dbd {ape}  R Documentation 
These functions compute the probability density under some birth–death models, that is the probability of obtaining x species after a time t giving how speciation and extinction probabilities vary through time (these may be constant, or even equal to zero for extinction).
dyule(x, lambda = 0.1, t = 1, log = FALSE) dbd(x, lambda, mu, t, conditional = FALSE, log = FALSE) dbdTime(x, birth, death, t, conditional = FALSE, BIRTH = NULL, DEATH = NULL, fast = FALSE)
x 
a numeric vector of species numbers (see Details). 
lambda 
a numerical value giving the probability of speciation;
can be a vector with several values for 
mu 
id. for extinction. 
t 
id. for the time(s). 
log 
a logical value specifying whether the probabilities should
be returned logtransformed; the default is 
conditional 
a logical specifying whether the probabilities
should be computed conditional under the assumption of no extinction
after time 
birth, death 
a (vectorized) function specifying how the
speciation or extinction probability changes through time (see

BIRTH, DEATH 
a (vectorized) function giving the primitive
of 
fast 
a logical value specifying whether to use faster
integration (see 
These three functions compute the probabilities to observe x
species starting from a single one after time t
(assumed to be
continuous). The first function is a shortcut for the second one with
mu = 0
and with default values for the two other arguments.
dbdTime
is for timevarying lambda
and mu
specified as R functions.
dyule
is vectorized simultaneously on its three arguments
x
, lambda
, and t
, according to R's rules of
recycling arguments. dbd
is vectorized simultaneously x
and t
(to make likelihood calculations easy), and
dbdTime
is vectorized only on x
; the other arguments are
eventually shortened with a warning if necessary.
The returned value is, logically, zero for values of x
out of
range, i.e., negative or zero for dyule
or if conditional
= TRUE
. However, it is not checked if the values of x
are
positive nonintegers and the probabilities are computed and returned.
The details on the form of the arguments birth
, death
,
BIRTH
, DEATH
, and fast
can be found in the links
below.
a numeric vector.
If you use these functions to calculate a likelihood function, it is
strongly recommended to compute the loglikelihood with, for instance
in the case of a Yule process, sum(dyule( , log = TRUE))
(see
examples).
Emmanuel Paradis
Kendall, D. G. (1948) On the generalized “birthanddeath” process. Annals of Mathematical Statistics, 19, 1–15.
x < 0:10 plot(x, dyule(x), type = "h", main = "Density of the Yule process") text(7, 0.85, expression(list(lambda == 0.1, t == 1))) y < dbd(x, 0.1, 0.05, 10) z < dbd(x, 0.1, 0.05, 10, conditional = TRUE) d < rbind(y, z) colnames(d) < x barplot(d, beside = TRUE, ylab = "Density", xlab = "Number of species", legend = c("unconditional", "conditional on\nno extinction"), args.legend = list(bty = "n")) title("Density of the birthdeath process") text(17, 0.4, expression(list(lambda == 0.1, mu == 0.05, t == 10))) ## Not run: ### generate 1000 values from a Yule process with lambda = 0.05 x < replicate(1e3, Ntip(rlineage(0.05, 0))) ### the correct way to calculate the loglikelihood...: sum(dyule(x, 0.05, 50, log = TRUE)) ### ... and the wrong way: log(prod(dyule(x, 0.05, 50))) ### a third, less preferred, way: sum(log(dyule(x, 0.05, 50))) ## End(Not run)