#Appendix S4: R code for MCMCglmm analyses

#set working directory
setwd("file/path/here")

##########
#LIBRARIES
##########

library(MCMCglmm) #ape is required



#####
#DATA
#####

#read in data (appendix S1)
TDdata<-read.csv("PartitioningDynamics2.csv",header=T)
TDdata<-TDdata[-which(TDdata$Type=="Alga"|TDdata$Type=="Epiphyte"),]

#read in phylogenetic tree (appendix S2)
fulltree<-read.nexus("Compadre_bl_280714.nex")
all(TDdata$Species%in%fulltree$tip.label)

#We have a problem. A bunch of Species aren't in the phylogeny. Which ones?
(missing<-as.character(unique(TDdata$Species[which(!TDdata$Species%in%fulltree$tip.label)])))
#can we find any using fuzzy matching? Maybe there are typos
fuzzymatches<-as.list(numeric(length(missing)))
for(i in 1:length(missing)){
    if(length(agrep(missing[i],fulltree$tip.label))>0){
        fuzzymatches[[i]]<-fulltree$tip.label[agrep(missing[i],fulltree$tip.label)]
    }
}
fuzzymatches
#there's more than one match per species
(fuzzymatches<-lapply(fuzzymatches,sort))
#the first one of each set works
fuzzymatches<-sapply(fuzzymatches,function(x){x<-x[1]}); fuzzymatches[fuzzymatches=="0"]<-NA
Original<-missing
Alternative<-fuzzymatches

#There are still some species missing. Which ones?
stillmissing<-as.character(Original[is.na(Alternative)])
#Maybe they have matching Genuses
stillmissingGenuses<-sapply(strsplit(stillmissing,"_"),function(x){x[1]})
Genusmatches<-as.list(numeric(length(stillmissing)))
for(i in 1:length(stillmissingGenuses)){
    if(length(agrep(stillmissingGenuses[i],fulltree$tip.label))>0){
        Genusmatches[[i]]<-fulltree$tip.label[agrep(stillmissingGenuses[i],fulltree$tip.label)]
    }
}
Genusmatches
#Maximum one match per species this time
Genusmatches<-paste(Genusmatches); Genusmatches[Genusmatches=="0"]<-NA
for(i in 1:length(stillmissing)){
    Alternative[Original==stillmissing[i]]<-Genusmatches[i]
}

#There are STILL some species missing. Which ones?
(STILLmissing<-as.character(Original[is.na(Alternative)]))
#Googling informs that this is a fern genus
#It has some synonyms
length(grep("Camptosorus",fulltree$tip.label))
length(grep("Ceterach",fulltree$tip.label))
length(grep("Loxoscaphe",fulltree$tip.label))
length(grep("Phyllitis",fulltree$tip.label))
length(grep("Tarachia",fulltree$tip.label))
#Nope, it's not there. Let's take it out the data
TDdata<-TDdata[-which(TDdata$Species%in%STILLmissing),]

(Original<-Original[-which(Original%in%STILLmissing)])
(Alternative<-Alternative[-which(is.na(Alternative))])
Speciesnew<-as.character(TDdata$Species)
for(i in 1:length(Alternative)){
    Speciesnew[Speciesnew==Original[i]]<-Alternative[i]
}
TDdata<-cbind(TDdata,Speciesnew,animal=Speciesnew)
all(TDdata$animal%in%fulltree$tip.label)

#We need to drop the Species that aren't in our data.
drop<-fulltree$tip.label[which(!fulltree$tip.label%in%TDdata$animal)]
length(drop)+length(unique(TDdata$animal))==length(fulltree$tip.label)

#Trim tree of Species we don't need
smalltree<-drop.tip(fulltree, drop)
all(sort(levels(TDdata$animal))==sort(smalltree$tip))
#Finally we have a little tree 
smalltree$node.label<-as.character(1:length(smalltree$node.label))
#There is a problem with MCMCglmm if the node labels aren't unique


any(TDdata[,c("Rel.Cont.Transients","Rel.Cont.VR","Mean.Prop.Transients")]==1)
which(TDdata[,c("Rel.Cont.Transients","Rel.Cont.VR","Mean.Prop.Transients")]==1,arr.ind=T)
any(TDdata[,c("Rel.Cont.Transients","Rel.Cont.VR","Mean.Prop.Transients")]==1)
#There is one entry for Rel.Cont.Transients which equals 1
#This creates problems for the analysis
#We will correct to approximately 1
TDdata$Rel.Cont.Transients[172]<-0.999



nitt<-500000
burnin<-0.1*nitt
thin<-0.0005*nitt


########################
#WITH PHYLOGENY (mX.1.X)
########################

logit<-function(x){log(x/(1-x))}


#Rel.Cont.Transients
prior1.1<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100), 
                        G2=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m1.1.1<-MCMCglmm(logit(Rel.Cont.Transients) ~ Dim.matrices + Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior1.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m1.1.2<-MCMCglmm(logit(Rel.Cont.Transients) ~ Dim.matrices,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior1.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m1.1.3<-MCMCglmm(logit(Rel.Cont.Transients) ~ Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior1.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m1.1.4<-MCMCglmm(logit(Rel.Cont.Transients) ~ 1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior1.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

#Rel.Cont.VR
prior2.1<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100), 
                        G2=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m2.1.1<-MCMCglmm(logit(Rel.Cont.VR) ~ Dim.matrices + Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior2.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m2.1.2<-MCMCglmm(logit(Rel.Cont.VR) ~ Dim.matrices,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior2.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m2.1.3<-MCMCglmm(logit(Rel.Cont.VR) ~ Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior2.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m2.1.4<-MCMCglmm(logit(Rel.Cont.VR) ~ 1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior2.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

#Mean.Prop.Transients
prior3.1<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100), 
                        G2=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m3.1.1<-MCMCglmm(logit(Mean.Prop.Transients) ~ Dim.matrices + Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior3.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m3.1.2<-MCMCglmm(logit(Mean.Prop.Transients) ~ Dim.matrices,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior3.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m3.1.3<-MCMCglmm(logit(Mean.Prop.Transients) ~ Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior3.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m3.1.4<-MCMCglmm(logit(Mean.Prop.Transients) ~ 1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior3.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)


#Stochastic.Growth
prior4.1<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100), 
                        G2=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m4.1.1<-MCMCglmm(Stochastic.Growth ~ Dim.matrices + Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior4.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m4.1.2<-MCMCglmm(Stochastic.Growth ~ Dim.matrices,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior4.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m4.1.3<-MCMCglmm(Stochastic.Growth ~ Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior4.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m4.1.4<-MCMCglmm(Stochastic.Growth ~ 1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior4.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

#Tot.dynamics
prior5.1<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100), 
                        G2=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m5.1.1<-MCMCglmm(Tot.dynamics ~ Dim.matrices + Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior5.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m5.1.2<-MCMCglmm(Tot.dynamics ~ Dim.matrices,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior5.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m5.1.3<-MCMCglmm(Tot.dynamics ~ Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior5.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m5.1.4<-MCMCglmm(Tot.dynamics ~ 1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior5.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

#Mean.Transient
prior6.1<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100), 
                        G2=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m6.1.1<-MCMCglmm(Mean.Transient ~ Dim.matrices + Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior6.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m6.1.2<-MCMCglmm(Mean.Transient ~ Dim.matrices,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior6.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m6.1.3<-MCMCglmm(Mean.Transient ~ Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior6.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m6.1.4<-MCMCglmm(Mean.Transient ~ 1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior6.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

#Mean.Vital.Rate
prior7.1<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100), 
                        G2=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m7.1.1<-MCMCglmm(Mean.Vital.Rate ~ Dim.matrices + Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior7.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m7.1.2<-MCMCglmm(Mean.Vital.Rate ~ Dim.matrices,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior7.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m7.1.3<-MCMCglmm(Mean.Vital.Rate ~ Type -1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior7.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m7.1.4<-MCMCglmm(Mean.Vital.Rate ~ 1,
                 random=~Speciesnew + animal, family="gaussian",
                 data=TDdata, pedigree=smalltree, nodes="TIPS",
                 prior=prior7.1, thin=thin, nitt=nitt, burnin=burnin, verbose=F)



###########################
#WITHOUT PHYLOGENY (mX.2.X)
###########################


#Rel.Cont.Transients
prior1.2<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m1.2.1<-MCMCglmm(logit(Rel.Cont.Transients) ~ Dim.matrices + Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior1.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m1.2.2<-MCMCglmm(logit(Rel.Cont.Transients) ~ Dim.matrices,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior1.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m1.2.3<-MCMCglmm(logit(Rel.Cont.Transients) ~ Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior1.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m1.2.4<-MCMCglmm(logit(Rel.Cont.Transients) ~ 1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior1.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

#Rel.Cont.VR
prior2.2<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m2.2.1<-MCMCglmm(logit(Rel.Cont.VR) ~ Dim.matrices + Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior2.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m2.2.2<-MCMCglmm(logit(Rel.Cont.VR) ~ Dim.matrices,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior2.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m2.2.3<-MCMCglmm(logit(Rel.Cont.VR) ~ Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior2.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m2.2.4<-MCMCglmm(logit(Rel.Cont.VR) ~ 1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior2.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

#Mean.Prop.Transients
prior3.2<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m3.2.1<-MCMCglmm(logit(Mean.Prop.Transients) ~ Dim.matrices + Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior3.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m3.2.2<-MCMCglmm(logit(Mean.Prop.Transients) ~ Dim.matrices,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior3.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m3.2.3<-MCMCglmm(logit(Mean.Prop.Transients) ~ Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior3.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m3.2.4<-MCMCglmm(logit(Mean.Prop.Transients) ~ 1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior3.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)



#Stochastic.Growth
prior4.2<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m4.2.1<-MCMCglmm(Stochastic.Growth ~ Dim.matrices + Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior4.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m4.2.2<-MCMCglmm(Stochastic.Growth ~ Dim.matrices,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior4.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m4.2.3<-MCMCglmm(Stochastic.Growth ~ Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior4.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m4.2.4<-MCMCglmm(Stochastic.Growth ~ 1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior4.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

#Tot.dynamics
prior5.2<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m5.2.1<-MCMCglmm(Tot.dynamics ~ Dim.matrices + Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior5.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m5.2.2<-MCMCglmm(Tot.dynamics ~ Dim.matrices,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior5.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m5.2.3<-MCMCglmm(Tot.dynamics ~ Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior5.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m5.2.4<-MCMCglmm(Tot.dynamics ~ 1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior5.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

#Mean.Transient
prior6.2<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m6.2.1<-MCMCglmm(Mean.Transient ~ Dim.matrices + Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior6.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m6.2.2<-MCMCglmm(Mean.Transient ~ Dim.matrices,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior6.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m6.2.3<-MCMCglmm(Mean.Transient ~ Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior6.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m6.2.4<-MCMCglmm(Mean.Transient ~ 1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior6.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

#Mean.Vital.Rate
prior7.2<-list(R = list(V = 1, nu=0.001),
               G = list(G1=list(V = 1, nu=0.001, alpha.mu=0, alpha.V=100)))

m7.2.1<-MCMCglmm(Mean.Vital.Rate ~ Dim.matrices + Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior7.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m7.2.2<-MCMCglmm(Mean.Vital.Rate ~ Dim.matrices,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior7.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m7.2.3<-MCMCglmm(Mean.Vital.Rate ~ Type -1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior7.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

m7.2.4<-MCMCglmm(Mean.Vital.Rate ~ 1,
                 random=~Speciesnew, family="gaussian",
                 data=TDdata, nodes="TIPS",
                 prior=prior7.2, thin=thin, nitt=nitt, burnin=burnin, verbose=F)

#results of these analyses are in appendix S5
#(subsets of models presented in the manuscript are not presented)