library(ape)
library(MASS)
library(phytools)
## Loading required package: maps
CompareRates.multTrait<-function(phy,x,TraitCov=T,ms.err=NULL,ms.cov=NULL){
build.chol<-function(b){
c.mat<-matrix(0,nrow = p,ncol = p)
c.mat[lower.tri(c.mat)]<-b[-1]
c.mat[p,p]<-exp(b[1])
c.mat[1,1]<-sqrt(sum((c.mat[p,])^2))
if(p>2){
for(i in 2:(p-1)){
c.mat[i,i]<-ifelse((c.mat[1,1]^2-sum((c.mat[i,])^2))>0,sqrt(c.mat[1,1]^2-sum((c.mat[i,])^2)),0)
}
}
return(c.mat)
}
x<-as.matrix(x)
N<-nrow(x)
p<-ncol(x)
C<-vcv.phylo(phy)
C<-C[rownames(x),rownames(x)]
I<-diag(1,N)
if (is.matrix(ms.err)){
ms.err<-as.matrix(ms.err[rownames(x),])}
if (is.matrix(ms.cov)){
ms.cov<-as.matrix(ms.cov[rownames(x),])}
a.obs<-colSums(solve(C)) %*% x / sum(solve(C))
one<-matrix(1,N,1)
R.obs<-t(x-one%*%a.obs)%*%solve(C)%*%(x-one%*%a.obs)/N
IIDcon<-function(trait=trait,mu=mu,sigma=sigma,C=C){
z<- (trait-mu)/sigma
eC<-eigen(C)
D.n5<-diag(1/sqrt(eC$values))
C.neg.5<-eC$vectors%*%D.n5%*%t(eC$vectors)
return(C.neg.5%*%trait)
}
D<-matrix(0,N*p,p)
for(i in 1:(N*p)){
for(j in 1:p){
if((j-1)*N < i && i<=j*N){
D[i,j]=1.0
}
}
}
y<-as.matrix(as.vector(x))
if (TraitCov==F){R.obs<-diag(diag(R.obs),p)}
LLik.obs<-ifelse(is.matrix(ms.err)==TRUE,
-t(y-D%*%t(a.obs))%*%ginv((kronecker(R.obs,C)+diag(as.vector(ms.err))))%*%(y-D%*%t(a.obs))/2-N*p*log(2*pi)/2-determinant((kronecker(R.obs,C)+ diag(as.vector(ms.err))))$modulus[1]/2,
-t(y-D%*%t(a.obs))%*%ginv(kronecker(R.obs,C))%*%(y-D%*%t(a.obs))/2-N*p*log(2*pi)/2-determinant(kronecker(R.obs,C))$modulus[1]/2)
sigma.mn<-mean(diag(R.obs))
if(is.matrix(ms.err) && is.matrix(ms.cov)){
within.spp<-cbind(ms.err,ms.cov)
rc.label<-NULL
for(i in 1:p){
rc.label<-rbind(rc.label,c(i,i))
}
for(j in 2:p){
if(i!=j&&i<j){
rc.label<-rbind(rc.label,c(i,j))
}
}
m.e<-NULL
for(i in 1:p){
temp<-NULL
for(j in 1:p){
for(k in 1:nrow(rc.label)){
if(setequal(c(i,j),rc.label[k,])==T)
{tmp<-cbind(tmp,diag(within.spp[,k]))}
}
}
m.e<-rbind(m.e,tmp)
}
}
lik.covF<-function(sigma){
R<-R.obs
diag(R)<-sigma
LLik<-ifelse(is.matrix(ms.err)==TRUE,
-t(y-D%*%t(a.obs))%*%ginv((kronecker(R,C)+m.e))%*%(y-D%*%t(a.obs))/2-N*p*log(2*pi)/2-determinant((kronecker(R,C)+ m.e))$modulus[1]/2,
-t(y-D%*%t(a.obs))%*%ginv(kronecker(R,C))%*%(y-D%*%t(a.obs))/2-N*p*log(2*pi)/2-determinant(kronecker(R,C))$modulus[1]/2)
if(LLik==-Inf){LLik<--1e+10}
return(-LLik)
}
################################
#h12<-(h1+h2)/2# HERE IS AN ISSUE
################################
#Sh12 <- h12^2*C + (1-h12^2)*I
lik.covT<-function(sigma){
low.chol<-build.chol(sigma)
R<-low.chol%*%t(low.chol)
LLik <- ifelse(is.matrix(ms.err)==TRUE,
-t(y-D%*%t(a.obs))%*%ginv(kronecker(R,C)+m.e)%*%(y-D%*%t(a.obs))/2-N*p*log(2*pi)/2-determinant(kronecker(R,C)+m.e)$modulus[1]/2,
-t(y-D%*%t(a.obs))%*%ginv(kronecker(R,C))%*%(y-D%*%t(a.obs))/2-N*p*log(2*pi)/2-determinant(kronecker(R,C))$modulus[1]/2
)
if(LLik==-Inf){LLik<--le+10}
return(-LLik)
}
#TraitCov=F
## Optimize for no trait covariation
if(TraitCov==F){model<-optim(sigma.mn,fn=lik.covF,method
="L-BFGS-B",hessian = TRUE,lower = c(0.0))}
sigma.upper<-2*max(apply(x,2,sd))
#TraitCov=T
## Optimize with trait covariation
R.offd<-rep(0,(p*(p-1)/2))
if(TraitCov==T){model1<-
# optim(par=c(sigma.mn,R.offd),fn=lik.covT,method="L-BFGS-B",lower = c(0,0))
optim(par=c(sigma.mn,R.offd),fn=lik.covT,method="L-BFGS-B",lower = c(0,0))
}
#sigma<-c(sigma.mn,R.offd)
#### Assemble R.constrained
if(TraitCov==F){R.constr<-diag(model$par,p)}
if(TraitCov==T){
chol.mat<-build.chol(model1$par)
R.constr<-chol.mat%*%t(chol.mat)
}
if(model1$convergence==0){
message<-"Optimization has converged."}else{
message<-"Optim may not have converrged.
Consideer changing startt value or lower/upper limits."}
LRT<-(-2*((-model1$value-LLik.obs)))
LRT.prob<-pchisq(LRT, (p-1),lower.tail = FALSE)
AIC.obs<- -2*LLik.obs+2*p+2*p #(2p twice: 1x for rates, 1x for anc.states)
AIC.common<--2*(-model1$value)+2+2*p #(2*1:for 1 rate 2p for anc.states)
return(
list(
Robs=R.obs,
Rconstrained=R.constr,
Lobs=LLik.obs,
Lconstrained=(-model1$value),
LRTest=LRT,
Prob=LRT.prob,
AICc.obs=AIC.obs,
AICc.constrained=AIC.common,
optimmessage=message
)
)
}
phy<-rcoal(5)
plot(phy)
x<- matrix(c(rnorm(5,2,1),rnorm(5,0,0.5)),ncol=2)
rownames(x)<-phy$tip.label#LETTERS[1:N]
CompareRates.multTrait(phy=phy,x=x,TraitCov=T,ms.err=NULL,ms.cov=NULL)
## $Robs
## [,1] [,2]
## [1,] 9.758637 -1.1807692
## [2,] -1.180769 0.9287916
##
## $Rconstrained
## [,1] [,2]
## [1,] 5.343718 0.000000
## [2,] 0.000000 5.343718
##
## $Lobs
## [1] -14.21705
##
## $Lconstrained
## [1] -17.50352
##
## $LRTest
## [1] 6.572937
##
## $Prob
## [1] 0.01035409
##
## $AICc.obs
## [1] 36.43411
##
## $AICc.constrained
## [1] 41.00704
##
## $optimmessage
## [1] "Optimization has converged."
tree<-read.tree("http://tonyjhwueng.info/phyrates/ple.nwk")
plot(tree)
tree$tip.label
## [1] "Plethodon_dorsalis" "Plethodon_ventralis"
## [3] "Plethodon_angusticlavius" "Plethodon_welleri"
## [5] "Plethodon_punctatus" "Plethodon_wehrlei"
## [7] "Plethodon_websteri" "Plethodon_teyahalee"
## [9] "Plethodon_cylindraceus" "Plethodon_variolatus"
## [11] "Plethodon_chlorobryonis" "Plethodon_chattahoochee"
## [13] "Plethodon_cheoah" "Plethodon_shermani"
## [15] "Plethodon_amplus" "Plethodon_meridianus"
## [17] "Plethodon_montanus" "Plethodon_albagula"
## [19] "Plethodon_sequoyah" "Plethodon_ocmulgee"
## [21] "Plethodon_savannah" "Plethodon_grobmani"
## [23] "Plethodon_kisatchie" "Plethodon_mississippi"
## [25] "Plethodon_kiamichi" "Plethodon_aureolus"
## [27] "Plethodon_glutinosus" "Plethodon_jordani"
## [29] "Plethodon_metcalfi" "Plethodon_ouachitae"
## [31] "Plethodon_fourchensis" "Plethodon_caddoensis"
## [33] "Plethodon_kentucki" "Plethodon_petraeus"
## [35] "Plethodon_yonahlossee" "Plethodon_hubrichti"
## [37] "Plethodon_nettingi" "Plethodon_richmondi"
## [39] "Plethodon_electromorphus" "Plethodon_cinereus"
## [41] "Plethodon_shenandoah" "Plethodon_hoffmani"
## [43] "Plethodon_virginia" "Plethodon_serratus"
df<-read.csv("http://tonyjhwueng.info/phyrates/Adams2012-SystBiolData.csv")
head(df)
## X HeadLength BodyWidth Forelimb
## 1 P_albagula 12.320000 8.160000 16.12000
## 2 P_amplus 11.120000 7.580000 16.44000
## 3 P_angusticlavius 7.033333 3.700000 8.10000
## 4 P_aureolus 9.200000 5.314286 12.52857
## 5 P_caddoensis 8.200000 3.600000 9.20000
## 6 P_chattahoochee 10.371429 6.400000 13.67143
spX<-strsplit(as.character(df$X),"_")
spname<-array(NA,length(tree$tip.label))
for(Index in 1:length(tree$tip.label)){
spname[Index]<-paste("Plethodon_", spX[[Index]][2],sep="")
}
spname
## [1] "Plethodon_albagula" "Plethodon_amplus"
## [3] "Plethodon_angusticlavius" "Plethodon_aureolus"
## [5] "Plethodon_caddoensis" "Plethodon_chattahoochee"
## [7] "Plethodon_cheoah" "Plethodon_chlorobryonis"
## [9] "Plethodon_cinereus" "Plethodon_cylindraceus"
## [11] "Plethodon_dorsalis" "Plethodon_electromorphus"
## [13] "Plethodon_fourchensis" "Plethodon_glutinosus"
## [15] "Plethodon_grobmani" "Plethodon_hoffmani"
## [17] "Plethodon_hubrichti" "Plethodon_jordani"
## [19] "Plethodon_kentucki" "Plethodon_kiamichi"
## [21] "Plethodon_kisatchie" "Plethodon_meridianus"
## [23] "Plethodon_metcalfi" "Plethodon_mississippi"
## [25] "Plethodon_montanus" "Plethodon_nettingi"
## [27] "Plethodon_ocmulgee" "Plethodon_ouachitae"
## [29] "Plethodon_petraeus" "Plethodon_punctatus"
## [31] "Plethodon_richmondi" "Plethodon_savannah"
## [33] "Plethodon_sequoyah" "Plethodon_serratus"
## [35] "Plethodon_shenandoah" "Plethodon_shermani"
## [37] "Plethodon_teyahalee" "Plethodon_variolatus"
## [39] "Plethodon_ventralis" "Plethodon_virginia"
## [41] "Plethodon_websteri" "Plethodon_wehrlei"
## [43] "Plethodon_welleri" "Plethodon_yonahlossee"
df$X<-spname
HeadLength<-df$HeadLength
names(HeadLength)<-spname
BodyWidth<-df$BodyWidth
names(BodyWidth)<-spname
HeadLength<-HeadLength[tree$tip.label]
BodyWidth<-BodyWidth[tree$tip.label]
x<-cbind(HeadLength,BodyWidth)
CompareRates.multTrait(phy=tree,x=x,TraitCov=T,ms.err=NULL,ms.cov=NULL)
## $Robs
## HeadLength BodyWidth
## HeadLength 0.2282753 0.1252281
## BodyWidth 0.1252281 0.1192467
##
## $Rconstrained
## [,1] [,2]
## [1,] 1.0154436 0.1252281
## [2,] 0.1252281 1.0154436
##
## $Lobs
## [1] -126.8484
##
## $Lconstrained
## [1] -188.316
##
## $LRTest
## [1] 122.9352
##
## $Prob
## [1] 1.440774e-28
##
## $AICc.obs
## [1] 261.6968
##
## $AICc.constrained
## [1] 382.632
##
## $optimmessage
## [1] "Optimization has converged."