Tree Simulation Under the Time-Dependent Birth–Death Models
These three functions simulate phylogenies under any time-dependent
birth–death model: rlineage generates a complete tree including
the species going extinct before present; rbdtree generates a
tree with only the species living at present (thus the tree is
ultrametric); rphylo generates a tree with a fixed number of
species at present time. drop.fossil is a utility function to
remove the extinct species.
rlineage(birth, death, Tmax = 50, BIRTH = NULL,
DEATH = NULL, eps = 1e-6)
rbdtree(birth, death, Tmax = 50, BIRTH = NULL,
DEATH = NULL, eps = 1e-6)
rphylo(n, birth, death, BIRTH = NULL, DEATH = NULL,
T0 = 50, fossils = FALSE, eps = 1e-06)
drop.fossil(phy, tol = 1e-8)birth, death |
a numeric value or a (vectorized) function specifying how speciation and extinction rates vary through time. |
Tmax |
a numeric value giving the length of the simulation. |
BIRTH, DEATH |
a (vectorized) function which is the primitive
of |
eps |
a numeric value giving the time resolution of the simulation; this may be increased (e.g., 0.001) to shorten computation times. |
n |
the number of species living at present time. |
T0 |
the time at present (for the backward-in-time algorithm). |
fossils |
a logical value specifying whether to output the lineages going extinct. |
phy |
an object of class |
tol |
a numeric value giving the tolerance to consider a species as extinct. |
These three functions use continuous-time algorithms: rlineage
and rbdtree use the forward-in-time algorithms described in
Paradis (2011), whereas rphylo uses a backward-in-time
algorithm from Stadler (2011). The models are time-dependent
birth–death models as described in Kendall (1948). Speciation
(birth) and extinction (death) rates may be constant or vary through
time according to an R function specified by the user. In the latter
case, BIRTH and/or DEATH may be used if the primitives
of birth and death are known. In these functions time is
the formal argument and must be named t.
Note that rphylo simulates trees in a way similar to what
the package TreeSim does, the difference is in the
parameterization of the time-dependent models which is here the same
than used in the two other functions. In this parameterization scheme,
time is measured from past to present (see details in Paradis 2015
which includes a comparison of these algorithms).
The difference between rphylo and rphylo(... fossils
= TRUE) is the same than between rbdtree and rlineage.
An object of class "phylo".
Emmanuel Paradis
Kendall, D. G. (1948) On the generalized “birth-and-death” process. Annals of Mathematical Statistics, 19, 1–15.
Paradis, E. (2011) Time-dependent speciation and extinction from phylogenies: a least squares approach. Evolution, 65, 661–672.
Paradis, E. (2015) Random phylogenies and the distribution of branching times. Journal of Theoretical Biology, 387, 39–45.
Stadler, T. (2011) Simulating trees with a fixed number of extant species. Systematic Biology, 60, 676–684.
set.seed(10)
plot(rlineage(0.1, 0)) # Yule process with lambda = 0.1
plot(rlineage(0.1, 0.05)) # simple birth-death process
b <- function(t) 1/(1 + exp(0.2*t - 1)) # logistic
layout(matrix(0:3, 2, byrow = TRUE))
curve(b, 0, 50, xlab = "Time", ylab = "")
mu <- 0.07
segments(0, mu, 50, mu, lty = 2)
legend("topright", c(expression(lambda), expression(mu)),
lty = 1:2, bty = "n")
plot(rlineage(b, mu), show.tip.label = FALSE)
title("Simulated with 'rlineage'")
plot(rbdtree(b, mu), show.tip.label = FALSE)
title("Simulated with 'rbdtree'")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.