#---------------------------------------------------------------------------------
                            #Allometrics MODEL 
#----------------------------------------------------------------------------------
par(mfrow=c(2,4))
jpeg("Figure 4.jpg", width=9, height=5, units="in", res=800) 
par(mfrow=c(2,4))
#----------------------------------------------------------
  #Locality Paucho; P. rodolfo vasquezii; Logistic Model
#----------------------------------------------------------
Paucho<- read.csv("DRPaucho.csv",";",header = T)
attach(Paucho)
head(Paucho)
PAUCHO<- nls(TH~a/(1+b*exp(-c*DGL)),start= list(a=7.4662, b=6.6637,c=0.2006)) 
summary(PAUCHO)
AIC(PAUCHO)
a=7.400511
b=6.267885
c=0.21001
plot(TH~DGL, main="Paucho         4156 m", ylab="TH(m)", bg="gray58", xlab = substitute(paste(italic("P.rodolfo-vasquezii"))),
     cex.lab=1.5, cex.axis=1.2, cex.main=1.3, cex.sub=1.5,col="black",lwd="1.4",pch=21, xlim=c(0, 40),ylim=c(0, 10))
curve(a/(1+b*exp(-c*x)), add=T, col="black",lty=3, lwd="7",pch=21, bg="green") 
paucho<- lm(TH~DGL)
summary(paucho)
AIC(paucho)
a=0.920203
b=0.295018
curve((a+b*x),add=T, col="gray46",lty=1,lwd="4",pch=21,bg="green",xlim=c(0,28))
#legend(x=15, y= 4,legend=c("0.72(299)", "0.70(303)"),col=c(1), bty = "n")
#----------------------------------------------------------------
  #Locality Quilcaycocha; P. rodolfo vasquezii; Logistic Model
#----------------------------------------------------------------
Quilcaycocha<- read.csv("DRQuilcaycocha.csv",";",header = T)
attach(Quilcaycocha)
head(Quilcaycocha)
Quilcaycocha<- nls(TH~a/(1+b*exp(-c*DGL)),start= list(a=5.1524, b=3.557,c=0.17)) 
summary(Quilcaycocha)
AIC(Quilcaycocha)
a=5.1524
b=3.557
c=0.171
plot(TH~DGL, main="Quilcaycocha     4350 m", ylab="", bg="gray58", xlab = substitute(paste(italic("P.rodolfo-vasquezii"))),
     cex.lab=1.5, cex.axis=1.2, cex.main=1.3, cex.sub=1.5,col="black",lwd="1.4",pch=21, xlim=c(0, 40),ylim=c(0, 8))
curve(a/(1+b*exp(-c*x)), add=T, col="black",lty=3, lwd="7",pch=21, bg="green") 
quilcaycocha<- lm(TH~DGL)
summary(quilcaycocha)
AIC(quilcaycocha)
a=1.177907
b=0.172754
curve((a+b*x),add=T, col="gray46",lty=1,lwd="4",pch=21,bg="green",xlim=c(0,35))
#legend(x=12, y=2.8,legend=c("0.69(330)", "0.68(332)"),col=c(1), bty = "n")
#----------------------------------------------------------------
#Locality Shaitura; P. flavipila; Logistic Model
#----------------------------------------------------------------
Shaitura<- read.csv("DRShaitura.csv",";",header = T)
attach(Shaitura)
head(Shaitura)
Shaitura<- nls(TH~a/(1+b*exp(-c*DGL)),start= list(a=9.755, b=5.381,c=0.1264)) 
summary(Shaitura)
AIC(Shaitura)
a=9.755
b=5.381
c=0.1264
plot(TH~DGL, main="Shaitura         4200 m", ylab="", bg="gray58", xlab = substitute(paste(italic("P. flavipila"))),
     cex.lab=1.5, cex.axis=1.2, cex.main=1.3, cex.sub=1.5,col="black",lwd="1.4",pch=21, xlim=c(0, 50),ylim=c(0, 12))
curve(a/(1+b*exp(-c*x)), add=T, col="black",lty=3, lwd="7",pch=21, bg="green") 
shaitura<- lm(TH~DGL)
summary(shaitura)
AIC(shaitura)
a=1.45388
b=0.244
curve((a+b*x),add=T, col="gray46",lty=1,lwd="4",pch=21,bg="green",xlim=c(0,38))
#legend(x=14, y= 4.3,legend=c("0.52(492)", "0.51(490)"),col=c(1), bty = "n")
#----------------------------------------------------------------
#Locality Chaqsii-Chaqsii; P. flavipila; Schumacher Model

#----------------------------------------------------------------
Chaqsii_Chaqsii<- read.csv("DRChaqssi.csv",";",header = T)
attach(Chaqsii_Chaqsii)
head(Chaqsii_Chaqsii)
Chaqsii_Chaqsii<- nls(TH~exp(a+b*(1/DGL)),start= list(a=1.2210, b=-1.48473)) 
summary(Chaqsii_Chaqsii)
AIC(Chaqsii_Chaqsii)
a=1.2210
b=-1.4846
plot(TH~DGL, main="Chaqsii-Chaqsii    4050 m", ylab="", bg="gray58", xlab = substitute(paste(italic("P. flavipila"))),
     cex.lab=1.5, cex.axis=1.2, cex.main=1.3, cex.sub=1.5,col="black",lwd="1.4",pch=21, xlim=c(0, 35),ylim=c(0,8))
curve(exp(a+b*(1/x)), add=T, col="black",lty=3, lwd="7",pch=21, bg="green") 
chaqsii_Chaqsii<- lm(TH~DGL)
summary(chaqsii_Chaqsii)
AIC(chaqsii_Chaqsii)
a=2.3204
b=0.0526
curve((a+b*x),add=T, col="gray46",lty=1,lwd="4",pch=21,bg="green",xlim=c(0, 33))
#legend(x=13, y=2.3,legend=c("0.031(591)", "0.055(591)"),col=c(1), bty = "n")
#----------------------------------------------------------------
#Locality Tasta; P. canoi; Schumacher Model
#----------------------------------------------------------------
Tasta<- read.csv("DRTasta.csv",";",header = T)
attach(Tasta)
head(Tasta)
Tasta<- nls(TH~a/(1+b*exp(-c*DGL)),start= list(a=14.18, b=4.21,c=0.04))  
summary(Tasta)
AIC(Tasta)
a=14.188
b=4.213
c=0.042
plot(TH~DGL, main="Tasta        4051 m", ylab="TH(m)", bg="gray58", xlab = substitute(paste(italic("P. canoi"))),
     cex.lab=1.5, cex.axis=1.2, cex.main=1.3, cex.sub=1.5,col="black",lwd="1.4",pch=21, xlim=c(0, 70),ylim=c(0, 15))
curve(a/(1+b*exp(-c*x)), add=T, col="black",lty=3, lwd="7",pch=21, bg="green") 
tasta<- lm(TH~DGL)
summary(tasta)
AIC(tasta)
a=2.496
b=0.136
curve((a+b*x),add=T, col="gray46",lty=1,lwd="4",pch=21,bg="green",xlim=c(0, 65))
#legend(x=15, y=4.3,legend=c("0.49(385)", "0.31(398)"),col=c(1), bty = "n")
#----------------------------------------------------------------
#Locality Nahuin; P. canoi; Logistico Model
#----------------------------------------------------------------
Nahuin<- read.csv("DRNahuin.csv",";",header = T)
attach(Nahuin)
head(Nahuin)
Nahuin<- nls(TH~a/(1+b*exp(-c*DGL)),start= list(a=10.924, b=5.9844,c=0.125)) 
summary(Nahuin)
AIC(Nahuin)
a=10.924
b=5.984
c=0.125
plot(TH~DGL, main="Nahuin        3800 m", ylab="", bg="gray58", xlab = substitute(paste(italic("P. canoi"))),
     cex.lab=1.5, cex.axis=1.2, cex.main=1.3, cex.sub=1.5,col="black",lwd="1.4",pch=21, xlim=c(0, 50),ylim=c(0, 17))
curve(a/(1+b*exp(-c*x)), add=T, col="black",lty=3, lwd="7",pch=21, bg="green") 
nahuin<- lm(TH~DGL)
summary(nahuin)
AIC(nahuin)
a=2.419
b=0.2179
curve((a+b*x),add=T, col="gray46",lty=1,lwd="4",pch=21,bg="green",xlim=c(0, 48))
#legend(x=15, y=5.3,legend=c("0.67(553)", "0.59(584)"),col=c(1), bty = "n")
#----------------------------------------------------------------
#Locality Jucha; P. canoi; Schumacher Model
#----------------------------------------------------------------
Jucha<- read.csv("DRJucha.csv",";",header = T)
attach(Jucha)
tail(Jucha)
Jucha<- nls(TH~exp(a+b*(1/DGL)),start= list(a=2.2222, b=-6.3390)) 
summary(Jucha)
AIC(Jucha)
a=2.23
b=-6.405
plot(TH~DGL, main="Jucha          3910 m", ylab="", bg="gray58",  xlab = substitute(paste(italic("P. canoi"))),
     cex.lab=1.5, cex.axis=1.2, cex.main=1.3, cex.sub=1.5,col="black",lwd="1.4",pch=21, xlim=c(0, 50),ylim=c(0, 15))
curve(exp(a+b*(1/x)), add=T, col="black",lty=3, lwd="7",pch=21, bg="green") 
jucha<- lm(TH~DGL)
summary(jucha)
AIC(jucha)
a=2.981
b=0.180
curve((a+b*x),add=T, col="gray46",lty=1,lwd="4",pch=21,bg="green",xlim=c(0, 43))
#legend(x=18, y=4.7,legend=c("0.37(684)", "0.30(702)"),col=c(1), bty = "n")
#----------------------------------------------------------------
#Locality Llantaco; P. canoi; Gompertz Model
#----------------------------------------------------------------
Llantaco<- read.csv("DRLlantaco.csv",";",header = T)
attach(Llantaco)
head(Llantaco)
Llantaco<- nls(TH~a*exp(-exp(b-c*DGL)),start= list(a=11.0432, b=0.6587,c=0.0852)) 
summary(Llantaco)
AIC(Llantaco)
a=13.478
b=0.765
c=0.078
plot(TH~DGL, main="Llantaco          3850 m", ylab="", bg="gray58",  xlab = substitute(paste(italic("P. canoi"))),
     cex.lab=1.5, cex.axis=1.2, cex.main=1.3, cex.sub=1.5,col="black",lwd="1.4",pch=21, xlim=c(0, 30),ylim=c(0, 15))
curve(a*exp(-exp(b-c*x)), add=T, col="black",lty=3, lwd="7",pch=21, bg="green") 
llantaco<- lm(TH~DGL)
summary(llantaco)
AIC(llantaco)
a=1.556
b=0.349 
curve((a+b*x),add=T, col="gray46",lty=1,lwd="4",pch=21,bg="green",xlim=c(0, 26))
#legend(x=14, y=4,legend=substitute(paste(italic(c("0.69(643)", "0.29(641)")))),col=c(1), bty = "n")
##### out 600 DPI in format JPG 
dev.off()