1 ## birthdeath.R (2010-11-04)
3 ## Estimation of Speciation and Extinction Rates
4 ## with Birth-Death Models
6 ## birthdeath: standard model
7 ## bd.ext: extended version
9 ## Copyright 2002-2010 Emmanuel Paradis
11 ## This file is part of the R-package `ape'.
12 ## See the file ../COPYING for licensing issues.
14 birthdeath <- function(phy)
16 if (!inherits(phy, "phylo")) stop('object "phy" is not of class "phylo"')
17 N <- length(phy$tip.label)
18 x <- c(NA, branching.times(phy))
19 dev <- function(a, r) {
20 if (r <= 0) return(1e50)
21 -2 * (lfactorial(N - 1)
25 - 2 * sum(log(exp(r * x[2:N]) - a)))
27 out <- nlm(function(p) dev(p[1], p[2]), c(0.1, 0.2), hessian = TRUE)
28 if (out$estimate[1] < 0) {
29 out <- nlm(function(p) dev(0, p), 0.2, hessian = TRUE)
30 para <- c(0, out$estimate)
31 se <- c(0, sqrt(diag(solve(out$hessian))))
35 se <- sqrt(diag(solve(out$hessian)))
38 ## compute the 95 % profile likelihood CIs
39 ## (not very clean... but seems to work -- EP 2003-03-29)
40 CI <- matrix(NA, 2, 2)
41 foo <- function(p) dev(p, para[2]) - 3.84 - Dev
45 while (foo(lo) < 0) lo <- lo - inc
46 while (foo(up) < 0) up <- up + inc
47 CI[1, 1] <- uniroot(foo, lower = lo, upper = para[1])$root
48 if (CI[1, 1] < 0) CI[1, 1] <- 0
49 CI[1, 2] <- uniroot(foo, lower = para[1], upper = up)$root
50 foo <- function(p) dev(para[1], p) - 3.84 - Dev
53 while (foo(lo) < 0) lo <- lo - inc
54 while (foo(up) < 0) up <- up + inc
55 CI[2, 1] <- uniroot(foo, lower = lo, upper = para[2])$root
56 CI[2, 2] <- uniroot(foo, lower = para[2], upper = up)$root
57 names(para) <- names(se) <- rownames(CI) <- c("d/b", "b-d")
58 colnames(CI) <- c("lo", "up")
59 obj <- list(tree = deparse(substitute(phy)), N = N,
60 dev = Dev, para = para, se = se, CI = CI)
61 class(obj) <- "birthdeath"
65 print.birthdeath <- function(x, ...)
67 cat("\nEstimation of Speciation and Extinction Rates\n")
68 cat(" with Birth-Death Models\n\n")
69 cat(" Phylogenetic tree:", x$tree, "\n")
70 cat(" Number of tips:", x$N, "\n")
71 cat(" Deviance:", x$dev, "\n")
72 cat(" Log-likelihood:", -(x$dev)/2, "\n")
73 cat(" Parameter estimates:\n")
74 cat(" d / b =", x$para[1], " StdErr =", x$se[1], "\n")
75 cat(" b - d =", x$para[2], " StdErr =", x$se[2], "\n")
76 cat(" (b: speciation rate, d: extinction rate)\n")
77 cat(" Profile likelihood 95% confidence intervals:\n")
78 cat(" d / b: [", x$CI[1, 1], ", ", x$CI[1, 2], "]", "\n", sep = "")
79 cat(" b - d: [", x$CI[2, 1], ", ", x$CI[2, 2], "]", "\n\n", sep = "")
82 bd.ext <- function(phy, S, conditional = TRUE)
84 if (!inherits(phy, "phylo"))
85 stop('object "phy" is not of class "phylo"')
86 if (!is.null(names(S))) {
87 if (all(names(S) %in% phy$tip.label)) S <- S[phy$tip.label]
88 else warning('the names of argument "S" and the tip labels
89 did not match: the former were ignored.')
92 x <- branching.times(phy)
94 trm.br <- phy$edge.length[phy$edge[, 2] <= N]
96 dev <- function(a, r) {
97 if (a >= 1 || a < 0 || r <= 0) return(1e50)
98 ert <- exp(r * trm.br)
99 zeta <- (ert - 1)/(ert - a)
100 -2 * (lfactorial(N - 1)
103 + 2 * r * sum(x[2:N])
104 - 2 * sum(log(exp(r * x[2:N]) - a))
105 + sum(log(1 - zeta) + (S - 1)*log(zeta)))
108 dev <- function(a, r) {
109 if (a >= 1 || a < 0 || r <= 0) return(1e50)
110 -2 * (lfactorial(N - 1)
112 + (3 * N) * log(1 - a)
113 + 2 * r * sum(x[2:N])
114 - 2 * sum(log(exp(r * x[2:N]) - a))
116 + sum((S - 1) * log(exp(r * trm.br) - 1))
117 - sum((S + 1) * log(exp(r * trm.br) - a)))
120 out <- nlm(function(p) dev(p[1], p[2]), c(0.1, 0.2), hessian = TRUE)
122 se <- sqrt(diag(solve(out$hessian)))
124 cat("\nExtended Version of the Birth-Death Models to\n")
125 cat(" Estimate Speciation and Extinction Rates\n\n")
126 cat(" Data: phylogenetic:", deparse(substitute(phy)), "\n")
127 cat(" taxonomic:", deparse(substitute(S)), "\n")
128 cat(" Number of tips:", N, "\n")
129 cat(" Deviance:", Dev, "\n")
130 cat(" Log-likelihood:", -Dev/2, "\n")
131 cat(" Parameter estimates:\n")
132 cat(" d / b =", para[1], " StdErr =", se[1], "\n")
133 cat(" b - d =", para[2], " StdErr =", se[2], "\n")
134 cat(" (b: speciation rate, d: extinction rate)\n")