bd: Fit Rate-Constant Birth-Death Model to Branching Times

Description

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.

Usage

bd(x, ai = c(0.1, 0.5, 0.9))

Arguments

a numeric vector of branching times

a vector of initial a parameterizations for the optimization algorithm

Value

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

Details

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.

References

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.

Examples

Run this code

  data(plethodon)
  result <- bd(plethodon)

Run the code above in your browser using DataLab