# birthdeath

From ape v3.2
0th

Percentile

##### 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:
• treethe name of the tree analysed.
• Nthe number of species.
• devthe deviance (= -2 log lik) at its minimum.
• parathe estimated parameters.
• sethe corresponding standard-errors.
• CIthe 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.

branching.times, diversi.gof, diversi.time, ltt.plot, yule, bd.ext, yule.cov, bd.time