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Fig.S1 code.R
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Fig.S1 code.R
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##take off exponential term +1 and interference competition
#setwd("C:\\Users\\jiaojin1\\Downloads\\PhD work")
library(deSolve)
library(reshape)
library(ggplot2)
library(scales)
library(pheatmap)
################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)
r<-c(1,1.5,2)
m<-seq(0,10,0.5)
F=0.25
##h is for MPA size, r is for differential movement
eqn1<-array(NA,dim=c(length(r),length(m),S))
eqn5<-array(NA,dim=c(length(r),length(m),S))
eqn9<-array(NA,dim=c(length(r),length(m),S))
eqn_before<-array(NA,dim=c(length(r),length(m),S))
for(i in 1:length(r))
{
for(j in 1:length(m))
{
for(z in 1:S)
{
parameters <- c(T=1,L=9,R=2,mu=0.5,D1=m[j]*r[i],D2=m[j],F=0.25)
out= ode(y = inits, times = times, func = JAP08, parms = parameters)
eqn1[i,j,z]<-out[Timesteps+1,z+1]
parameters <- c(T=5,L=5,R=2,mu=0.5,D1=m[j]*r[i],D2=m[j],F=0.25)
out= ode(y = inits, times = times, func = JAP08, parms = parameters)
eqn5[i,j,z]<-out[Timesteps+1,z+1]
parameters <- c(T=9,L=1,R=2,mu=0.5,D1=m[j]*r[i],D2=m[j],F=0.25)
out= ode(y = inits, times = times, func = JAP08, parms = parameters)
eqn9[i,j,z]<-out[Timesteps+1,z+1]
parameters_before <- c(T=5,L=5,R=2,mu=0.5,D1=0,D2=0,F=0.25)
out= ode(y = inits, times = times, func = JAP08, parms = parameters)
eqn_before[i,j,z]<-out[Timesteps+1,z+1]
}
}
}
###before MPA
###cell density
den_bef<-eqn_before[1,1,1]
###local effect: =1 since there is no MPA
loc_before=1
###regional abundance:eqnmean_ba[1,1,1]=2.666667
reg_before<-eqn_before[1,1,1]*10
###fishing yield
fis_before<-F*reg_before
bind1<-rbind(eqn1[,10,]/den_bef,eqn5[,10,]/den_bef,eqn9[,10,]/den_bef)
bind<-bind1
tiff("Fig.S1 in Appendix.tiff", width=5,height=5, units='in',res=600)
####standardized by Before density instead of eqn5[]
par(mfrow=c(3,3))
par(mar=c(2,2,1.5,2))
yval6<-eqn9[1,10,]/den_bef
plot(seq(1,10,1),eqn9[1,10,]/den_bef,lwd=2,xlab="",ylab="",ylim=c(min(bind),2),pch=16,col="#31A9B8")
points(seq(1,10,1),eqn9[1,10,]/den_bef,lwd=1,type="p",col="black")
points(1,yval6[1],type="p",pch=16,lwd=2,col="red")
abline(v=1.5,lwd=2,lty=5)
text(4,1.0,paste("LE=",round(mean(eqn9[1,10,2:10])/mean(eqn9[1,10,1]),digits=2)))
yval7<-eqn9[2,10,]/den_bef
plot(seq(1,10,1),eqn9[2,10,]/den_bef,lwd=2,type="p",lty=2,ylim=c(min(bind),2),pch=16,col="#31A9B8")
points(seq(1,10,1),eqn9[2,10,]/den_bef,lwd=1,type="p",col="black")
points(1,yval7[1],type="p",pch=16,lwd=2,col="red")
abline(v=1.5,lwd=2,lty=5)
text(4,1.0,paste("LE=",round(mean(eqn9[2,10,2:10])/mean(eqn9[2,10,1]),digits=2)))
yval8<-eqn9[3,10,]/den_bef
plot(seq(1,10,1),eqn9[3,10,]/den_bef,lwd=2,type="p",lty=3,ylim=c(min(bind),2),pch=16,col="#31A9B8")
points(seq(1,10,1),eqn9[3,10,]/den_bef,lwd=1,type="p",col="black")
points(1,yval8[1],type="p",pch=16,col="red")
abline(v=1.5,lwd=2,lty=5)
text(4,1.0,paste("LE=",round(mean(eqn9[3,10,2:10])/mean(eqn9[3,10,1]),digits=2)))
###at medium MPA size SM=5
yval3<-eqn5[1,10,]/den_bef
plot(seq(1,10,1),eqn5[1,10,]/den_bef,lwd=2,xlab="",ylab="",ylim=c(min(bind),2),pch=16,col="#31A9B8")
points(seq(1,10,1),eqn5[1,10,]/den_bef,lwd=1,type="p",col="black")
points(1:5,yval3[1:5],type="p",pch=16,lwd=2,col="red")
abline(v=5.5,lwd=2,lty=5)
text(3.3,1.3,paste("LE=",round(mean(eqn5[1,10,6:10])/mean(eqn5[1,10,1:5]),digits=2)))
yval4<-eqn5[2,10,]/den_bef
plot(seq(1,10,1),eqn5[2,10,]/den_bef,lwd=2,type="p",lty=3,ylim=c(min(bind),2),pch=16,col="#31A9B8")
points(seq(1,10,1),eqn5[2,10,]/den_bef,lwd=1,type="p",col="black")
points(1:5,yval4[1:5],type="p",pch=16,lwd=2,col="red")
abline(v=5.5,lwd=2,lty=5)
text(3.3,1.3,paste("LE=",round(mean(eqn5[2,10,6:10])/mean(eqn5[2,10,1:5]),digits=2)))
yval5<-eqn5[3,10,]/den_bef
plot(seq(1,10,1),eqn5[3,10,]/den_bef,lwd=2,type="p",lty=3,ylim=c(min(bind),2),pch=16,col="#31A9B8")
points(seq(1,10,1),eqn5[3,10,]/den_bef,lwd=1,type="p",col="black")
points(1:5,yval5[1:5],type="p",pch=16,lwd=2,col="red")
abline(v=5.5,lwd=2,lty=5)
text(3.3,1.3,paste("LE=",round(mean(eqn5[3,10,6:10])/mean(eqn5[3,10,1:5]),digits=2)))
###at large MPA size SM=9
yval<-eqn1[1,10,]/den_bef
plot(seq(1,10,1),eqn1[1,10,]/den_bef,lwd=2,xlab="",ylab="",ylim=c(min(bind),2),pch=16,col="#31A9B8")
points(seq(1,10,1),eqn1[1,10,]/den_bef,lwd=1,type="p",col="black")
points(1:9,yval[1:9],type="p",pch=16,lwd=2,col="#CF3721")
abline(v=9.5,lwd=2,col="black",lty=5)
text(3.5,1.3,paste("LE=", round(mean(eqn1[1,10,10])/mean(eqn1[1,10,1:9]),digits=2)))
yval1<-eqn1[2,10,]/den_bef
plot(seq(1,10,1),eqn1[2,10,]/den_bef,lwd=2,type="p",lty=2,ylim=c(min(bind),2),pch=16,col="#31A9B8")
points(seq(1,10,1),eqn1[2,10,]/den_bef,lwd=1,type="p",col="black")
points(1:9,yval1[1:9],type="p",pch=16,lwd=2,col="#CF3721")
abline(v=9.5,lwd=2,col="black",lty=5)
text(3.5,1.3,paste("LE=",round(mean(eqn1[2,10,10])/mean(eqn1[2,10,1:9]),digits=2)))
yval2<-eqn1[3,10,]/den_bef
plot(seq(1,10,1),eqn1[3,10,]/den_bef,lwd=2,type="p",lty=3,ylim=c(min(bind),2),pch=16,col="#31A9B8")
points(seq(1,10,1),eqn1[3,10,]/den_bef,lwd=1,type="p",col="black")
points(1:9,yval2[1:9],type="p",pch=16,lwd=2,col="#CF3721")
abline(v=9.5,lwd=2,col="black",lty=5)
text(3.5,1.3,paste("LE=",round(mean(eqn1[3,10,10])/mean(eqn1[3,10,1:9]),digits=2)))
dev.off()