Nothing
R/ABneutral.R
In AlphaBeta: Computational inference of epimutation rates and spectra from high-throughput DNA methylation data in plants
Defines functions
ABneutral
Documented in
ABneutral
#' Run Model with no selection (ABneutral)
#'
#' This model assumes that heritable gains and losses in cytosine methylation are selectively neutral.
#'
#' @param pedigree.data pedigree data.
#' @param p0uu initial proportion of unmethylated cytosines.
#' @param eqp equilibrium proportion of unmethylated cytosines.
#' @param eqp.weight weight assigned to equilibrium function.
#' @param Nstarts iterations for non linear LSQ optimization.
#' @param out.dir output directory.
#' @param out.name output file name.
#' @import optimx
#' @import expm
#' @importFrom stats runif
#' @return ABneutral RData file.
#' @export
#' @examples
#' #Get some toy data
#' inFile <- readRDS(system.file("extdata/dm/","output.rds", package="AlphaBeta"))
#' pedigree <- inFile$Pdata
#' p0uu_in <- inFile$tmpp0
#' eqp.weight <- 1
#' Nstarts <- 2
#' out.name <- "CG_global_estimates_ABneutral"
#' out <- ABneutral(pedigree.data = pedigree,
#' p0uu=p0uu_in,
#' eqp=p0uu_in,
#' eqp.weight=eqp.weight,
#' Nstarts=Nstarts,
#' out.dir=getwd(),
#' out.name=out.name)
#'
#' summary(out)
#'
ABneutral<-function(pedigree.data, p0uu, eqp, eqp.weight, Nstarts, out.dir, out.name)
{
##### Defining the divergence function
divergence <- function(pedigree, p0mm, p0um, p0uu, param)
{
## Initializing parameters
PrMM <- p0mm
PrUM <- p0um
PrUU <- p0uu
alpha <- param[1]
bet <- param[2]
weight <- param[3]
## State probabilities at G0; first element = PrUU, second element = PrUM, third element = PrMM
svGzero <- c(PrUU, (weight)*PrMM, (1-weight)*PrMM)
## Defining the generation (or transition) matrix
Genmatrix <- matrix(c((1-alpha)^2, 2*(1-alpha)*alpha, alpha^2,
1/4*(bet + 1 - alpha)^2, 1/2*(bet + 1 - alpha)*(alpha + 1 - bet), 1/4*(alpha + 1 - bet)^2,
bet^2, 2*(1-bet)*bet, (1-bet)^2), nrow=3, byrow=TRUE)
## Calculating theoretical divergence for every observed pair in 'pedigree.txt'
Dt1t2<-NULL
for (p in seq_len(NROW(pedigree)))
{
## Define state vectors for t1,t2 and t0 from pedigree using matrix multiplications from library(expm)
svt0 <- t(svGzero) %*% ((Genmatrix)%^% as.numeric(pedigree[p,1]))
svt1.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
svt1.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
svt1.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
## Conditional divergences
dt1t2.MM <- 1/2*(svt1.MM[,1] * svt2.MM[,2] + svt1.MM[,2] * svt2.MM[,1] + svt1.MM[,2] * svt2.MM[,3] +
svt1.MM[,3] * svt2.MM[,2]) + 1*(svt1.MM[,1] * svt2.MM[,3] + svt1.MM[,3] * svt2.MM[,1])
dt1t2.UM <- 1/2*(svt1.UM[,1] * svt2.UM[,2] + svt1.UM[,2] * svt2.UM[,1] + svt1.UM[,2] * svt2.UM[,3] +
svt1.UM[,3] * svt2.UM[,2]) + 1*(svt1.UM[,1] * svt2.UM[,3] + svt1.UM[,3] * svt2.UM[,1])
dt1t2.UU <- 1/2*(svt1.UU[,1] * svt2.UU[,2] + svt1.UU[,2] * svt2.UU[,1] + svt1.UU[,2] * svt2.UU[,3] +
svt1.UU[,3] * svt2.UU[,2]) + 1*(svt1.UU[,1] * svt2.UU[,3] + svt1.UU[,3] * svt2.UU[,1])
## Total (weighted) divergence
Dt1t2[p]<- svt0[,1]*dt1t2.UU + svt0[,2]*dt1t2.UM + svt0[,3]*dt1t2.MM
}
# Pr(UU) at equilibrium given alpha and beta
puuinf.est<- (bet* ((1-bet)^2 - (1-alpha)^2 -1))/((alpha + bet)*((alpha + bet -1)^2 - 2))
divout<-list(puuinf.est, Dt1t2)
return(divout)
}
###### Defining the Least Square function to be minimized
###### Note the equilibrium constraint, which can be made as small as desired.
LSE_intercept<-function(param_int)
{
sum((pedigree[,4] - param_int[4] - divergence(pedigree, p0mm, p0um, p0uu, param_int[1:3])[[2]])^2) +
eqp.weight*nrow(pedigree)*((divergence(pedigree, p0mm, p0um, p0uu, param_int[1:3])[[1]]- eqp)^2)
}
###### Calculating the initial proportions
###### We always assume that:
# 1. p0mm is larger than actually observed. This means if p0um is available from measurements,
# we will just add it to p0mm.
# 2. As a consequence of (1.) we also assume that p0um = 0.
p0uu<-p0uu
p0mm<-1-p0uu
p0um<-0
if(is.null(p0uu ==TRUE | is.null(eqp)==TRUE))
{stop("Both eqp value AND p0uu have to be supplied")}
if(sum(c(p0mm, p0um, p0uu), na.rm =TRUE) != 1)
{stop("The initial state probabilities don't sum to 1")}
##### Initializing
optim.method<-"Nelder-Mead"
final<-NULL
counter<-0
opt.out<-NULL
pedigree<-pedigree.data
for (s in seq_len(Nstarts))
{
## Draw random starting values
alpha.start <-10^(runif(1, log10(10^-9), log10(10^-2)))
beta.start <-10^(runif(1, log10(10^-9), log10(10^-2)))
weight.start <-runif(1,0,0.1)
intercept.start <-runif(1,0,max(pedigree[,4]))
param_int0 = c(alpha.start, beta.start, weight.start, intercept.start)
## Initializing
counter<-counter+1
message("Progress: ", counter/Nstarts, "\n")
opt.out <- suppressWarnings(optimx(par = param_int0, fn = LSE_intercept, method=optim.method))
alphafinal<-opt.out[1]
betfinal<-opt.out[2]
PrMMinf <- (alphafinal* ((1-alphafinal)^2 - (1-betfinal)^2 -1))/((alphafinal + betfinal)*((alphafinal + betfinal -1)^2 - 2))
PrUMinf <- (4*alphafinal*betfinal*(alphafinal + betfinal -2))/((alphafinal + betfinal)*((alphafinal + betfinal -1)^2 -2))
PrUUinf <- (betfinal* ((1-betfinal)^2 - (1-alphafinal)^2 -1))/((alphafinal + betfinal)*((alphafinal + betfinal -1)^2 - 2))
opt.out <-cbind(opt.out, PrMMinf, PrUMinf, PrUUinf, alpha.start, beta.start, weight.start, intercept.start)
final[[s]]<- opt.out
} # End of Nstarts loop
final <- do.call("rbind", final)
colnames(final)[1:4]<-c("alpha", "beta", "weight", "intercept")
colnames(final)[13:15]<-c("PrMMinf", "PrUMinf", "PrUUinf")
##### Calculating the least square of the first part of the minimized function
lsqpart<-NULL
for (l in seq_len(NROW(final)))
{
PrMM <- p0mm
PrUM <- p0um
PrUU <- p0uu
alpha <- final[l, "alpha"]
bet <- final[l, "beta"]
weight <- final[l, "weight"]
intercept<-final[l,"intercept"]
## State probabilities at G0; first element = PrUU, second element = PrUM, third element = PrMM
svGzero <- c(PrUU, (weight)*PrMM, (1-weight)*PrMM)
## Defining the generation (or transition) matrix
Genmatrix <- matrix(c((1-alpha)^2, 2*(1-alpha)*alpha, alpha^2,
1/4*(bet + 1 - alpha)^2, 1/2*(bet + 1 - alpha)*(alpha + 1 - bet), 1/4*(alpha + 1 - bet)^2,
bet^2, 2*(1-bet)*bet, (1-bet)^2), nrow=3, byrow=TRUE)
## Calculating theoretical divergence for every observed pair in 'pedigree.txt'
Dt1t2<-NULL
for (p in seq_len(NROW(pedigree)))
{
## Define state vectors for t1,t2 and t0 from pedigree using matrix multiplications from library(expm)
svt0 <- t(svGzero) %*% ((Genmatrix)%^% as.numeric(pedigree[p,1]))
svt1.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
svt1.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
svt1.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
## Conditional divergences
dt1t2.MM <- 1/2*(svt1.MM[,1] * svt2.MM[,2] + svt1.MM[,2] * svt2.MM[,1] + svt1.MM[,2] * svt2.MM[,3] +
svt1.MM[,3] * svt2.MM[,2]) + 1*(svt1.MM[,1] * svt2.MM[,3] + svt1.MM[,3] * svt2.MM[,1])
dt1t2.UM <- 1/2*(svt1.UM[,1] * svt2.UM[,2] + svt1.UM[,2] * svt2.UM[,1] + svt1.UM[,2] * svt2.UM[,3] +
svt1.UM[,3] * svt2.UM[,2]) + 1*(svt1.UM[,1] * svt2.UM[,3] + svt1.UM[,3] * svt2.UM[,1])
dt1t2.UU <- 1/2*(svt1.UU[,1] * svt2.UU[,2] + svt1.UU[,2] * svt2.UU[,1] + svt1.UU[,2] * svt2.UU[,3] +
svt1.UU[,3] * svt2.UU[,2]) + 1*(svt1.UU[,1] * svt2.UU[,3] + svt1.UU[,3] * svt2.UU[,1])
## Total (weighted) divergence
Dt1t2[p]<- svt0[,1]*dt1t2.UU + svt0[,2]*dt1t2.UM + svt0[,3]*dt1t2.MM
}
## Calculating the least square part
lsqpart[l]<-sum((pedigree[,4] - intercept - Dt1t2)^2)
}
final<-cbind(final, lsqpart)
colnames(final)[ncol(final)]<-c("value.part")
final<-final[order(final[,"value"]),]
index.1<-which(final["alpha"] > 0 & final["beta"] > 0 & final["intercept"] > 0 & final[,"weight"] > 0, final["convcode"] == 0)
#index.1<-which(final["alpha"] > 0 & final["beta"] > 0 & final["intercept"] > 0)
index.2<-setdiff(seq_len(NROW(final)) , index.1)
final.1<-final[index.1,]
final.2<-final[index.2,]
##### Calculting the predicted values based on the 'best' model (i.e. that with the lowest least square)
#cat("Caution: Calculating predicted divergence based on lowest LSQ model: check the biology!", "\n")
PrMM <- p0mm
PrUM <- p0um
PrUU <- p0uu
alpha <- final.1[1, "alpha"]
bet <- final.1[1, "beta"]
weight <- final.1[1, "weight"]
intercept<-final.1[1,"intercept"]
## State probabilities at G0; first element = PrUU, second element = PrUM, third element = PrMM
svGzero <- c(PrUU, (weight)*PrMM, (1-weight)*PrMM)
## Defining the generation (or transition) matrix
Genmatrix <- matrix(c((1-alpha)^2, 2*(1-alpha)*alpha, alpha^2,
1/4*(bet + 1 - alpha)^2, 1/2*(bet + 1 - alpha)*(alpha + 1 - bet), 1/4*(alpha + 1 - bet)^2,
bet^2, 2*(1-bet)*bet, (1-bet)^2), nrow=3, byrow=TRUE)
## Calculating theoretical divergence for every observed pair in 'pedigree.txt'
Dt1t2<-NULL
Residual<-NULL
for (p in seq_len(NROW(pedigree)))
{
## Define state vectors for t1,t2 and t0 from pedigree using matrix multiplications from library(expm)
svt0 <- t(svGzero) %*% ((Genmatrix)%^% as.numeric(pedigree[p,1]))
svt1.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
svt1.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
svt1.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
## Conditional divergences
dt1t2.MM <- 1/2*(svt1.MM[,1] * svt2.MM[,2] + svt1.MM[,2] * svt2.MM[,1] + svt1.MM[,2] * svt2.MM[,3] +
svt1.MM[,3] * svt2.MM[,2]) + 1*(svt1.MM[,1] * svt2.MM[,3] + svt1.MM[,3] * svt2.MM[,1])
dt1t2.UM <- 1/2*(svt1.UM[,1] * svt2.UM[,2] + svt1.UM[,2] * svt2.UM[,1] + svt1.UM[,2] * svt2.UM[,3] +
svt1.UM[,3] * svt2.UM[,2]) + 1*(svt1.UM[,1] * svt2.UM[,3] + svt1.UM[,3] * svt2.UM[,1])
dt1t2.UU <- 1/2*(svt1.UU[,1] * svt2.UU[,2] + svt1.UU[,2] * svt2.UU[,1] + svt1.UU[,2] * svt2.UU[,3] +
svt1.UU[,3] * svt2.UU[,2]) + 1*(svt1.UU[,1] * svt2.UU[,3] + svt1.UU[,3] * svt2.UU[,1])
## Total (weighted) divergence
Dt1t2[p]<- svt0[,1]*dt1t2.UU + svt0[,2]*dt1t2.UM + svt0[,3]*dt1t2.MM
}
## Calculating the least square part
Residual<-(pedigree[,4] - intercept - Dt1t2)
##### Augmenting pedigree
delta.t<-pedigree[,2] + pedigree[,3] - 2*pedigree[,1]
#pedigree<-cbind(pedigree,delta.t)
pedigree<-cbind(pedigree, delta.t, Dt1t2 + intercept, Residual)
colnames(pedigree)[c(4,5,6,7)]<-c("div.obs", "delta.t","div.pred", "residual")
##### Making info about settings
info<-c("p0mm", "p0um", "p0uu", "eqp", "eqp.weight", "Nstarts", "optim.method")
info2<-c(p0mm, p0um, p0uu, eqp, eqp.weight, Nstarts, optim.method)
info.out<-data.frame(info, info2)
colnames(info.out)<-c("Para", "Setting")
###### Generating theoretical fit
## Reading in pedigree
obs<-pedigree[,"div.obs"]
dtime<-pedigree[,"delta.t"]
## Reading in parameter estimates
est <-final.1
alpha <-as.numeric(est[1,1])
beta<-as.numeric(est[1,2])
weight<-as.numeric(est[1,3])
intercept<-as.numeric(est[1,4])
## Reading initial state vector
settings<-info.out
PrMM<-p0mm<-as.numeric(as.character(settings[1,2]))
PrUM<-p0um<-as.numeric(as.character(settings[2,2]))
PrUU<-p0uu<-as.numeric(as.character(settings[3,2]))
time1<- seq(1,max(c(pedigree[,2], pedigree[,3])))
time2<- seq(1,max(c(pedigree[,2], pedigree[,3])))
time.out<-expand.grid(time1,time2)
#time0<- rep(min(pedigree[,1]), nrow(time.out))
time0<- rep(0, nrow(time.out))
pedigree.new<-as.matrix(cbind(time0,time.out))
pedigree.new<-cbind(pedigree.new, c(pedigree.new[,2] + pedigree.new[,3] - 2*pedigree.new[,1]))
pedigree.new<-pedigree.new[!duplicated(pedigree.new[,4]), ]
pedigree.new<-pedigree.new[,1:3]
## State probabilities at G0; first element = PrUU, second element = PrUM, third element = PrMM
svGzero <- c(PrUU, PrMM*weight, (1-weight)*PrMM)
alphafinal<-alpha
betfinal<-beta
interceptfinal<-intercept
## Defining the generation (or transition) matrix
Genmatrix <- matrix(c((1-alphafinal)^2, 2*(1-alphafinal)*alphafinal, alphafinal^2,
1/4*(betfinal + 1 - alphafinal)^2, 1/2*(betfinal + 1 - alphafinal)*(alphafinal + 1 - betfinal),
1/4*(alphafinal + 1 - betfinal)^2,
betfinal^2, 2*(1-betfinal)*betfinal, (1-betfinal)^2), nrow=3, byrow=TRUE)
## Calculating theoretical divergence for every observed pair in 'pedigree.txt'
Dt1t2<-NULL
for (p in seq_len(NROW(pedigree.new)))
{
## Define state vectors for t1,t2 and t0 from pedigree using matrix multiplications from library(expm)
svt0 <- t(svGzero) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,1]))
svt1.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,2] - pedigree.new[p,1]))
svt2.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,3] - pedigree.new[p,1]))
svt1.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,2] - pedigree.new[p,1]))
svt2.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,3] - pedigree.new[p,1]))
svt1.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,2] - pedigree.new[p,1]))
svt2.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,3] - pedigree.new[p,1]))
## Conditional divergences
dt1t2.MM <- 1/2*(svt1.MM[,1] * svt2.MM[,2] + svt1.MM[,2] * svt2.MM[,1] + svt1.MM[,2] * svt2.MM[,3] +
svt1.MM[,3] * svt2.MM[,2]) + 1*(svt1.MM[,1] * svt2.MM[,3] + svt1.MM[,3] * svt2.MM[,1])
dt1t2.UM <- 1/2*(svt1.UM[,1] * svt2.UM[,2] + svt1.UM[,2] * svt2.UM[,1] + svt1.UM[,2] * svt2.UM[,3] +
svt1.UM[,3] * svt2.UM[,2]) + 1*(svt1.UM[,1] * svt2.UM[,3] + svt1.UM[,3] * svt2.UM[,1])
dt1t2.UU <- 1/2*(svt1.UU[,1] * svt2.UU[,2] + svt1.UU[,2] * svt2.UU[,1] + svt1.UU[,2] * svt2.UU[,3] +
svt1.UU[,3] * svt2.UU[,2]) + 1*(svt1.UU[,1] * svt2.UU[,3] + svt1.UU[,3] * svt2.UU[,1])
## Total (weighted) divergence
Dt1t2[p]<- svt0[,1]*dt1t2.UU + svt0[,2]*dt1t2.UM + svt0[,3]*dt1t2.MM
}
pedigree.new<-cbind(pedigree.new, Dt1t2+interceptfinal, c(pedigree.new[,2] + pedigree.new[,3] - 2*pedigree.new[,1]))
colnames(pedigree.new)<-c("time0", "time1", "time2", "div.sim", "delta.t")
pedigree.new<-pedigree.new[order(pedigree.new[,5]),]
model<-"ABneutral.R"
abfree.out<-list(final.1, final.2, pedigree, info.out, model, pedigree.new)
names(abfree.out)<-c("estimates", "estimates.flagged", "pedigree", "settings", "model", "for.fit.plot")
## Ouputting result datasets
dput(abfree.out, paste0(out.dir,"/", out.name, ".Rdata", sep=""))
return(abfree.out)
} #End of function
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Defines functions ABneutral
Documented in ABneutral
#' Run Model with no selection (ABneutral)
#'
#' This model assumes that heritable gains and losses in cytosine methylation are selectively neutral.
#'
#' @param pedigree.data pedigree data.
#' @param p0uu initial proportion of unmethylated cytosines.
#' @param eqp equilibrium proportion of unmethylated cytosines.
#' @param eqp.weight weight assigned to equilibrium function.
#' @param Nstarts iterations for non linear LSQ optimization.
#' @param out.dir output directory.
#' @param out.name output file name.
#' @import optimx
#' @import expm
#' @importFrom stats runif
#' @return ABneutral RData file.
#' @export
#' @examples
#' #Get some toy data
#' inFile <- readRDS(system.file("extdata/dm/","output.rds", package="AlphaBeta"))
#' pedigree <- inFile$Pdata
#' p0uu_in <- inFile$tmpp0
#' eqp.weight <- 1
#' Nstarts <- 2
#' out.name <- "CG_global_estimates_ABneutral"
#' out <- ABneutral(pedigree.data = pedigree,
#' p0uu=p0uu_in,
#' eqp=p0uu_in,
#' eqp.weight=eqp.weight,
#' Nstarts=Nstarts,
#' out.dir=getwd(),
#' out.name=out.name)
#'
#' summary(out)
#'
ABneutral<-function(pedigree.data, p0uu, eqp, eqp.weight, Nstarts, out.dir, out.name)
{
##### Defining the divergence function
divergence <- function(pedigree, p0mm, p0um, p0uu, param)
{
## Initializing parameters
PrMM <- p0mm
PrUM <- p0um
PrUU <- p0uu
alpha <- param[1]
bet <- param[2]
weight <- param[3]
## State probabilities at G0; first element = PrUU, second element = PrUM, third element = PrMM
svGzero <- c(PrUU, (weight)*PrMM, (1-weight)*PrMM)
## Defining the generation (or transition) matrix
Genmatrix <- matrix(c((1-alpha)^2, 2*(1-alpha)*alpha, alpha^2,
1/4*(bet + 1 - alpha)^2, 1/2*(bet + 1 - alpha)*(alpha + 1 - bet), 1/4*(alpha + 1 - bet)^2,
bet^2, 2*(1-bet)*bet, (1-bet)^2), nrow=3, byrow=TRUE)
## Calculating theoretical divergence for every observed pair in 'pedigree.txt'
Dt1t2<-NULL
for (p in seq_len(NROW(pedigree)))
{
## Define state vectors for t1,t2 and t0 from pedigree using matrix multiplications from library(expm)
svt0 <- t(svGzero) %*% ((Genmatrix)%^% as.numeric(pedigree[p,1]))
svt1.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
svt1.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
svt1.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
## Conditional divergences
dt1t2.MM <- 1/2*(svt1.MM[,1] * svt2.MM[,2] + svt1.MM[,2] * svt2.MM[,1] + svt1.MM[,2] * svt2.MM[,3] +
svt1.MM[,3] * svt2.MM[,2]) + 1*(svt1.MM[,1] * svt2.MM[,3] + svt1.MM[,3] * svt2.MM[,1])
dt1t2.UM <- 1/2*(svt1.UM[,1] * svt2.UM[,2] + svt1.UM[,2] * svt2.UM[,1] + svt1.UM[,2] * svt2.UM[,3] +
svt1.UM[,3] * svt2.UM[,2]) + 1*(svt1.UM[,1] * svt2.UM[,3] + svt1.UM[,3] * svt2.UM[,1])
dt1t2.UU <- 1/2*(svt1.UU[,1] * svt2.UU[,2] + svt1.UU[,2] * svt2.UU[,1] + svt1.UU[,2] * svt2.UU[,3] +
svt1.UU[,3] * svt2.UU[,2]) + 1*(svt1.UU[,1] * svt2.UU[,3] + svt1.UU[,3] * svt2.UU[,1])
## Total (weighted) divergence
Dt1t2[p]<- svt0[,1]*dt1t2.UU + svt0[,2]*dt1t2.UM + svt0[,3]*dt1t2.MM
}
# Pr(UU) at equilibrium given alpha and beta
puuinf.est<- (bet* ((1-bet)^2 - (1-alpha)^2 -1))/((alpha + bet)*((alpha + bet -1)^2 - 2))
divout<-list(puuinf.est, Dt1t2)
return(divout)
}
###### Defining the Least Square function to be minimized
###### Note the equilibrium constraint, which can be made as small as desired.
LSE_intercept<-function(param_int)
{
sum((pedigree[,4] - param_int[4] - divergence(pedigree, p0mm, p0um, p0uu, param_int[1:3])[[2]])^2) +
eqp.weight*nrow(pedigree)*((divergence(pedigree, p0mm, p0um, p0uu, param_int[1:3])[[1]]- eqp)^2)
}
###### Calculating the initial proportions
###### We always assume that:
# 1. p0mm is larger than actually observed. This means if p0um is available from measurements,
# we will just add it to p0mm.
# 2. As a consequence of (1.) we also assume that p0um = 0.
p0uu<-p0uu
p0mm<-1-p0uu
p0um<-0
if(is.null(p0uu ==TRUE | is.null(eqp)==TRUE))
{stop("Both eqp value AND p0uu have to be supplied")}
if(sum(c(p0mm, p0um, p0uu), na.rm =TRUE) != 1)
{stop("The initial state probabilities don't sum to 1")}
##### Initializing
optim.method<-"Nelder-Mead"
final<-NULL
counter<-0
opt.out<-NULL
pedigree<-pedigree.data
for (s in seq_len(Nstarts))
{
## Draw random starting values
alpha.start <-10^(runif(1, log10(10^-9), log10(10^-2)))
beta.start <-10^(runif(1, log10(10^-9), log10(10^-2)))
weight.start <-runif(1,0,0.1)
intercept.start <-runif(1,0,max(pedigree[,4]))
param_int0 = c(alpha.start, beta.start, weight.start, intercept.start)
## Initializing
counter<-counter+1
message("Progress: ", counter/Nstarts, "\n")
opt.out <- suppressWarnings(optimx(par = param_int0, fn = LSE_intercept, method=optim.method))
alphafinal<-opt.out[1]
betfinal<-opt.out[2]
PrMMinf <- (alphafinal* ((1-alphafinal)^2 - (1-betfinal)^2 -1))/((alphafinal + betfinal)*((alphafinal + betfinal -1)^2 - 2))
PrUMinf <- (4*alphafinal*betfinal*(alphafinal + betfinal -2))/((alphafinal + betfinal)*((alphafinal + betfinal -1)^2 -2))
PrUUinf <- (betfinal* ((1-betfinal)^2 - (1-alphafinal)^2 -1))/((alphafinal + betfinal)*((alphafinal + betfinal -1)^2 - 2))
opt.out <-cbind(opt.out, PrMMinf, PrUMinf, PrUUinf, alpha.start, beta.start, weight.start, intercept.start)
final[[s]]<- opt.out
} # End of Nstarts loop
final <- do.call("rbind", final)
colnames(final)[1:4]<-c("alpha", "beta", "weight", "intercept")
colnames(final)[13:15]<-c("PrMMinf", "PrUMinf", "PrUUinf")
##### Calculating the least square of the first part of the minimized function
lsqpart<-NULL
for (l in seq_len(NROW(final)))
{
PrMM <- p0mm
PrUM <- p0um
PrUU <- p0uu
alpha <- final[l, "alpha"]
bet <- final[l, "beta"]
weight <- final[l, "weight"]
intercept<-final[l,"intercept"]
## State probabilities at G0; first element = PrUU, second element = PrUM, third element = PrMM
svGzero <- c(PrUU, (weight)*PrMM, (1-weight)*PrMM)
## Defining the generation (or transition) matrix
Genmatrix <- matrix(c((1-alpha)^2, 2*(1-alpha)*alpha, alpha^2,
1/4*(bet + 1 - alpha)^2, 1/2*(bet + 1 - alpha)*(alpha + 1 - bet), 1/4*(alpha + 1 - bet)^2,
bet^2, 2*(1-bet)*bet, (1-bet)^2), nrow=3, byrow=TRUE)
## Calculating theoretical divergence for every observed pair in 'pedigree.txt'
Dt1t2<-NULL
for (p in seq_len(NROW(pedigree)))
{
## Define state vectors for t1,t2 and t0 from pedigree using matrix multiplications from library(expm)
svt0 <- t(svGzero) %*% ((Genmatrix)%^% as.numeric(pedigree[p,1]))
svt1.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
svt1.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
svt1.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
## Conditional divergences
dt1t2.MM <- 1/2*(svt1.MM[,1] * svt2.MM[,2] + svt1.MM[,2] * svt2.MM[,1] + svt1.MM[,2] * svt2.MM[,3] +
svt1.MM[,3] * svt2.MM[,2]) + 1*(svt1.MM[,1] * svt2.MM[,3] + svt1.MM[,3] * svt2.MM[,1])
dt1t2.UM <- 1/2*(svt1.UM[,1] * svt2.UM[,2] + svt1.UM[,2] * svt2.UM[,1] + svt1.UM[,2] * svt2.UM[,3] +
svt1.UM[,3] * svt2.UM[,2]) + 1*(svt1.UM[,1] * svt2.UM[,3] + svt1.UM[,3] * svt2.UM[,1])
dt1t2.UU <- 1/2*(svt1.UU[,1] * svt2.UU[,2] + svt1.UU[,2] * svt2.UU[,1] + svt1.UU[,2] * svt2.UU[,3] +
svt1.UU[,3] * svt2.UU[,2]) + 1*(svt1.UU[,1] * svt2.UU[,3] + svt1.UU[,3] * svt2.UU[,1])
## Total (weighted) divergence
Dt1t2[p]<- svt0[,1]*dt1t2.UU + svt0[,2]*dt1t2.UM + svt0[,3]*dt1t2.MM
}
## Calculating the least square part
lsqpart[l]<-sum((pedigree[,4] - intercept - Dt1t2)^2)
}
final<-cbind(final, lsqpart)
colnames(final)[ncol(final)]<-c("value.part")
final<-final[order(final[,"value"]),]
index.1<-which(final["alpha"] > 0 & final["beta"] > 0 & final["intercept"] > 0 & final[,"weight"] > 0, final["convcode"] == 0)
#index.1<-which(final["alpha"] > 0 & final["beta"] > 0 & final["intercept"] > 0)
index.2<-setdiff(seq_len(NROW(final)) , index.1)
final.1<-final[index.1,]
final.2<-final[index.2,]
##### Calculting the predicted values based on the 'best' model (i.e. that with the lowest least square)
#cat("Caution: Calculating predicted divergence based on lowest LSQ model: check the biology!", "\n")
PrMM <- p0mm
PrUM <- p0um
PrUU <- p0uu
alpha <- final.1[1, "alpha"]
bet <- final.1[1, "beta"]
weight <- final.1[1, "weight"]
intercept<-final.1[1,"intercept"]
## State probabilities at G0; first element = PrUU, second element = PrUM, third element = PrMM
svGzero <- c(PrUU, (weight)*PrMM, (1-weight)*PrMM)
## Defining the generation (or transition) matrix
Genmatrix <- matrix(c((1-alpha)^2, 2*(1-alpha)*alpha, alpha^2,
1/4*(bet + 1 - alpha)^2, 1/2*(bet + 1 - alpha)*(alpha + 1 - bet), 1/4*(alpha + 1 - bet)^2,
bet^2, 2*(1-bet)*bet, (1-bet)^2), nrow=3, byrow=TRUE)
## Calculating theoretical divergence for every observed pair in 'pedigree.txt'
Dt1t2<-NULL
Residual<-NULL
for (p in seq_len(NROW(pedigree)))
{
## Define state vectors for t1,t2 and t0 from pedigree using matrix multiplications from library(expm)
svt0 <- t(svGzero) %*% ((Genmatrix)%^% as.numeric(pedigree[p,1]))
svt1.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
svt1.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
svt1.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,2] - pedigree[p,1]))
svt2.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree[p,3] - pedigree[p,1]))
## Conditional divergences
dt1t2.MM <- 1/2*(svt1.MM[,1] * svt2.MM[,2] + svt1.MM[,2] * svt2.MM[,1] + svt1.MM[,2] * svt2.MM[,3] +
svt1.MM[,3] * svt2.MM[,2]) + 1*(svt1.MM[,1] * svt2.MM[,3] + svt1.MM[,3] * svt2.MM[,1])
dt1t2.UM <- 1/2*(svt1.UM[,1] * svt2.UM[,2] + svt1.UM[,2] * svt2.UM[,1] + svt1.UM[,2] * svt2.UM[,3] +
svt1.UM[,3] * svt2.UM[,2]) + 1*(svt1.UM[,1] * svt2.UM[,3] + svt1.UM[,3] * svt2.UM[,1])
dt1t2.UU <- 1/2*(svt1.UU[,1] * svt2.UU[,2] + svt1.UU[,2] * svt2.UU[,1] + svt1.UU[,2] * svt2.UU[,3] +
svt1.UU[,3] * svt2.UU[,2]) + 1*(svt1.UU[,1] * svt2.UU[,3] + svt1.UU[,3] * svt2.UU[,1])
## Total (weighted) divergence
Dt1t2[p]<- svt0[,1]*dt1t2.UU + svt0[,2]*dt1t2.UM + svt0[,3]*dt1t2.MM
}
## Calculating the least square part
Residual<-(pedigree[,4] - intercept - Dt1t2)
##### Augmenting pedigree
delta.t<-pedigree[,2] + pedigree[,3] - 2*pedigree[,1]
#pedigree<-cbind(pedigree,delta.t)
pedigree<-cbind(pedigree, delta.t, Dt1t2 + intercept, Residual)
colnames(pedigree)[c(4,5,6,7)]<-c("div.obs", "delta.t","div.pred", "residual")
##### Making info about settings
info<-c("p0mm", "p0um", "p0uu", "eqp", "eqp.weight", "Nstarts", "optim.method")
info2<-c(p0mm, p0um, p0uu, eqp, eqp.weight, Nstarts, optim.method)
info.out<-data.frame(info, info2)
colnames(info.out)<-c("Para", "Setting")
###### Generating theoretical fit
## Reading in pedigree
obs<-pedigree[,"div.obs"]
dtime<-pedigree[,"delta.t"]
## Reading in parameter estimates
est <-final.1
alpha <-as.numeric(est[1,1])
beta<-as.numeric(est[1,2])
weight<-as.numeric(est[1,3])
intercept<-as.numeric(est[1,4])
## Reading initial state vector
settings<-info.out
PrMM<-p0mm<-as.numeric(as.character(settings[1,2]))
PrUM<-p0um<-as.numeric(as.character(settings[2,2]))
PrUU<-p0uu<-as.numeric(as.character(settings[3,2]))
time1<- seq(1,max(c(pedigree[,2], pedigree[,3])))
time2<- seq(1,max(c(pedigree[,2], pedigree[,3])))
time.out<-expand.grid(time1,time2)
#time0<- rep(min(pedigree[,1]), nrow(time.out))
time0<- rep(0, nrow(time.out))
pedigree.new<-as.matrix(cbind(time0,time.out))
pedigree.new<-cbind(pedigree.new, c(pedigree.new[,2] + pedigree.new[,3] - 2*pedigree.new[,1]))
pedigree.new<-pedigree.new[!duplicated(pedigree.new[,4]), ]
pedigree.new<-pedigree.new[,1:3]
## State probabilities at G0; first element = PrUU, second element = PrUM, third element = PrMM
svGzero <- c(PrUU, PrMM*weight, (1-weight)*PrMM)
alphafinal<-alpha
betfinal<-beta
interceptfinal<-intercept
## Defining the generation (or transition) matrix
Genmatrix <- matrix(c((1-alphafinal)^2, 2*(1-alphafinal)*alphafinal, alphafinal^2,
1/4*(betfinal + 1 - alphafinal)^2, 1/2*(betfinal + 1 - alphafinal)*(alphafinal + 1 - betfinal),
1/4*(alphafinal + 1 - betfinal)^2,
betfinal^2, 2*(1-betfinal)*betfinal, (1-betfinal)^2), nrow=3, byrow=TRUE)
## Calculating theoretical divergence for every observed pair in 'pedigree.txt'
Dt1t2<-NULL
for (p in seq_len(NROW(pedigree.new)))
{
## Define state vectors for t1,t2 and t0 from pedigree using matrix multiplications from library(expm)
svt0 <- t(svGzero) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,1]))
svt1.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,2] - pedigree.new[p,1]))
svt2.MM <- t(c(0,0,1)) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,3] - pedigree.new[p,1]))
svt1.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,2] - pedigree.new[p,1]))
svt2.UM <- t(c(0,1,0)) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,3] - pedigree.new[p,1]))
svt1.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,2] - pedigree.new[p,1]))
svt2.UU <- t(c(1,0,0)) %*% ((Genmatrix)%^% as.numeric(pedigree.new[p,3] - pedigree.new[p,1]))
## Conditional divergences
dt1t2.MM <- 1/2*(svt1.MM[,1] * svt2.MM[,2] + svt1.MM[,2] * svt2.MM[,1] + svt1.MM[,2] * svt2.MM[,3] +
svt1.MM[,3] * svt2.MM[,2]) + 1*(svt1.MM[,1] * svt2.MM[,3] + svt1.MM[,3] * svt2.MM[,1])
dt1t2.UM <- 1/2*(svt1.UM[,1] * svt2.UM[,2] + svt1.UM[,2] * svt2.UM[,1] + svt1.UM[,2] * svt2.UM[,3] +
svt1.UM[,3] * svt2.UM[,2]) + 1*(svt1.UM[,1] * svt2.UM[,3] + svt1.UM[,3] * svt2.UM[,1])
dt1t2.UU <- 1/2*(svt1.UU[,1] * svt2.UU[,2] + svt1.UU[,2] * svt2.UU[,1] + svt1.UU[,2] * svt2.UU[,3] +
svt1.UU[,3] * svt2.UU[,2]) + 1*(svt1.UU[,1] * svt2.UU[,3] + svt1.UU[,3] * svt2.UU[,1])
## Total (weighted) divergence
Dt1t2[p]<- svt0[,1]*dt1t2.UU + svt0[,2]*dt1t2.UM + svt0[,3]*dt1t2.MM
}
pedigree.new<-cbind(pedigree.new, Dt1t2+interceptfinal, c(pedigree.new[,2] + pedigree.new[,3] - 2*pedigree.new[,1]))
colnames(pedigree.new)<-c("time0", "time1", "time2", "div.sim", "delta.t")
pedigree.new<-pedigree.new[order(pedigree.new[,5]),]
model<-"ABneutral.R"
abfree.out<-list(final.1, final.2, pedigree, info.out, model, pedigree.new)
names(abfree.out)<-c("estimates", "estimates.flagged", "pedigree", "settings", "model", "for.fit.plot")
## Ouputting result datasets
dput(abfree.out, paste0(out.dir,"/", out.name, ".Rdata", sep=""))
return(abfree.out)
} #End of function
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