# birthdeath

##### Estimation of Speciation and Extinction Rates With Birth-Death Models

This function fits by maximum likelihood a birth-death model to the branching times computed from a phylogenetic tree using the method of Nee et al. (1994).

- Keywords
- models

##### Usage

```
birthdeath(phy)
## S3 method for class 'birthdeath':
print(x, ...)
```

##### Arguments

- phy
- an object of class
`"phylo"`

. - x
- an object of class
`"birthdeath"`

. - ...
- further arguments passed to the
`print`

function.

##### Details

Nee et al. (1994) used a re-parametrization of the birth-death model
studied by Kendall (1948) so that the likelihood has to be maximized
over *d/b* and *b - d*, where *b* is the birth rate,
and *d* the death rate. This is the approach used by the present
function.

This function computes the standard-errors of the estimated parameters
using a normal approximations of the maximum likelihood estimates:
this is likely to be inaccurate because of asymmetries of the
likelihood function (Nee et al. 1995). In addition, 95 intervals of both parameters are computed using profile likelihood:
they are particularly useful if the estimate of *d/b* is at the
boundary of the parameter space (i.e. 0, which is often the case).

Note that the function does not check that the tree is effectively ultrametric, so if it is not, the returned result may not be meaningful.

##### Value

- An object of class
`"birthdeath"`

which is a list with the following components: tree the name of the tree analysed. N the number of species. dev the deviance (= -2 log lik) at its minimum. para the estimated parameters. se the corresponding standard-errors. CI the 95% profile-likelihood confidence intervals.

##### References

Kendall, D. G. (1948) On the generalized ``birth-and-death''
process. *Annals of Mathematical Statistics*, **19**, 1--15.

Nee, S., May, R. M. and Harvey, P. H. (1994) The reconstructed
evolutionary process. *Philosophical Transactions of the Royal
Society of London. Series B. Biological Sciences*, **344**, 305--311.

Nee, S., Holmes, E. C., May, R. M. and Harvey, P. H. (1995) Estimating
extinctions from molecular phylogenies. in *Extinction Rates*,
eds. Lawton, J. H. and May, R. M., pp. 164--182, Oxford University Press.

##### See Also

`branching.times`

, `diversi.gof`

,
`diversi.time`

, `ltt.plot`

,
`yule`

, `bd.ext`

, `yule.cov`

,
`bd.time`

*Documentation reproduced from package ape, version 3.2, License: GPL (>= 2)*