff", width=5,height=5, units='in',res=600)
p1 <- ggplot(loceff2, aes(beta[X1], h[X2]/10)) + geom_tile(aes(fill = value))+guides(fill = guide_colorbar(title=""))
p1+xlab("")+ylab('')+ scale_fill_gradient2(low = 'red', mid='white',high = 'steelblue' ,
midpoint=1, space = "rgb", na.value = "grey50", guide =
"colourbar")+scale_x_continuous(expand = c(0, 0)) + scale_y_continuous(expand
= c(0, 0))
dev.off()
tiff("5-11-18-Fig.4_regional-effect-0.25.tiff", width=5,height=5, units='in',res=600)
p1 <- ggplot(regeff2, aes(beta[X1], h[X2]/10)) + geom_tile(aes(fill = value)) +guides(fill = guide_colorbar(title=""))
p1+xlab("")+ylab('')+ scale_fill_gradient2(low = 'red', mid='white',high = 'steelblue',
midpoint=1, space = "rgb", na.value = "grey50", guide =
"colourbar")+scale_x_continuous(expand = c(0, 0)) + scale_y_continuous(expand
= c(0, 0))
dev.off()