# bd.time

##### Time-Dependent Birth-Death Models

This function fits a used-defined time-dependent birth-death model.

##### Usage

```
bd.time(phy, birth, death, BIRTH = NULL, DEATH = NULL,
ip, lower, upper, fast = FALSE, boot = 0, trace = 0)
```

##### Details

Details on how to specify the birth and death functions and their
primitives can be found in the help page of `yule.time`

.

The model is fitted by minimizing the least squares deviation between
the observed and the predicted distributions of branching times. These
computations rely heavily on numerical integrations. If ```
fast =
FALSE
```

, integrations are done with R's `integrate`

function. If `fast = TRUE`

, a faster but less accurate function
provided in `fast = FALSE`

.

##### Value

A list with the following components:

- par

`nlminb`

.##### References

Paradis, E. (2011) Time-dependent speciation and extinction from
phylogenies: a least squares approach. *Evolution*, **65**,
661--672.

##### See Also

##### Examples

```
set.seed(3)
tr <- rbdtree(0.1, 0.02)
bd.time(tr, 0, 0) # fits a simple BD model
bd.time(tr, 0, 0, ip = c(.1, .01)) # 'ip' is useful here
## the classic logistic:
birth.logis <- function(a, b) 1/(1 + exp(-a*t - b))
bd.time(tr, birth.logis, 0, ip = c(0, -2, 0.01))
## slow to get:
## $par
## a b death
## -0.003486961 -1.995983179 0.016496454
##
## $SS
## [1] 20.73023
```

*Documentation reproduced from package ape, version 3.0-2, License: GPL (>= 2)*