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## node.dating.R (2021-03-03)
## This file is part of the R-package `ape'.
## See the file COPYING in the package ape available at cran.r-project.org for licensing issues.
# Copyright (c) 2016, Bradley R. Jones, BC Centre for Excellence in HIV/AIDS
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
# * Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
# * Neither the name of the BC Centre for Excellence in HIV/AIDS nor the
# names of its contributors may be used to endorse or promote products
# derived from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
# DISCLAIMED. IN NO EVENT SHALL The BC Centre for Excellence in HIV/AIDS BE LIABLE FOR ANY
# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
# (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
# ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
# Estimate the mutation rate and node dates based on tip dates.
#
# Felsenstein, Joseph. "Evolutionary trees from DNA sequences: A maximum
# likelihood approach." Journal of Molecular Evolution 17 (1981):368-376.
#
# Rambaut, Andrew. "Estimating the rate of molecular evolution: incorporating
# non-contemporaneous sequences into maximum likelihood phylogenies."
# Bioinformatics 16.4 (2000): 395-399.
# Estimate the mutation rate of a phylogenetic tree from the tip dates using
# linear regression. This model assumes that the tree follows a molecular
# clock.
#
# t: rooted tree with edge lengths equal to genetic distance
#
# tip.dates: vector of dates for the tips, in the same order as t$tip.label.
# Tip dates can be censored with NA values
#
# p: p-value cutoff for failed regression (default=0.05)
#
# returns the mutation rate as a double
estimate.mu <- function(t, node.dates, p.tol=0.05) {
# fit linear model
g <- glm(node.depth.edgelength(t)[1:length(node.dates)] ~ node.dates, na.action=na.omit)
p <- anova(g, test="Chisq")[2,5]
# test fit
if (p > p.tol) {
warning(paste("Cannot reject null hypothesis (p=", p, ")"))
}
coef(g)[[2]]
}
# Estimate the dates of the internal nodes of a phylogenetic tree.
#
# t: rooted tree with edge lengths equal to genetic distance
#
# node.dates: either a vector of dates for the tips, in the same order as
# t$tip.label; or a vector of dates to initalize each node
#
# mu: mutation rate, either a vector of size one for a strict molecular clock
# or a vector with a local molecular clock along each edge
#
# min.date: the minimum date that a node can have (needed for optimize()). The
# default is -.Machine$double.xmax
#
# show.steps: set to print the log likelihood every show.steps. Set to 0 to
# supress output
#
# opt.tol: tolerance for optimization precision. By default, the optimize()
# function uses a tolerance of .Machine$double.eps^0.25 (see ?optimize)
#
# lik.tol: tolerance for likelihood comparison. estimate.dates will stop when
# the log likelihood between successive trees is less than like.tol. If
# 0 will stop after nsteps steps.
#
# nsteps: the maximum number of steps to run. If 0 will run until the log
# likelihood between successive runs is less than lik.tol. The default
# is 1000.
#
# is.binary: if the phylogentic tree is binary, setting is.binary to TRUE, will
# run a optimization method
#
# If lik.tol and nsteps are both 0 then estimate.dates will only run the inital
# step.
#
# returns a vector of the estimated dates of the tips and internal nodes
estimate.dates <- function(t, node.dates, mu = estimate.mu(t, node.dates), min.date = -.Machine$double.xmax, show.steps = 0, opt.tol = 1e-8, nsteps = 1000, lik.tol = 0, is.binary = is.binary.phylo(t)) {
# check parameters
if (any(mu < 0))
stop(paste("mu (", mu, ") less than 0", sep=""))
# init vars
mu <- if (length(mu) == 1) rep(mu, length(t$edge.length)) else mu
n.tips <- length(t$tip.label)
dates <- if (length(node.dates) == n.tips) {
c(node.dates, rep(NA, t$Nnode))
} else if (length(node.dates) == n.tips + t$Nnode) {
node.dates
} else {
stop(paste0("node.dates must be a vector with length equal to the number of tips or equal to the number of nodes plus the number of tips"))
}
lik.sens <- if (lik.tol == 0) opt.tol else lik.tol
# Don't count initial step if all values are seeded
iter.step <- if (any(is.na(dates))) 0 else 1
children <- lapply(1:t$Nnode,
function(x) {
which(t$edge[,1] == x + n.tips)
})
parent <- lapply(1:t$Nnode,
function(x) {
which(t$edge[,2] == x + n.tips)
})
# to process children before parents
nodes <- c(1)
for (i in 1:t$Nnode) {
to.add <- t$edge[children[[nodes[i]]], 2] - n.tips
nodes <- c(nodes, to.add[to.add > 0])
i <- i + 1
}
nodes <- rev(nodes)
# calculate likelihood functions
scale.lik <- sum(-lgamma(t$edge.length+1)+(t$edge.length+1)*log(mu))
calc.Like <- function(ch.node, ch.edge, x) {
tim <- ch.node - x
t$edge.length[ch.edge]*log(tim)-mu[ch.edge]*tim
}
opt.fun <- function(x, ch, p, ch.edge, p.edge, use.parent=T) {
sum(if (!use.parent || length(dates[p]) == 0 || is.na(dates[p])) {
calc.Like(dates[ch], ch.edge, x)
} else {
calc.Like(c(dates[ch], x), c(ch.edge, p.edge), c(rep(x, length(dates[ch])), dates[p]))
})
}
solve.lin <- function(bounds, ch.times, ch.edge) {
y <- (mu[ch.edge] * ch.times - t$edge.length[ch.edge]) / mu[ch.edge]
x <- c(bounds[1] + opt.tol, bounds[2] - opt.tol)
if (bounds[1] < y && y < bounds[2])
x <- c(x, y)
x[which.max(unlist(lapply(x, function(y) sum(calc.Like(ch.times, ch.edge, y)))))]
}
solve.poly2 <- function(bounds, a, b, c.0) {
x <- c(bounds[1] + opt.tol, bounds[2] - opt.tol)
if (b ^ 2 - 4 * a * c.0 >= 0) {
if (a == 0) {
y <- -c.0 / b
if (bounds[1] < y && y < bounds[2])
x <- c(x, y)
} else {
x.1 <- (-b + sqrt(b ^ 2 - 4 * a * c.0)) / (2 * a)
x.2 <- (-b - sqrt(b ^ 2 - 4 * a * c.0)) / (2 * a)
if (bounds[1] < x.1 && x.1 < bounds[2])
x <- c(x, x.1)
if (bounds[1] < x.2 && x.2 < bounds[2])
x <- c(x, x.2)
}
}
x
}
solve.bin <- function(bounds, ch.times, ch.edge) {
ch.edge.length <- t$edge.length[ch.edge]
a <- sum(mu[ch.edge])
b <- ch.edge.length[1] + ch.edge.length[2] - a * (ch.times[1] + ch.times[2])
c.0 <- a*ch.times[1] * ch.times[2] - ch.times[1] * ch.edge.length[2] - ch.times[2] * ch.edge.length[1]
x <- solve.poly2(bounds, a, b, c.0)
x[which.max(unlist(lapply(x, function(y) sum(calc.Like(ch.times, ch.edge, y)))))]
}
solve.bin2 <- function(bounds, ch.times, ch.edge, par.time, par.edge) {
ch.edge.length <- t$edge.length[ch.edge]
par.edge.length <- t$edge.length[par.edge]
a <- mu[ch.edge] - mu[par.edge]
b <- ch.edge.length + par.edge.length - a * (ch.times + par.time)
c.0 <- a*ch.times * par.time - ch.times * par.edge.length - par.time * ch.edge.length
cat(sprintf("a: %f, b: %f, c: %f\n", a, b, c.0))
x <- solve.poly2(bounds, a, b, c.0)
x[which.max(unlist(lapply(x, function(y) sum(calc.Like(c(ch.times, y), c(ch.edge, par.edge), c(y, par.time))))))]
}
solve.poly3 <- function(bounds, a, b, c.0, d) {
x <- c(bounds[1] + opt.tol, bounds[2] - opt.tol)
if (a == 0)
x <- c(x, solve.poly2(bounds, b, c.0, d))
else {
delta.0 <- complex(real=b^2 - 3 * a * c.0)
delta.1 <- complex(real=2 * b^3 - 9 * a * b * c.0 + 27 * a^2 * d)
C <- ((delta.1 + sqrt(delta.1^2 - 4 * delta.0^3)) / 2)^(1/3)
x.1 <- Re(-1 / (3 * a) * (b + complex(real=1) * C + delta.0 / (complex(real=1) * C)))
x.2 <- Re(-1 / (3 * a) * (b + complex(real=-1/2, imaginary=sqrt(3)/2) * C + delta.0 / (complex(real=-1/2, imaginary=sqrt(3)/2) * C)))
x.3 <- Re(-1 / (3 * a) * (b + complex(real=-1/2, imaginary=-sqrt(3)/2) * C + delta.0 / (complex(real=-1/2, imaginary=-sqrt(3)/2) * C)))
if (bounds[1] < x.1 && x.1 < bounds[2])
x <- c(x, x.1)
if (bounds[1] < x.2 && x.2 < bounds[2])
x <- c(x, x.2)
if (bounds[1] < x.3 && x.3 < bounds[2])
x <- c(x, x.3)
}
x
}
solve.cube <- function(bounds, ch.times, ch.edge, par.time, par.edge) {
ch.edge.length <- t$edge.length[ch.edge]
par.edge.length <- t$edge.length[par.edge]
a <- sum(mu[ch.edge]) - mu[par.edge]
b <- sum(ch.edge.length) + par.edge.length - a * (sum(ch.times) + par.time)
c.0 <- a * (ch.times[1] * ch.times[2] + ch.times[1] * par.time + ch.times[2] * par.time) - (ch.times[1] + ch.times[2]) * par.edge.length - (ch.times[1] + par.time) * ch.edge.length[2] - (ch.times[2] + par.time) * ch.edge.length[1]
d <- ch.edge.length[1] * ch.times[2] * par.time + ch.edge.length[2] * ch.times[1] * par.time + par.edge.length * ch.times[1] * ch.times[2] - a * prod(ch.times) * par.time
x <- solve.poly3(bounds, a, b, c.0, d)
x[which.max(unlist(lapply(x, function(y) sum(calc.Like(c(ch.times, y), c(ch.edge, par.edge), c(y, y, par.time))))))]
}
estimate <- function(node) {
ch.edge <- children[[node]]
ch <- t$edge[ch.edge, 2]
p.edge <- parent[[node]]
p <- t$edge[p.edge, 1]
m <- if (length(p) == 0 || is.na(dates[p])) {
min.date
} else {
dates[p]
}
if (is.binary) {
if (m + 2 * opt.tol >= min(dates[ch])) {
mean(c(m, min(dates[ch])))
} else if (length(dates[p]) == 0 || is.na(dates[p])) {
if (length(ch.edge) == 2)
solve.bin(c(m, min(dates[ch])), dates[ch], ch.edge)
else
solve.lin(c(m, min(dates[ch])), dates[ch], ch.edge)
} else {
if (length(ch.edge) == 2)
solve.cube(c(m, min(dates[ch])), dates[ch], ch.edge, dates[p], p.edge)
else
solve.bin2(c(m, min(dates[ch])), dates[ch], ch.edge, dates[p], p.edge)
}
} else {
res <- suppressWarnings(optimize(opt.fun, c(m, min(dates[ch])), ch, p, ch.edge, p.edge, maximum=T))
res$maximum
}
}
# iterate to estimate dates
lik <- NA
repeat
{
for (n in nodes) {
dates[n + n.tips] <- estimate(n)
}
all.lik <- calc.Like(dates[t$edge[,2]], 1:length(t$edge.length), dates[t$edge[,1]]) + scale.lik
new.lik <- sum(all.lik)
if (show.steps > 0 && ((iter.step %% show.steps) == 0)) {
cat(paste("Step: ", iter.step, ", Likelihood: ", new.lik, "\n", sep=""))
}
if ((lik.tol > 0 && (!is.na(lik) && (is.infinite(lik) || is.infinite(new.lik) || new.lik - lik < lik.tol))) || (nsteps > 0 && iter.step >= nsteps) || (lik.tol <= 0 && nsteps <= 0)) {
if (is.infinite(lik) || is.infinite(new.lik)) {
warning("Likelihood infinite")
}
else if (!is.na(lik) && new.lik + lik.sens < lik) {
warning("Likelihood less than previous estimate")
}
break
} else {
lik <- new.lik
}
iter.step <- iter.step + 1
}
if (show.steps > 0) {
cat(paste("Step: ", iter.step, ", Likelihood: ", new.lik, "\n", sep=""))
}
dates
}
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