1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
|
\name{LTT}
\alias{LTT}
\title{Theoretical Lineage-Through Time Plots}
\description{
This function draws the lineage-through time (LTT) plots predicted
under a speciation-extinction model (aka birth-death model) with
specified values of speciation and extinction rates (which may vary
with time).
A prediction interval is plotted by default which requires to define a
sample size (100 by default), and different curves can be combined.
}
\usage{
LTT(birth = 0.1, death = 0, N = 100, Tmax = 50, PI = 95,
scaled = TRUE, eps = 0.1, add = FALSE, backward = TRUE,
ltt.style = list("black", 1, 1), pi.style = list("blue", 1, 2), ...)
}
\arguments{
\item{birth}{the speciation rate, this may be either a numeric value
or a funtion of time (named \code{t} in the code of the function).}
\item{death}{id. for the extinction rate.}
\item{N}{the size of the tree.}
\item{Tmax}{the age of the root of the tree.}
\item{PI}{the percentage value of the prediction interval; set this
value to 0 to not draw this interval.}
\item{scaled}{a logical values specifying whether to scale the
\eqn{y}-axis between 0 and 1.}
\item{eps}{a numerical value giving the resolution of the time axis.}
\item{add}{a logical values specifying whether to make a new plot (the
default).}
\item{backward}{a logical value: should the time axis be traced from
the present (the default), or from the root of the tree?}
\item{ltt.style}{a list with three elements giving the style of the
LTT curve with, respectively, the colour (\code{"col"}), the line
thickness (\code{"lwd"}), and the line type (\code{"lty"}).}
\item{pi.style}{id. for the prediction interval.}
\item{\dots}{arguments passed to \code{plot} (e.g., \code{log="y"}).}
}
\details{
For the moment, this works well when \code{birth} and \code{death} are
constant. Some improvements are under progress for time-dependent
rates (but see below for an example).
}
\references{
Hallinan, N. (2012) The generalized time variable reconstructed
birth--death process. \emph{Journal of Theoretical Biology},
\bold{300}, 265--276.
Paradis, E. (2011) Time-dependent speciation and extinction from
phylogenies: a least squares approach. \emph{Evolution}, \bold{65},
661--672.
Paradis, E. (2015) Random phylogenies and the distribution of
branching times. \emph{Journal of Theoretical Biology}, \bold{387},
39--45.
}
\author{Emmanuel Paradis}
\seealso{
\code{\link{ltt.plot}}
}
\examples{
### predicted LTT plot under a Yule model with lambda = 0.1
### and 50 species after 50 units of time...
LTT(N = 50)
### ... and with a birth-death model with the same rate of
### diversification (try with N = 500):
LTT(0.2, 0.1, N = 50, PI = 0, add = TRUE, ltt.style = list("red", 2, 1))
### predictions under different tree sizes:
layout(matrix(1:4, 2, 2, byrow = TRUE))
for (N in c(50, 100, 500, 1000)) {
LTT(0.2, 0.1, N = N)
title(paste("N =", N))
}
layout(1)
\dontrun{
### speciation rate decreasing with time
birth.logis <- function(t) 1/(1 + exp(0.02 * t + 4))
LTT(birth.logis)
LTT(birth.logis, 0.05)
LTT(birth.logis, 0.1)
}
}
\keyword{hplot}
|
