Description Usage Arguments Details Value Author(s) References See Also Examples

Finds maximum likelihood estimates of the net diversification rate *r*
(speciation rate *S* minus the extinction rate *E*) and the extinction
fraction *a* = *E/S*, using branching times derived from an
ultrametric phylogenetic tree.

1 |

`x` |
a numeric vector of branching times |

`ai` |
a vector of initial |

Non-linear optimization can be exceedingly difficult, and the algorithms used here can become trapped
on local (rather than global) optima. The default 'ai' parameters specified above fit the constant-rate
birth-death model to branching times using three initial *a* values. You should check your results
against those obtained using the `pureBirth`

model. If the log-likelihood under bd is
less than pureBirth, you should explore alternative initial parameterizations. For example,
ai = seq(0.05, 0.99, length.out = 20) would attempt the optimization with 20 equally spaced *a*
values on the interval (0.05, 0.99).

I have found the default option to be satisfactory for all phylogenies I have examined.

a list with the following components:

`LH ` |
the log-likelihood at the maximum |

`aic` |
the Akaike Information Criterion |

`r` |
the net diversification rate giving the maximum log-likelihood |

`a` |
the extinction fraction giving the maximum log-likelihood |

Dan Rabosky drabosky@umich.edu

Kendall, D. G. 1948. On the generalized "birth-and-death" process.
*Ann. Math. Stat.* 19:1-15.

Nee, S., E. C. Holmes, R. M. May, and P. H. Harvey. 1994a. Extinction rates
can be estimated from molecular phylogenies. *Philos. Trans. R. Soc. Lond. B* 344:77-82.

Nee, S., R. M. May, and P. H. Harvey. 1994b. The reconstructed evolutionary process.
*Philos. Trans. R. Soc. Lond. B 344:305-311.*

`pureBirth`

, `fitdAICrc`

,`yule-n-rate`

1 2 |

```
Loading required package: ape
Loading required package: geiger
```

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