## birthdeath.R (2010-11-04)
## Estimation of Speciation and Extinction Rates
## with Birth-Death Models
## birthdeath: standard model
## bd.ext: extended version
## Copyright 2002-2010 Emmanuel Paradis
## This file is part of the R-package `ape'.
## See the file ../COPYING for licensing issues.
birthdeath <- function(phy)
{
if (!inherits(phy, "phylo")) stop('object "phy" is not of class "phylo"')
N <- length(phy$tip.label)
x <- c(NA, branching.times(phy))
dev <- function(a, r) {
if (r <= 0) return(1e50)
-2 * (lfactorial(N - 1)
+ (N - 2) * log(r)
+ r * sum(x[3:N])
+ N * log(1 - a)
- 2 * sum(log(exp(r * x[2:N]) - a)))
}
out <- nlm(function(p) dev(p[1], p[2]), c(0.1, 0.2), hessian = TRUE)
if (out$estimate[1] < 0) {
out <- nlm(function(p) dev(0, p), 0.2, hessian = TRUE)
para <- c(0, out$estimate)
se <- c(0, sqrt(diag(solve(out$hessian))))
}
else {
para <- out$estimate
se <- sqrt(diag(solve(out$hessian)))
}
Dev <- out$minimum
## compute the 95 % profile likelihood CIs
## (not very clean... but seems to work -- EP 2003-03-29)
CI <- matrix(NA, 2, 2)
foo <- function(p) dev(p, para[2]) - 3.84 - Dev
inc <- 1e-2
lo <- para[1] - inc
up <- para[1] + inc
while (foo(lo) < 0) lo <- lo - inc
while (foo(up) < 0) up <- up + inc
CI[1, 1] <- uniroot(foo, lower = lo, upper = para[1])$root
if (CI[1, 1] < 0) CI[1, 1] <- 0
CI[1, 2] <- uniroot(foo, lower = para[1], upper = up)$root
foo <- function(p) dev(para[1], p) - 3.84 - Dev
lo <- para[2] - inc
up <- para[2] + inc
while (foo(lo) < 0) lo <- lo - inc
while (foo(up) < 0) up <- up + inc
CI[2, 1] <- uniroot(foo, lower = lo, upper = para[2])$root
CI[2, 2] <- uniroot(foo, lower = para[2], upper = up)$root
names(para) <- names(se) <- rownames(CI) <- c("d/b", "b-d")
colnames(CI) <- c("lo", "up")
obj <- list(tree = deparse(substitute(phy)), N = N,
dev = Dev, para = para, se = se, CI = CI)
class(obj) <- "birthdeath"
obj
}
print.birthdeath <- function(x, ...)
{
cat("\nEstimation of Speciation and Extinction Rates\n")
cat(" with Birth-Death Models\n\n")
cat(" Phylogenetic tree:", x$tree, "\n")
cat(" Number of tips:", x$N, "\n")
cat(" Deviance:", x$dev, "\n")
cat(" Log-likelihood:", -(x$dev)/2, "\n")
cat(" Parameter estimates:\n")
cat(" d / b =", x$para[1], " StdErr =", x$se[1], "\n")
cat(" b - d =", x$para[2], " StdErr =", x$se[2], "\n")
cat(" (b: speciation rate, d: extinction rate)\n")
cat(" Profile likelihood 95% confidence intervals:\n")
cat(" d / b: [", x$CI[1, 1], ", ", x$CI[1, 2], "]", "\n", sep = "")
cat(" b - d: [", x$CI[2, 1], ", ", x$CI[2, 2], "]", "\n\n", sep = "")
}
bd.ext <- function(phy, S, conditional = TRUE)
{
if (!inherits(phy, "phylo"))
stop('object "phy" is not of class "phylo"')
if (!is.null(names(S))) {
if (all(names(S) %in% phy$tip.label)) S <- S[phy$tip.label]
else warning('the names of argument "S" and the tip labels
did not match: the former were ignored.')
}
N <- length(S)
x <- branching.times(phy)
x <- c(x[1], x)
trm.br <- phy$edge.length[phy$edge[, 2] <= N]
if (conditional) {
dev <- function(a, r) {
if (a >= 1 || a < 0 || r <= 0) return(1e50)
ert <- exp(r * trm.br)
zeta <- (ert - 1)/(ert - a)
-2 * (lfactorial(N - 1)
+ (N - 2) * log(r)
+ N * log(1 - a)
+ 2 * r * sum(x[2:N])
- 2 * sum(log(exp(r * x[2:N]) - a))
+ sum(log(1 - zeta) + (S - 1)*log(zeta)))
}
} else {
dev <- function(a, r) {
if (a >= 1 || a < 0 || r <= 0) return(1e50)
-2 * (lfactorial(N - 1)
+ (N - 2) * log(r)
+ (3 * N) * log(1 - a)
+ 2 * r * sum(x[2:N])
- 2 * sum(log(exp(r * x[2:N]) - a))
+ r * sum(trm.br)
+ sum((S - 1) * log(exp(r * trm.br) - 1))
- sum((S + 1) * log(exp(r * trm.br) - a)))
}
}
out <- nlm(function(p) dev(p[1], p[2]), c(0.1, 0.2), hessian = TRUE)
para <- out$estimate
se <- sqrt(diag(solve(out$hessian)))
Dev <- out$minimum
cat("\nExtended Version of the Birth-Death Models to\n")
cat(" Estimate Speciation and Extinction Rates\n\n")
cat(" Data: phylogenetic:", deparse(substitute(phy)), "\n")
cat(" taxonomic:", deparse(substitute(S)), "\n")
cat(" Number of tips:", N, "\n")
cat(" Deviance:", Dev, "\n")
cat(" Log-likelihood:", -Dev/2, "\n")
cat(" Parameter estimates:\n")
cat(" d / b =", para[1], " StdErr =", se[1], "\n")
cat(" b - d =", para[2], " StdErr =", se[2], "\n")
cat(" (b: speciation rate, d: extinction rate)\n")
}
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