setwd("/Users/ivangonzalez/Desktop/GREENLAND-R1/paper Groenlandia -R1") 
dir()
data <- read.table("data.csv", header=TRUE, sep=";", row.names=1)
library(vegan)
########################################
##### Testing differences in Physical-chemical properties of freshwater between colonies and controls
#########################################
data$birds<-as.factor(data$birds)
str(data)
head(data)
#1) PERMANOVA
MyVar <- c( "pH", "DO", "Cond", "TN", "NO","TP", "PO4", "Chla")
env1<-(as.matrix(data[,MyVar])) ### 
good<-complete.cases(env1) 
tot <- data[good,]###  
y<-env1[good,]## 

str(tot) #
str(y)
head(y)
### 
mod<-adonis(decostand(y,"standardize") ~ birds, data=tot, permutations=999, method="euclidean")
mod ### w


### this makes a plot to see the data more clearly
mod <- rda(y, scale =TRUE)## 

plot(mod, type = "n")
text(mod, display = "sites", , cex = 0.8, col = c("black","green")[tot$birds])
text(mod, display = "species", , cex = 0.8, col="red")
with(data, legend("topright", legend = c("no birds","birds"), bty = "n",
                  pch = 20, col = c("black","green")))
### puts hulls around the groups
ordihull(mod, group=tot$birds, show="0", col="black")
ordihull(mod, group=tot$birds, show="1", col="green")


### now pairwise models with space included if needed .
# as some data  does not have homogeneity of variance
#we use GLS then we can put space in too if needed.

#################################################
####ANOVAS for pH, DO,TN NO, PO3, PT, CHL 
#################################################

### for pH
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(data$pH~data$birds)
shapiro.test(residuals(aov(data$pH~data$birds)))
## suggests normality is acccomplished
bartlett.test(data$pH~data$birds)
## means we have homogeneity of variance-
############################################################################
## we try GlS anyway..
#####################################
library(nlme)
testpH<-data[which(data$pH >0 ), ]### this I made to remove NAs 
pHmod<-gls(pH~birds, data=testpH)
summary(pHmod) 
### No need to add variance structure as there is homogeneity of variance
# now check for spatial autocorrelation 
E<- resid(pHmod, type="normalized") ### get the residuals 
F<- fitted (pHmod) ## and the fittefd whilst we are at it
plot(E~testpH$birds)## 
xyplot(n1 ~ e1, aspect = "iso", data = data,
       col= testpH$birds, pch=16)
#Spatial independence, this plots residuals in the map, size of symbol is residual size and colour is plus or minus resdual
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testpH,
       main = "Spatial plot of residuals")
### there might be a pattern there ..
str(data)
plot(E~testpH$birds)
### this makes a variogram to look for spatial autocorrelation 
variopHmod<- Variogram(pHmod, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(variopHmod)
## actually i does not look too bad but there is a hint of autocorrelation, so we'll put space in the model
## this model puts in a wieghting stricture to account for spatial autocorrelation so the significance test can be trusted.
pHmodspace<-gls(pH~birds,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testpH)
AIC(pHmod, pHmodspace)
anova(pHmod, pHmodspace)## the model with space in improves 
summary(pHmodspace)### with space in, Bird colony is still massively sig. There are no R2 values for GLS, but we can compare observed vs predicted
F1<-fitted(pHmodspace)
cor(F1,testpH$pH)^2 ##  0.33 for the cor^2 value
## ANOVA  including spatial autocorrelation
pHanova<-aov(pH~birds, data=testpH)
summary(pHanova)
## this model puts in a wieghting stricture to account for spatial autocorrelation so the significance test can be trusted.
pHanovaspace<-gls(pH~birds,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testpH)##### 
AIC(pHanova, pHanovaspace)
anova(pHmod, pHanovaspace)#### with space in the model improves
summary(pHanovaspace)###
F1<-fitted(pHanovaspace)
cor(F1,testpH$pH)^2 ##  0.33 for the cor^2 value
###### There are significant differences with ANOVA with space included

#### for conductivity
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(data$Cond~data$birds)
shapiro.test(residuals(aov(data$Cond~data$birds)))
## suggests  normality is NOT acccomplished
bartlett.test(data$Cond~data$birds)
############################################################################
## we try GlS
#####################################
library(nlme)
testcond<-data[which(data$Cond >0 ), ]
condmod<-gls(Cond~birds, data=testcond)
summary(condmod) 
### Need to add variance structure as there is no homogeneity of variance
vf1<- varIdent(form=~1|birds)### this code allows for a different variance stucture across the two groups
condmod1<-gls(Cond~birds, weights = vf1, data=testcond) # with the variance structure in the mode
summary(condmod1)
anova(condmod,condmod1) # model with the variance structure in significant improvement
AIC(condmod,condmod1)
# now check for spatial autocorrelation 
E<- resid(condmod1, type="normalized") ### get the residuals 
F<- fitted (condmod1) ## and the fittefd whilst we are at it
plot(E~testcond$birds)## 
xyplot(n1 ~ e1, aspect = "iso", data = data,
       col= testcond$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testcond,
       main = "Spatial plot of residuals")
### there might be a pattern there ..
str(data)
plot(E~testpH$birds)
### this makes a variogram to look for spatial autocorrelation 
variocondmod<- Variogram(condmod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(variocondmod)
condmodspace<-gls(Cond~birds,weights = vf1, correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testcond)
AIC(condmod1, condmodspace)
anova(condmod1, condmodspace)##  
summary(condmodspace)### 

#### for DO
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(data$DO~data$birds)
shapiro.test(residuals(aov(data$DO~data$birds)))
## Normality is  acccomplished
bartlett.test(data$DO~data$birds)
##We have homogeneity of variance--
############################################################################
## we try GlS
#####################################
library(nlme)
testDO<-data[which(data$DO >0 ), ]### this I made to remove NAs 
DOmod<-gls(DO~birds, data=testDO)
summary(DOmod) 
### NO Need to add variance structure as there is no homogeneity of variance
# now check for spatial autocorrelation 
E<- resid(DOmod, type="normalized") ### get the residuals 
F<- fitted (DOmod) ## and the fittefd whilst we are at it
plot(E~testDO$birds)## 
xyplot(n1 ~ e1, aspect = "iso", data = data,
       col= testDO$birds, pch=16)
#Spatial independence,
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testDO,
       main = "Spatial plot of residuals")
### there is no spatial autocorrelation here ..
str(data)
plot(E~testDO$birds)
### this makes a variogram to look for spatial autocorrelation 
varioDOmod<- Variogram(DOmod, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(varioDOmod)
## looks good, no spatial autocorrelation
DOmodspace<-gls(DO~birds, correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testDO)
AIC(DOmod, DOmodspace)
anova(DOmod, DOmodspace)## 
summary(DOmodspace)### 


#### For Total Nitrogen
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(data$TN~data$birds)
shapiro.test(residuals(aov(data$TN~data$birds)))
## Normality is NOT acccomplished
bartlett.test(data$TN~data$birds)
##We have homogeneity of variance NOT accomplished--
## we try GlS
#####################################
library(nlme)
testTN<-data[which(data$TN >0 ), ]### this I made to remove NAs 
TNmod<-gls(TN~birds, data=testTN)
summary(TNmod) 
### Need to add variance structure as there is no homogeneity of variance
vf1<- varIdent(form=~1|birds)### this code allows for a different variance stucture across the two groups
TNmod1<-gls(TN~birds, weights = vf1, data=testTN) # with the variance structure in the mode
summary(TNmod1)
anova(TNmod,TNmod1) # model with the variance structure in significant improvement
AIC(TNmod,TNmod1)
# now check for spatial autocorrelation 
E<- resid(TNmod1, type="normalized") ### get the residuals 
F<- fitted (TNmod1) ## and the fittefd whilst we are at it
plot(E~testTN$birds)## 
#can we see spatial autocorrelation?
xyplot(n1 ~ e1, aspect = "iso", data = data,
       col= testTN$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testTN,
       main = "Spatial plot of residuals")
### there might be a pattern there ..
str(data)
plot(E~testTN$birds)
### this makes a variogram to look for spatial autocorrelation 
varioTNmod<- Variogram(TNmod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(varioTNmod)
## looks good
## this model puts in a wieghting stricture to account for spatial autocorrelation so the significance test can be trusted.
TNmodspace<-gls(TN~birds,weights = vf1, correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testTN)
AIC(TNmod1, TNmodspace)
anova(TNmod1, TNmodspace)## 
summary(TNmodspace)### 

######################################
## for NO2+ NO3
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(data$NO~data$birds)
shapiro.test(residuals(aov(data$NO~data$birds)))
## Normality is NOT acccomplished
bartlett.test(data$NO~data$birds)
## homogeneity of variance NOT accomplished--
## we try GlS
library(nlme)
testNO<-data[which(data$NO >0 ), ]### this I made to remove NAs 
NOmod<-gls(NO~birds, data=testNO)
summary(NOmod) 
### Need to add variance structure as there is no homogeneity of variance
vf1<- varIdent(form=~1|birds)### this code allows for a different variance stucture across the two groups
NOmod1<-gls(NO~birds, weights = vf1, data=testNO) # with the variance structure in the mode
summary(NOmod1)
anova(NOmod,NOmod1) # model with the variance structure in significant improvement
##continue with model woth diffrent variance structure
# now check for spatial autocorrelation 
E<- resid(NOmod1, type="normalized") ### get the residuals 
F<- fitted (NOmod1) ## and the fittefd whilst we are at it
plot(E~testNO$birds)## 
xyplot(n1 ~ e1, aspect = "iso", data = data,
       col= testNO$birds, pch=16)
#Spatial independence, 
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testNO,
       main = "Spatial plot of residuals")
### does not seem to be any pattern here ..
str(data)
plot(E~testNO$birds)
### this makes a variogram to look for spatial autocorrelation 
varioNOmod<- Variogram(NOmod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(varioNOmod)
## looks good
## this model puts in a wieghting stricture to account for spatial autocorrelation so the significance test can be trusted.
NOmodspace<-gls(NO~birds,weights = vf1, correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testNO)
AIC(NOmod1, NOmodspace)
anova(NOmod1, NOmodspace)##
summary(NOmodspace)### 

######################################
## for TP
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(data$TP~data$birds)
shapiro.test(residuals(aov(data$TP~data$birds)))
## Normality is NOT acccomplished
bartlett.test(data$TP~data$birds)
## homogeneity of variance NOT accomplished--
## we try GlS
library(nlme)
testTP<-data[which(data$TP >0 ), ]#
TPmod<-gls(TP~birds, data=testTP)
summary(TPmod) 
vf1<- varIdent(form=~1|birds)### 
TPmod1<-gls(TP~birds, weights = vf1, data=testTP) # 
summary(TPmod1)
anova(TPmod,TPmod1) # 
# now check for spatial autocorrelation 
E<- resid(TPmod1, type="normalized") ### get the residuals 
F<- fitted (TPmod1) ## and the fittefd whilst we are at it
plot(E~testNO$birds)## 
#can we see spatial autocorrelation?
xyplot(n1 ~ e1, aspect = "iso", data = testTP,
       col= testTP$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testTP,
       main = "Spatial plot of residuals")
str(data)
plot(E~testTP$birds)
varioTPmod<- Variogram(TPmod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(varioTPmod)
TPmodspace<-gls(TP~birds,weights = vf1, correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testTP)
AIC(TPmod1, TPmodspace)
anova(TPmod1, TPmodspace)##  
summary(TPmodspace)### 

######################################
## for PO4
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(data$PO4~data$birds)
shapiro.test(residuals(aov(data$PO4~data$birds)))
## Normality is NOT acccomplished
bartlett.test(data$PO4~data$birds)
## homogeneity of variance NOT accomplished--
## we try GlS
library(nlme)
testPO4<-data[which(data$PO4 >0 ), ]### this I made to remove NAs 
PO4mod<-gls(PO4~birds, data=testPO4)
summary(PO4mod) 
### Need to add variance structure as there is no homogeneity of variance
vf1<- varIdent(form=~1|birds)### this code allows for a different variance stucture across the two groups
PO4mod1<-gls(PO4~birds, weights = vf1, data=testPO4) # with the variance structure in the mode
summary(PO4mod1)
anova(PO4mod,PO4mod1) # model with the variance structure in significant improvement
##continue with model woth diffrent variance structure
# now check for spatial autocorrelation 
E<- resid(PO4mod1, type="normalized") ### get the residuals 
F<- fitted (PO4mod1) ## and the fittefd whilst we are at it
plot(E~testNO$birds)## 
xyplot(n1 ~ e1, aspect = "iso", data = testPO4,
       col= testPO4$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testPO4,
       main = "Spatial plot of residuals")
str(data)
plot(E~testPO4$birds)
varioPO4mod<- Variogram(PO4mod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(varioPO4mod)
PO4modspace<-gls(PO4~birds,weights = vf1, correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testPO4)
AIC(PO4mod1, PO4modspace)
anova(PO4mod1, PO4modspace)##adding space does improve  the model  
summary(PO4modspace)### with space in, Bird colony does not affect 



######################################
## for richness of taxa
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(data$Consumer.taxa.diversity~data$birds)
shapiro.test(residuals(aov(data$Consumer.taxa.diversity~data$birds)))
## Normality is NOT acccomplished
bartlett.test(data$Consumer.taxa.diversity~data$birds)
## homogeneity of variance NOT accomplished--
library(nlme)
testrich<-data[which(data$Consumer.taxa.diversity >-1 ), ]### 
richmod<-gls(Consumer.taxa.diversity~birds, data=testrich)
summary(richmod) 
vf1<- varIdent(form=~1|birds)### 
richmod1<-gls(Consumer.taxa.diversity~birds, weights = vf1, data=testrich) #
summary(richmod1)
anova(richmod,richmod1) #
E<- resid(richmod1, type="normalized") ###
F<- fitted (richmod1) ## 
plot(E~testrich$birds)## 
xyplot(n1 ~ e1, aspect = "iso", data = testrich,
       col= testrich$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testrich,
       main = "Spatial plot of residuals")
str(data)
plot(E~testrich$birds)
variorichmod<- Variogram(richmod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(variorichmod)
richmodspace<-gls(Consumer.taxa.diversity~birds,weights = vf1, correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testrich)
AIC(richmod1, richmodspace)
anova(richmod1, richmodspace)##adding space does improve  the model  
summary(richmodspace)### with space in, Bird colony does not affect 
summary(richmod1)


##for EVI
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(data$EVI.500.max~data$birds)
shapiro.test(residuals(aov(data$EVI.500.max~data$birds)))
## Normality is  acccomplished
bartlett.test(data$EVI.500.max~data$birds)
##We have homogeneity of variance--
## we try GlS
#####################################
library(nlme)
EVImod<-gls(EVI.500.max~birds, data=data)
summary(EVImod) 
### NO Need to add variance structure as there is no homogeneity of variance
# now check for spatial autocorrelation 
E<- resid(EVImod, type="normalized") ### get the residuals 
F<- fitted (EVImod) ## and the fittefd whilst we are at it
plot(E~data$birds)## 
#can we see spatial autocorrelation?
xyplot(n1 ~ e1, aspect = "iso", data = data,
       col= data$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2

xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = data,
       main = "Spatial plot of residuals")
str(data)
plot(E~data$birds)
looks fine..
varioEVImod<- Variogram(EVImod, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(varioEVImod)
EVImodspace<-gls(EVI.500.max~birds, correlation=corGaus(form=~n1+e1,nugget=TRUE), data=data)
AIC(EVImod, EVImodspace)
anova(EVImod, EVImodspace)## adding space improves the model
summary(EVImodspace)###


####  Chl NOW only for Lentic systems####
###################################################################################
datalent<-data[which(data$lentvlot=="lentic" ), ]
##for Algae
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(datalent$Chla~datalent$birds)
shapiro.test(residuals(aov(datalent$Chla~datalent$birds)))
## Normality is  acccomplished
bartlett.test(datalent$Chla~datalent$birds)
##We do not have homogeneity of variance--
## we try GlS
#####################################
library(nlme)
testChl<-datalent[which(datalent$Chla >0 ), ]
Chlmod<-gls(Chla~birds, data=testChl)
summary(Chlmod) 
### Need to add variance structure as there is no homogeneity of variance
vf1<- varIdent(form=~1|birds)### this code allows for a different variance stucture across the two groups
Chlmod1<-gls(Chla~birds, weights = vf1, data=testChl) # with the variance structure in the mode
summary(Chlmod1)
anova(richmod,Chlmod1) # model with the variance structure in significant improvement
##continue with model woth diffrent variance structure
# now check for spatial autocorrelation 
E<- resid(Chlmod1, type="normalized") ### get the residuals 
F<- fitted (Chlmod1) ## and the fittefd whilst we are at it
plot(E~testrich$birds)## 
xyplot(n1 ~ e1, aspect = "iso", data = testChl,
       col= testrich$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testChl,
       main = "Spatial plot of residuals")
str(datalent)
plot(E~testrich$birds)
variochlmod<- Variogram(Chlmod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(variochlmod)
CHLmodspace<-gls(Chla~birds,weights = vf1, correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testChl)
AIC(Chlmod1, CHLmodspace)
anova(Chlmod1, CHLmodspace)##adding space does NOT improve  the model  
summary(Chlmod1)


#### for LOTIC systems####
datalot<-data[which(data$lentvlot=="lotic" ), ]
######################################
##for Algae
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(datalot$Chla~datalot$birds)
shapiro.test(residuals(aov(datalot$Chla~datalot$birds)))
## Normality is  acccomplished
bartlett.test(datalot$Chla~datalot$birds)
##We do not have homogeneity of variance--
## we try GlS
#####################################
library(nlme)
testChl<-datalot[which(datalot$Chla >0 ), ]
Chlmod<-gls(Chla~birds, data=testChl)
summary(Chlmod) 
vf1<- varIdent(form=~1|birds)### this code allows for a different variance stucture across the two groups
Chlmod1<-gls(Chla~birds, weights = vf1, data=testChl) # with the variance structure in the mode
summary(Chlmod1)
anova(Chlmod,Chlmod1) # model with the variance structure in significant improvement
# now check for spatial autocorrelation 
E<- resid(Chlmod1, type="normalized") ### get the residuals 
F<- fitted (Chlmod1) ## and the fittefd whilst we are at it
plot(E~testChl$birds)## 
xyplot(n1 ~ e1, aspect = "iso", data = testChl,
       col= testChl$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2

xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testChl,
       main = "Spatial plot of residuals")
str(datalot)
plot(E~testChl$birds)
### this makes a variogram to look for spatial autocorrelation 
variochlmod<- Variogram(Chlmod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(variochlmod)
## this model puts in a wieghting stricture to account for spatial autocorrelation so the significance test can be trusted.
CHLmodspace<-gls(Chla~birds,weights = vf1, correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testChl)
AIC(Chlmod1, CHLmodspace)
anova(Chlmod1, CHLmodspace)##adding space does NOT improve  the model  
summary(Chlmod1)

####################################################
################################################
## Test of Isotopic signatures
#################################################
##### 1) PERMANOVA
dataiso <- read.csv("dataisotopes.csv", header=TRUE, sep=";")
dataiso$birds<-as.factor(dataiso$birds)
str(dataiso)
head(dataiso)
MyVariso <- c( "X13C.Aqmoss", "X13C.peri", "X13C.inv", "X15N.Aqmoss","X15N.peri", "X15N.inv")
env1iso<-(as.matrix(dataiso[,MyVariso])) ### 
goodiso<-complete.cases(env1iso) ### 
totiso <- dataiso[goodiso,]### 
yiso<-env1iso[goodiso,]## 

str(totiso) # 
str(yiso)
head(yiso)

mod<-adonis(yiso ~ birds, data=totiso, permutations=999, method="euclidean")
mod
mod <- rda(yiso, scale =TRUE)## says RDA but is a PCA, scale =TRUE, means data are standardised

plot(mod, type = "n")
text(mod, display = "sites", , cex = 0.5, col = c("black","green")[tot$birds])
text(mod, display = "species", , cex = 0.5, col="red")
with(data, legend("topright", legend = c("no birds","birds"), bty = "n",
                  pch = 20, col = c("black","green")))
### puts hulls around the groups
ordihull(mod, group=totiso$birds, show="0", col="black")
ordihull(mod, group=totiso$birds, show="1", col="green")
################################################################


#################################################################
## Testing differences in isotopic signatures one by one  now...
########## d15N in benthic algae
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X15N.peri~dataiso$birds)
plot(dataiso$X13C.peri~dataiso$birds)
par(op)
### can see large difference in variance between the two groups so ANOVA no ok anyway.. we use GLS then we can put space in too if needed.
library(nlme)
peri15nmod<-gls(X15N.peri~birds, data=dataiso)
summary(peri15nmod)
vf1<- varIdent(form=~1|birds)### this code allows for a different variance stucture across the two groups
peri15mod1<-gls(X15N.peri~birds, weights = vf1, data=dataiso) # with the variance structure in the mode
summary(peri15mod1)
anova(peri15nmod,peri15mod1) # model with the variance structure in significant improvement
AIC(peri15nmod,peri15mod1)
## two ways of comparing the models both say model with the data structure in to account for the heterogeneity is better.
# now check for spatial autocorrelation 
E<- resid(peri15mod1, type="normalized") ### get the residuals 
F<- fitted (peri15mod1) ## and the fittefd whilst we are at it
plot(E~dataiso$birds)## residual spread looks good
xyplot(n1 ~ e1, aspect = "iso", data = dataiso,
       col= dataiso$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = dataiso,
       main = "Spatial plot of residuals")
str(data)
plot(E~dataiso$birds)
vario15nperomod1<- Variogram(peri15mod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario15nperomod1)
nperimodspace<-gls(X15N.peri~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=dataiso)
AIC(peri15mod1, nperimodspace)
anova(peri15mod1, nperimodspace)
summary(nperimodspace)### with space in, Bird colony is still massively sig. There are no R2 values for GLS, but we can compare observed vs predicted
F1<-fitted(nperimodspace)
cor(F1,dataiso$X15N.peri)^2 ## pretty good at 0.5539 for the cor^2 value
## this is just one way of putting space in, we should see if the others are any better
A1<-gls(X15N.peri~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=dataiso)
A2<-gls(X15N.peri~birds, weights = vf1,correlation=corSpher(form=~n1+e1,nugget=TRUE), data=dataiso)
A3<-gls(X15N.peri~birds, weights = vf1,correlation=corLin(form=~n1+e1,nugget=TRUE), data=dataiso)#
A4<-gls(X15N.peri~birds, weights = vf1,correlation=corExp(form=~n1+e1,nugget=TRUE), data=dataiso)
A5<-gls(X15N.peri~birds, weights = vf1,correlation=corRatio(form=~n1+e1,nugget=TRUE), data=dataiso)
AIC (A1,A2,A4,A5)## 
d15Nfinalmodel<-gls(X15N.peri~birds, weights = vf1,correlation=corExp(form=~n1+e1,nugget=TRUE),method="ML", data=dataiso)
summary(d15Nfinalmodel)

###########################################
### d15N  in chiroromidae
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X15N.chiro~dataiso$birds)
par(op)
library(nlme)
testchiron<-dataiso[which(dataiso$X15N.chiro >-7 ),]
chiro15nmod<-gls(X15N.chiro~birds, data=testchiron)
summary(chiro15nmod)
vf1<- varIdent(form=~1|birds)
chiro15mod1<-gls(X15N.chiro~birds, weights = vf1, data=testchiron) 
summary(chiro15mod1)
anova(chiro15nmod,chiro15mod1)
E<- resid(chiro15mod1, type="normalized") 
F<- fitted (chiro15mod1) 
plot(E~testchiron$birds)
xyplot(n1 ~ e1, aspect = "iso", data = testchiron,
       col= testchiron$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testchiron,
       main = "Spatial plot of residuals")
str(data)
plot(E~testchiron$birds)
vario15nchiromod1<- Variogram(chiro15mod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario15nchiromod1)
nchiromodspace<-gls(X15N.chiro~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testchiron)
AIC(chiro15mod1, nchiromodspace)
anova(chiro15mod1, nchiromodspace)
summary(nchiromodspace)

### d15N in aquatic moss
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X15N.Aqmoss~dataiso$birds)
par(op)
library(nlme)
testaqmossn<-dataiso[which(dataiso$X15N.Aqmoss >-7 ),]
aqmoss15nmod<-gls(X15N.Aqmoss~birds, data=testaqmossn)
summary(aqmoss15nmod)
vf1<- varIdent(form=~1|birds)
aqmoss15mod1<-gls(X15N.Aqmoss~birds, weights = vf1, data=testaqmossn) 
summary(aqmoss15mod1)
anova(aqmoss15nmod,aqmoss15mod1) #
E<- resid(aqmoss15mod1, type="normalized") ###
F<- fitted (aqmoss15mod1) #
plot(E~testaqmossn$birds)##
xyplot(n1 ~ e1, aspect = "iso", data = testaqmossn,
       col= testaqmossn$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testaqmossn,
       main = "Spatial plot of residuals")
str(data)
plot(E~testaqmossn$birds)
vario15naqmossmod1<- Variogram(aqmoss15mod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario15naqmossmod1)
naqmossmodspace<-gls(X15N.Aqmoss~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testaqmossn)
AIC(aqmoss15mod1, naqmossmodspace)
anova(aqmoss15mod1, naqmossmodspace)## space does not improve 
summary(aqmoss15mod1)

### d15N in debris
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X15N.deb~dataiso$birds)
par(op)
library(nlme)
testdebn<-dataiso[which(dataiso$X15N.deb >-7 ),]
deb15nmod<-gls(X15N.deb~birds, data=testdebn)
summary(deb15nmod)
vf1<- varIdent(form=~1|birds)### 
deb15mod1<-gls(X15N.deb~birds, weights = vf1, data=testdebn) # with the variance structure in the mode
summary(deb15mod1)
anova(deb15nmod,deb15mod1) # 
E<- resid(deb15mod1, type="normalized") ### 
F<- fitted (deb15mod1) ## 
plot(E~testdebn$birds)## 
xyplot(n1 ~ e1, aspect = "iso", data = testdebn,
       col= testdebn$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2

xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testdebn,
       main = "Spatial plot of residuals")
str(data)
plot(E~testdebn$birds)
vario15ndebmod1<- Variogram(deb15mod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario15ndebmod1)
ndebmodspace<-gls(X15N.deb~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testdebn)
AIC(deb15mod1, ndebmodspace)
anova(deb15mod1, ndebmodspace)## space does not improve  model
summary(deb15mod1)

###########################################
### d15N of other invertebrates
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X15N.inv~dataiso$birds)
shapiro.test(residuals(aov(dataiso$X15N.inv~dataiso$birds)))
## suggests normality is acccomplished
bartlett.test(dataiso$X15N.inv~dataiso$birds)
## NOT  homogeneity of variance-- 
par(op)
library(nlme)
testinvn<-dataiso[which(dataiso$X15N.inv >-7 ),]
inv15nmod<-gls(X15N.inv~birds, data=testinvn)
summary(inv15nmod)
vf1<- varIdent(form=~1|birds)
inv15mod1<-gls(X15N.inv~birds, weights = vf1, data=testinvn) #
summary(inv15mod1)
anova(inv15nmod,inv15mod1) 
E<- resid(inv15mod1, type="normalized") ###
F<- fitted (inv15mod1) ##
plot(E~testinvn$birds)##
xyplot(n1 ~ e1, aspect = "iso", data = testinvn,
       col= testinvn$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testinvn,
       main = "Spatial plot of residuals")
str(data)
plot(E~testinvn$birds)

vario15ninvmod1<- Variogram(inv15mod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario15ninvmod1)
ninvmodspace<-gls(X15N.inv~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testinvn)
AIC(inv15mod1, ninvmodspace)
anova(inv15mod1, ninvmodspace)## space does not improve  model
summary(inv15mod1)


### 15N peat
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X15N.peat~dataiso$birds)
shapiro.test(residuals(aov(dataiso$X15N.peat~dataiso$birds)))
## suggests normality is acccomplished
bartlett.test(dataiso$X15N.peat~dataiso$birds)
##  homogeneity of variance-- 
par(op)
library(nlme)
testpeatn<-dataiso[which(dataiso$X15N.peat >-7 ),]
peat15nmod<-gls(X15N.peat~birds, data=testpeatn)
summary(peat15nmod)
E<- resid(peat15nmod, type="normalized") ### 
F<- fitted (peat15nmod) ## 
plot(E~testpeatn$birds)##
xyplot(n1 ~ e1, aspect = "iso", data = testpeatn,
       col= testpeatn$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2

xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testpeatn,
       main = "Spatial plot of residuals")
str(data)
plot(E~testpeatn$birds)

vario15npeatmod1<- Variogram(peat15nmod, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario15npeatmod1)
npeatmodspace<-gls(X15N.peat~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testpeatn)
AIC(peat15nmod, npeatmodspace)
anova(peat15nmod, npeatmodspace)## space does not improve  model
summary(peat15nmod)

###########################################
### d15N in terrestrial vegetation
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X15N.tveg~dataiso$birds)
shapiro.test(residuals(aov(dataiso$X15N.tveg~dataiso$birds)))
## suggests normality is acccomplished
bartlett.test(dataiso$X15N.tveg~dataiso$birds)
##  homogeneity of variance-- 
par(op)
library(nlme)
testtvegn<-dataiso[which(dataiso$X15N.tveg >-7 ),]
tveg15nmod<-gls(X15N.tveg~birds, data=testtvegn)
summary(tveg15nmod)
E<- resid(tveg15nmod, type="normalized") ###
F<- fitted (tveg15nmod) ## 
plot(E~testtvegn$birds)## 
xyplot(n1 ~ e1, aspect = "iso", data = testtvegn,
       col= testtvegn$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testtvegn,
       main = "Spatial plot of residuals")
str(data)
plot(E~testtvegn$birds)
vario15ntvegmod1<- Variogram(tveg15nmod, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario15ntvegmod1)
ntvegmodspace<-gls(X15N.tveg~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testtvegn)
AIC(tveg15nmod, ntvegmodspace)
anova(tveg15nmod, ntvegmodspace)## 
summary(tveg15nmod)


###for d13C signatures
###############################################################
########## d13C in benthic algae
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X13C.peri~dataiso$birds)
shapiro.test(residuals(aov(dataiso$X13C.peri~dataiso$birds)))
## suggests normality is acccomplished
bartlett.test(dataiso$X13C.peri~dataiso$birds)
##  homogeneity of variance-- 
par(op)
library(nlme)
peri13Cmod<-gls(X13C.peri~birds, data=dataiso)
summary(peri13Cmod) 
E<- resid(peri13Cmod, type="normalized") ### 
F<- fitted (peri13Cmod) #
plot(E~dataiso$birds)#
xyplot(n1 ~ e1, aspect = "iso", data = dataiso,
       col= dataiso$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2

xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = dataiso,
       main = "Spatial plot of residuals")
str(data)
plot(E~dataiso$birds)
vario13Cperomod1<- Variogram(peri13Cmod, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario13Cperomod1)
nperimodspace<-gls(X13C.peri~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=dataiso)
AIC(peri13Cmod, nperimodspace)
anova(peri13Cmod, nperimodspace)
summary(peri13Cmod)

#
### d13C in chironomidae
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X13C.chiro~dataiso$birds)
shapiro.test(residuals(aov(dataiso$X13C.chiro~dataiso$birds)))
## suggests normality is acccomplished
bartlett.test(dataiso$X13C.chiro~dataiso$birds)
##  homogeneity of variance--
par(op)
library(nlme)
testchiron<-dataiso[which(dataiso$X13C.chiro <0 ),]
chiro13Cmod<-gls(X13C.chiro~birds, data=testchiron)
summary(chiro13Cmod)
E<- resid(chiro13Cmod, type="normalized") 
F<- fitted (chiro13Cmod) 
plot(E~testchiron$birds)#
xyplot(n1 ~ e1, aspect = "iso", data = testchiron,
       col= testchiron$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testchiron,
       main = "Spatial plot of residuals")
str(data)
plot(E~testchiron$birds)
vario13Cchiromod1<- Variogram(chiro13Cmod, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario13Cchiromod1)
nchiromodspace<-gls(X13C.chiro~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testchiron)
AIC(chiro13Cmod, nchiromodspace)
anova(chiro13Cmod, nchiromodspace)
summary(chiro13Cmod)
###########################################

### d13C in aquatic moss
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X13C.Aqmoss~dataiso$birds)
shapiro.test(residuals(aov(dataiso$X13C.Aqmoss~dataiso$birds)))
## suggests normality is acccomplished
bartlett.test(dataiso$X13C.Aqmoss~dataiso$birds)
## not homogeneity
par(op)
library(nlme)
testaqmossn<-dataiso[which(dataiso$X13C.Aqmoss <0 ),]
aqmoss13Cmod<-gls(X13C.Aqmoss~birds, data=testaqmossn)
summary(aqmoss13Cmod)
vf1<- varIdent(form=~1|birds)#
aqmoss15mod1<-gls(X13C.Aqmoss~birds, weights = vf1, data=testaqmossn)
summary(aqmoss15mod1)
anova(aqmoss13Cmod,aqmoss15mod1) 
E<- resid(aqmoss15mod1, type="normalized") # 
F<- fitted (aqmoss15mod1) #
plot(E~testaqmossn$birds)#
xyplot(n1 ~ e1, aspect = "iso", data = testaqmossn,
       col= testaqmossn$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testaqmossn,
       main = "Spatial plot of residuals")
str(data)
plot(E~testaqmossn$birds) 
vario13Caqmossmod1<- Variogram(aqmoss15mod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario13Caqmossmod1)
naqmossmodspace<-gls(X13C.Aqmoss~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testaqmossn)
AIC(aqmoss15mod1, naqmossmodspace)
anova(aqmoss15mod1, naqmossmodspace)#
summary(aqmoss15mod1)

### d13C in debris
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X13C.deb~dataiso$birds)
shapiro.test(residuals(aov(dataiso$X13C.deb~dataiso$birds)))
## suggests normality is acccomplished
bartlett.test(dataiso$X13C.deb~dataiso$birds)
## not homogeneity
par(op)
library(nlme)
testdebn<-dataiso[which(dataiso$X13C.deb <0 ),]
deb13Cmod<-gls(X13C.deb~birds, data=testdebn)
summary(deb13Cmod)
vf1<- varIdent(form=~1|birds)

deb15mod1<-gls(X13C.deb~birds, weights = vf1, data=testdebn)
summary(deb15mod1)
anova(deb13Cmod,deb15mod1)
E<- resid(deb15mod1, type="normalized") 
F<- fitted (deb15mod1)
plot(E~testdebn$birds)##
xyplot(n1 ~ e1, aspect = "iso", data = testdebn,
       col= testdebn$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2

xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testdebn,
       main = "Spatial plot of residuals")
str(data)
plot(E~testdebn$birds)

vario13Cdebmod1<- Variogram(deb15mod1, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario13Cdebmod1)
ndebmodspace<-gls(X13C.deb~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testdebn)
AIC(deb15mod1, ndebmodspace)
anova(deb15mod1, ndebmodspace)#
summary(deb15mod1)

###########################################
### d13C in other invertebrates

op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X13C.inv~dataiso$birds)
shapiro.test(residuals(aov(dataiso$X13C.inv~dataiso$birds)))
bartlett.test(dataiso$X13C.inv~dataiso$birds)
par(op)
library(nlme)
testinvn<-dataiso[which(dataiso$X13C.inv <0 ),]
inv13Cmod<-gls(X13C.inv~birds, data=testinvn)
summary(inv13Cmod)
E<- resid(inv13Cmod, type="normalized") 
F<- fitted (inv13Cmod) 
plot(E~testinvn$birds)
xyplot(n1 ~ e1, aspect = "iso", data = testinvn,
       col= testinvn$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2

xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testinvn,
       main = "Spatial plot of residuals")

str(data)
plot(E~testinvn$birds)
vario13Cinvmod1<- Variogram(inv13Cmod, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario13Cinvmod1)
ninvmodspace<-gls(X13C.inv~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testinvn)
AIC(inv13Cmod, ninvmodspace)
anova(inv13Cmod, ninvmodspace)## space does not improve  model
summary(inv13Cmod)

###########################################
### d13C in peat
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X13C.peat~dataiso$birds)
shapiro.test(residuals(aov(dataiso$X13C.peat~dataiso$birds)))
bartlett.test(dataiso$X13C.peat~dataiso$birds)
par(op)
library(nlme)
testpeatn<-dataiso[which(dataiso$X13C.peat <0 ),]
peat13Cmod<-gls(X13C.peat~birds, data=testpeatn)
summary(peat13Cmod)
E<- resid(peat13Cmod, type="normalized")
F<- fitted (peat13Cmod) 
plot(E~testpeatn$birds)
xyplot(n1 ~ e1, aspect = "iso", data = testpeatn,
       col= testpeatn$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2

xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testpeatn,
       main = "Spatial plot of residuals")
str(data)
plot(E~testpeatn$birds)
vario13Cpeatmod1<- Variogram(peat13Cmod, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario13Cpeatmod1)
npeatmodspace<-gls(X13C.peat~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testpeatn)
AIC(peat13Cmod, npeatmodspace)
anova(peat13Cmod, npeatmodspace)## 
summary(peat13Cmod)

###########################################
### d13C in terrestrial vegetation
op<-par(mfrow=c(2,1),mar=c(4,4,1,1)) 
plot(dataiso$X13C.tveg~dataiso$birds)
shapiro.test(residuals(aov(dataiso$X13C.tveg~dataiso$birds)))
## suggests normality is acccomplished
bartlett.test(dataiso$X13C.tveg~dataiso$birds)
##  homogeneity of variance-- 
par(op)
library(nlme)
testtvegn<-dataiso[which(dataiso$X13C.tveg <0 ),]
tveg13Cmod<-gls(X13C.tveg~birds, data=testtvegn)
summary(tveg13Cmod)
E<- resid(tveg13Cmod, type="normalized") ### 
F<- fitted (tveg13Cmod) #
plot(E~testtvegn$birds)
xyplot(n1 ~ e1, aspect = "iso", data = testtvegn,
       col= testtvegn$birds, pch=16)
MyCex <- abs(E) / max(abs(E))
MyCol <- E
MyCol[E >= 0 ] <- 1
MyCol[E < 0 ] <- 2
xyplot(n1~ e1,
       cex = 4* MyCex,
       pch = 1,
       col = MyCol,
       data = testtvegn,
       main = "Spatial plot of residuals")
str(data)
plot(E~testtvegn$birds) 
vario13Ctvegmod1<- Variogram(tveg13Cmod, form=~n1+e1, robust=TRUE, maxDist=100000, restype="normalized")
plot(vario13Ctvegmod1)
ntvegmodspace<-gls(X13C.tveg~birds, weights = vf1,correlation=corGaus(form=~n1+e1,nugget=TRUE), data=testtvegn)
AIC(tveg13Cmod, ntvegmodspace)
anova(tveg13Cmod, ntvegmodspace)
summary(tveg13Cmod)




######### Testing changesin pHysicochemical properties along a gradient in algal d15N
#setwd("/Users/ivangonzalez/Desktop/paper Groenlandia -R1")
####
data <- read.csv("data.csv", header=TRUE, sep=";")
data$birds<-as.factor(data$birds)
library(nlme)
require(lattice)
require(mgcv)


op<-par(mfrow=c(3,2),mar=c(4,4,1,1)) 

pHgrad<-data[which(data$pH>0 ),]
### PH model and plot
pHmod<-lm(pH~d15Nperi, data=pHgrad)
summary(pHmod)

plot(pHgrad$d15Nperi, pHgrad$pH, ylab="System pH",
     xlab=expression(paste(delta^{15}, "N")), pch=c(1,19)[pHgrad$birds])
#Pmod<-predict(pHmod, newdata=md1)
#lines(md1$d15Nperi, Pmod)
ND <- data.frame(d15Nperi=seq(from=-2,to=33.2))
prd<-predict(pHmod,newdata=ND,interval = c("confidence"), 
             level = 0.90,type="response")
lines(ND$d15Nperi, prd[,1])
lines(ND$d15Nperi,prd[,2],col="gray",lty=2)
lines(ND$d15Nperi,prd[,3],col="gray",lty=2)

##### TN
TNgrad<-data[which(data$TN>0 ),]
require(mgcv)

library(nlme)
require(lattice)
vf5<-varIdent(form=~1|birds)## ident power
M3 <- gamm(TN~s(d15Nperi),
           weights = vf5,
           method = "REML",
           data = TNgrad)
summary(M3$gam)
summary(M3$lme)
ND <- data.frame(d15Nperi=seq(from=-2,to=33.2),100)
PM3 <- predict(M3$gam,ND, se = TRUE)
plot(TNgrad$d15Nperi, TNgrad$TN, pch=c(1,19)[TNgrad$birds],
     ylab=expression(paste("TN  (mg l"^-1,")")), xlab=expression(paste(delta^{15}, "N")))
lines(ND$d15Nperi,PM3$fit)
lines(ND$d15Nperi,(PM3$fit+PM3$se), lty=2)
lines(ND$d15Nperi,(PM3$fit-PM3$se), lty=2)


#### TP takes much the same model as there is a non-linear response and heterogeniety of variance - see model mess for details
TPgrad<-data[which(data$TP>0 ),]
M3 <- gamm(TP~s(d15Nperi),
           weights = vf5,
           method = "REML",
           data = TPgrad)

summary(M3$gam)
summary(M3$lme)
ND <- data.frame(d15Nperi=seq(from=-2,to=33.2),100)
PM3 <- predict(M3$gam,ND, se = TRUE)
plot(TPgrad$d15Nperi, TPgrad$TP, pch=c(1,19)[TPgrad$birds],
     ylab=expression(paste("TP (",mu,"g l"^-1,")")), xlab=expression(paste(delta^{15}, "N")))

lines(ND$d15Nperi,PM3$fit)
lines(ND$d15Nperi,(PM3$fit+PM3$se), lty=2)
lines(ND$d15Nperi,(PM3$fit-PM3$se), lty=2)


##### Lentic Chla
Chlagrad<-data[which(data$ChlaLent>0 ),]#
M3 <- gamm(Chla~s(d15Nperi),
           weights = vf5,
           method = "REML",
           data = Chlagrad)
summary(M3$gam)
summary(M3$lme)
range(Chlagrad$d15Nperi)
ND <- data.frame(d15Nperi=seq(from=-1.56,to=24.96))
PM3 <- predict(M3$gam,ND, se = TRUE)
plot(Chlagrad$d15Nperi, Chlagrad$Chla, pch=c(1,19)[Chlagrad$birds], 
     ylab=expression(paste("Lentic Chla (",mu,"g l"^-1,")")), xlab=expression(paste(delta^{15}, "N")))
lines(ND$d15Nperi,PM3$fit)
lines(ND$d15Nperi,(PM3$fit+PM3$se), lty=2)
lines(ND$d15Nperi,(PM3$fit-PM3$se), lty=2)


### Lotic Chla
Chlagrad<-data[which(data$ChlaLot>0 ),]#
vf2<- varPower(form=~d15Nperi)## power
M3 <- gamm(Chla~s(d15Nperi),
           weights = vf2,
           method = "REML",
           data = Chlagrad)
summary(M3$gam)
summary(M3$lme)
range(Chlagrad$d15Nperi)
ND <- data.frame(d15Nperi=seq(from=-2.07,to=33.2))
PM3 <- predict(M3$gam,ND, se = TRUE)
plot(Chlagrad$d15Nperi, Chlagrad$Chla, pch=c(1,19)[Chlagrad$birds], 
     ylab=expression(paste("Lotic Chla (",mu,"g l"^-1,")")), xlab=expression(paste(delta^{15}, "N")))
lines(ND$d15Nperi,PM3$fit)
lines(ND$d15Nperi,(PM3$fit+PM3$se), lty=2)
lines(ND$d15Nperi,(PM3$fit-PM3$se), lty=2)



# Here is EVI code in case you need/want it.. 
# ####EVI plot
# #evigrad<-data[which(data$EVI.500.max>0 ),]
# #evimod<-lm(EVI.500.max~d15Nperi, data=evigrad)
# #summary(evimod)
# 
# plot(evigrad$d15Nperi, evigrad$EVI.500.max, ylab="EVI", xlab="15N", pch=c(1,19)[evigrad$birds])
# #Pmod<-predict(pHmod, newdata=md1)
# #lines(md1$d15Nperi, Pmod)
# prd<-predict(evimod,newdata=ND,interval = c("confidence"), 
#              level = 0.90,type="response")
# lines(ND$d15Nperi, prd[,1])
# lines(ND$d15Nperi,prd[,2],col="gray",lty=2)
# lines(ND$d15Nperi,prd[,3],col="gray",lty=2)


################richness
richgrad<-data[-(34:35),]
is.na(richgrad$ Consumer.taxa.diversity)
richgrad$rich<-richgrad$ Consumer.taxa.diversity## this is just to make the typing easier
M3 <- gamm(rich~s(d15Nperi),
           weights = vf5,
           method = "REML",
           data = richgrad)
summary(M3$gam)
summary(M3$lme)
range(richgrad$d15Nperi)
ND <- data.frame(d15Nperi=seq(from=-2.07,to=33.2))
PM3 <- predict(M3$gam,ND, se = TRUE)
plot(richgrad$d15Nperi, richgrad$rich, pch=c(1,19)[richgrad$birds], ylab="Number of consumer taxa",
     xlab=expression(paste(delta^{15}, "N")))
lines(ND$d15Nperi,PM3$fit)
lines(ND$d15Nperi,(PM3$fit+PM3$se), lty=2)
lines(ND$d15Nperi,(PM3$fit-PM3$se), lty=2)
par(op)




#####################################################################
##            DISTANCE PLOTS
#####################################################################
op<-par(mfrow=c(4,2),mar=c(4,4,1,1)) 
####### Lentic Chla - no satisfactory model..
Chlagrad<-data[which(data$ChlaLent>0 ),]#
plot(Chlagrad$distance, Chlagrad$Chla, pch=c(1,19)[Chlagrad$birds],
     ylab=expression(paste("Lentic Chla (",mu,"g l"^-1,")")), xlab=("Distance from colony (m)"))
Chlagrad<-Chlagrad[Chlagrad$distance < 5000,]
plot(Chlagrad$distance, Chlagrad$Chla, pch=c(1,19)[Chlagrad$birds],
     ylab=expression(paste("Lentic Chla (",mu,"g l"^-1,")")), xlab=("Distance from colony (m)"))


#### LOTIC CHla
Chlagrad<-data[which(data$ChlaLot>0 ),]#
plot(Chlagrad$distance, Chlagrad$Chla, pch=c(1,19)[Chlagrad$birds],
     ylab=expression(paste("Lotic Chla (",mu,"g l"^-1,")")), xlab=("Distance from colony (m)"))
vf3<- varExp(form=~distance)## exponential
M3 <- gls(Chla~distance,
          weights=vf3,
          data = Chlagrad)
summary(M3)
ND <- data.frame(distance=seq(from=0,to=50000, by=100))
require(AICcmodavg)
PM3<-predictSE.gls (M3, ND, se.fit=T)
lines(ND$distance,PM3$fit)
lines(ND$distance,(PM3$fit+PM3$se), lty=2)
lines(ND$distance,(PM3$fit-PM3$se), lty=2)
F<-fitted(M3)
cor(Chlagrad$Chla, F)^2

### sites close to colonies.. 
Chlagrad<-Chlagrad[Chlagrad$distance < 5000,]
plot(Chlagrad$distance, Chlagrad$Chla, pch=c(1,19)[Chlagrad$birds],
     ylab=expression(paste("Lotic Chla (",mu,"g l"^-1,")")), xlab=("Distance from colony (m)"))
require(AICcmodavg)
vf3<- varExp(form=~distance)## exponential
M3 <- gls(Chla~distance,
          weights=vf3,
          data = Chlagrad)
summary(M3)
ND <- data.frame(distance=seq(from=0,to=2500, by=100))
PM3<-predictSE.gls (M3, ND, se.fit=T)
lines(ND$distance,PM3$fit)
lines(ND$distance,(PM3$fit+PM3$se), lty=2)
lines(ND$distance,(PM3$fit-PM3$se), lty=2)

F<-fitted(M3)
cor(Chlagrad$Chla, F)^2


### distance and EVI
### all data
evigrad<-data[which(data$EVI.500.max>0 ),]
plot(evigrad$distance, evigrad$EVI.500.max, pch=c(1,19)[evigrad$birds], ylab="EVI.500.max", 
     xlab="Distance from colony (m)")

M3 <- gls(EVI.500.max~distance,
          weights=vf3,
          data = evigrad)
summary(M3)
ND <- data.frame(distance=seq(from=0,to=50000, by=100))

require(AICcmodavg)
PM3<-predictSE.gls (M3, ND, se.fit=T)
lines(ND$distance,PM3$fit)
lines(ND$distance,(PM3$fit+PM3$se), lty=2)
lines(ND$distance,(PM3$fit-PM3$se), lty=2)

F<-fitted(M3)
cor(evigrad$EVI.500.max, F)^2


###<3000 
evigrad<-data[which(data$EVI.500.max>0 ),]### this way I use alll available data and remove NAs
evigrad<-evigrad[evigrad$distance < 5000,]
plot(evigrad$distance, evigrad$EVI.500.max, pch=c(1,19)[evigrad$birds], ylab="EVI.500.max", 
     xlab="Distance from colony (m)")
evimod<-lm(EVI.500.max~distance, data=evigrad)
summary(evimod)
ND <- data.frame(distance=seq(from=0,to=50000, by=100))
prd<-predict(evimod,newdata=ND,interval = c("confidence"), 
             level = 0.90,type="response")
lines(ND$distance, prd[,1])
lines(ND$distance,prd[,2],col="gray",lty=2)
lines(ND$distance,prd[,3],col="gray",lty=2)

F<-fitted(M3)
cor(evigrad$EVI.500.max, F)^2

#### delta 15 N ALL DATA
d15Ngrad<-data[which(data$d15Nperi>0 ),]### this way I use alll available data and remove NAs

plot(d15Ngrad$distance, d15Ngrad$d15Nperi, pch=c(1,19)[d15Ngrad$birds], ylab=expression(paste(delta^{15}, "N")), 
     xlab="Distance from colony (m)")

M3 <- gls(d15Nperi~distance,
          weights=vf3,
          data = d15Ngrad)
summary(M3)
ND <- data.frame(distance=seq(from=0,to=50000, by=100))

require(AICcmodavg)
PM3<-predictSE.gls (M3, ND, se.fit=T)
lines(ND$distance,PM3$fit)
lines(ND$distance,(PM3$fit+PM3$se), lty=2)
lines(ND$distance,(PM3$fit-PM3$se), lty=2)
F<-fitted(M3)
cor(d15Ngrad$d15Nperi, F)^2

################ sites closer to colonies

### 
d15Ngrad<-d15Ngrad[d15Ngrad$distance < 3000,]
plot(d15Ngrad$distance, d15Ngrad$d15Nperi, pch=c(1,19)[d15Ngrad$birds], ylab=expression(paste(delta^{15}, "N")), 
     xlab="Distance from colony (m)")
M3 <- gls(d15Nperi~distance,
          weights=vf3,
          data = d15Ngrad)
summary(M3)
ND <- data.frame(distance=seq(from=0,to=25000, by=100))
require(AICcmodavg)
PM3<-predictSE.gls (M3, ND, se.fit=T)
lines(ND$distance,PM3$fit)
lines(ND$distance,(PM3$fit+PM3$se), lty=2)
lines(ND$distance,(PM3$fit-PM3$se), lty=2)
F<-fitted(M3)
cor(d15Ngrad$d15Nperi, F)^2

par(op)



########################################################################
######################### for Savissivik island dataset
##########################################################################
Savissivik<-data[which(data$Area == "Savi" ), ]

par(mfrow=c(2, 1), mar=c(2, 4.5, 1,1))
plot(Savissivik$d15Nperi~Savissivik$OverfleightIntensity, xlab="Flight intensity", ylab=expression(delta^15*N), pch=16, cex=1.2, xaxt="n")
modelsav<-lm(Savissivik$OverfleightIntensity~Savissivik$d15Nperi)
summary(modelsav)
abline(lm(Savissivik$d15Nperi~Savissivik$OverfleightIntensity))
text(42.473232, 15.059022 , "NOW 9",cex = 0.7, adj = c(1.2,0.1)) 
text(41.791172, 13.086962, "NOW 13",cex = 0.7, adj = c(1.2,1.4 ))
text(17.029095 , 9.577321, "NOW 12",cex = 0.7, adj = c(1.2,1.4))
text(2.480434, 5.137263, "NOW 11",cex = 0.7, adj = c(-0.2,0.1))
text(1.540072, 4.495496, "NOW 10",cex = 0.7, adj = c(-0.2,0.1))


plot(Savissivik$EVI.500.max~Savissivik$OverfleightIntensity, pch=16)
modelosavi<-lm(Savissivik$EVI.500.max~Savissivik$OverfleightIntensity)
summary(modelosavi)
abline(lm(Savissivik$EVI.500.max~Savissivik$OverfleightIntensity))
text(42.473232, 0.3399 , "NOW 9",cex = 0.7, adj = c(1.2,0.1)) 
text(41.791172, 0.2604, "NOW 13",cex = 0.7, adj = c(1.2,1.4 ))
text(17.029095 , 0.1291, "NOW 12",cex = 0.7, adj = c(1.2,1.4))
text(2.480434, 0.0677, "NOW 11",cex = 0.7, adj = c(-0.2,0.1))
text(1.540072, 0.0732, "NOW 10",cex = 0.7, adj = c(-0.1,-0.4))

plot(Savissivik$d15Nperi~Savissivik$EVI.500.max, pch=16)
modelosavi<-lm(Savissivik$d15Nperi~Savissivik$EVI.500.max)
summary(modelosavi)
abline(lm(Savissivik$d15Nperi~Savissivik$EVI.500.max))






#obj 3: mechanisms for periphyton increase and richnesss decrease, nutrients increase productivity 
#and ph decrease richness of consumers


############# Relationship of PH and lotic richness
par(mfrow=c(3, 2), mar=c(4, 4, 2, 2))
streams<-data[which(data$lentvlot=="lotic" ),]
birdstreams<-streams[which(streams$birds=="1" ),]
birdlessstreams<-streams[which(streams$birds=="0" ),]
lakes<-data[which(data$lentvlot=="lentic" ),]
birdlakes<-  lakes[which(lakes$birds=="1" ), ]
birdlesslakes<-  lakes[which(lakes$birds=="0" ), ]

##Total Nitrogen increase stream Chl
plot(streams$ChlaLot~streams$TN, ylab="Stream Chl", xlab="System total nitrogen") 
testrelnutchl<-lm(ChlaLot~TN, data=streams) 
#plot(testrelnutchl)
shapiro.test(residuals(testrelnutchl))
summary(testrelnutchl)
abline(lm(streams$ChlaLot~ streams$TN))
points(birdstreams$ChlaLot~birdstreams$TN, pch=16, )
points(birdlessstreams$ChlaLot~birdlessstreams$TN, pch=5)
legend("topleft", cex=0.8, legend=" linear regression p<0.0001, r2=0.77", bty="n")
###### 90 % CI
library(nlme)
require(lattice)
require(mgcv)
CI1 <- data.frame(TN=seq(0.111 ,5.550))
ic1 <- predict(testrelnutchl, CI1, interval = "confidence", level = 0.90,type="response")
lines(CI1$TN, ic1[, 2], lty = 2)
lines(CI1$TN, ic1[, 3], lty = 2)

##
##Total Phosphorous increase stream Chl
plot(streams$ChlaLot~streams$TP, ylab="", xlab="System total phosphorous") 
testrelnutchlP<-lm(ChlaLot~TP, data=streams) 
summary(testrelnutchlP)
abline(lm(ChlaLot~ TP,data=streams))
points(birdstreams$ChlaLot~birdstreams$TP, pch=16, )
points(birdlessstreams$ChlaLot~birdlessstreams$TP, pch=5)
legend("topleft", cex=0.8,  legend=" linear regression p<0.0001, r2=0.75", bty="n")
#plot(testrelnutchlP)
shapiro.test(residuals(testrelnutchlP))
CI2<-data.frame(TP=seq(from=0,to=1))
ic2<-predict(testrelnutchlP, CI2, interval = "confidence", level = 0.90,type="response")
lines(CI2$ TP, ic2[, 2], lty = 2)
lines(CI2$ TP, ic2[, 3], lty = 2)


##Total Nitrogen increase lentic Chl
plot(lakes$ChlaLent~lakes$TN, ylab="phytoplankton Chl", xlab="System total nitrogen") 
testrelnutchllentic<-lm(ChlaLent~TN, data=lakes) 
summary(testrelnutchllentic)
abline(lm(ChlaLent~ TN, data=lakes))
points(birdlakes$ChlaLent~birdlakes$TN, pch=16, )
points(birdlesslakes$ChlaLent~birdlesslakes$TN, pch=5)
legend("topleft", cex=0.8, legend=" linear regression p<0.0001, r2=0.89", bty="n")
#plot(testrelnutchllentic)
shapiro.test(residuals(testrelnutchllentic))

CI3<- data.frame(TN=seq(from=0 ,to=4))
ic3<- predict(testrelnutchllentic, CI3, interval = "confidence", level = 0.90, type="response")
lines(CI3$TN, ic3[, 2], lty = 2)
lines(CI3$TN, ic3[, 3], lty = 2)


##
##Total Phosphorous increase lentic Chl
plot(lakes$ChlaLent~lakes$TP, ylab="", xlab="System total phosphorous") 
testrelnutchlPlentic<-lm(ChlaLent~TP, data=lakes) 
summary(testrelnutchlPlentic)
points(birdlakes$ChlaLent~birdlakes$TP, pch=16, )
points(birdlesslakes$ChlaLent~birdlesslakes$TP, pch=5)
abline(lm(ChlaLent~ TP, data=lakes))
legend("topleft", cex=0.8, , legend=" linear regression p<0.0001, r2=0.99", bty="n")
#plot(testrelnutchlPlentic)
shapiro.test(residuals(testrelnutchlPlentic))

CI4<- data.frame(TP=seq(from=0 ,to=1))
ic4<- predict(testrelnutchlPlentic, CI4, interval = "confidence", level = 0.90, type="response")
lines(CI4$TP, ic4[, 2], lty = 2)
lines(CI4$TP, ic4[, 3], lty = 2)



data$birds<-as.factor(data$birds)
library(nlme)
require(lattice)
require(mgcv)

streams<-data[which(data$lentvlot=="lotic" ),]

strambirds<-streams[which(streams$birds=="1" ),]

streampH<-streams[which(streams$pH>0 ),]

vf5<-varIdent(form=~1|birds)## ident power


Mphrich <- gamm(Consumer.taxa.diversity~s(pH),
                weights = vf5,
                method = "REML",
                data = streampH)

summary(Mphrich$gam)
summary(Mphrich$lme)
ND <- data.frame(pH=seq(from=0,to=9),100)
PM3 <- predict(Mphrich$gam,ND, se = TRUE)
plot(Mphrich$Consumer.taxa.diversity, Mphrich$pH, pch=c(1,19)[Mphrich$birds],xlim=c(3, 8),ylim=c(0, 4),
     ylab="Taxa richness", xlab="Stream pH")

lines(ND$pH,PM3$fit)
lines(ND$pH,(PM3$fit+PM3$se), lty=2)
lines(ND$pH,(PM3$fit-PM3$se), lty=2)

points(streampH$Consumer.taxa.diversity~streampH$pH)
points(strambirds$Consumer.taxa.diversity~strambirds$pH, pch=16)
legend("topleft", cex=0.8, legend=" GAM p<0.0001, r2=0.44", bty="n")



#### lentic pH
lenticpH<-lakes[which(lakes$pH<8.9 ),]
birdlenticpH<-lenticpH[which(lenticpH$birds=="1" ),]

plot(lenticpH$Consumer.taxa.diversity~lenticpH$pH, ylab="", xlab="System pH", ylim=c(0, 5)) 
testphconslake<-lm(Consumer.taxa.diversity~pH, data=lenticpH) 
summary(testphconslake)
abline(lm(Consumer.taxa.diversity~pH, data=lenticpH))
points(lenticpH$Consumer.taxa.diversity~lenticpH$pH )
points(birdlenticpH$Consumer.taxa.diversity~birdlenticpH$pH, pch=16)
legend("topleft", cex=0.8, legend=" linear regression p<0.001, r2=0.49", bty="n")

#plot(testphconslake)
shapiro.test(residuals(testphconslake))

CI5<- data.frame(pH=seq(from=0 ,to=9))
ic5<- predict(testphconslake, CI5, interval = "confidence", level = 0.90, type="response")
lines(CI5$pH, ic5[, 2], lty = 2)
lines(CI5$pH, ic5[, 3], lty = 2)