diversi.gof: Tests of Constant Diversification Rates

Description

This function computes two tests of the distribution of branching times using the Cram�r-von Mises and Anderson-Darling goodness-of-fit tests. By default, it is assumed that the diversification rate is constant, and an exponential distribution is assumed for the branching times. In this case, the expected distribution under this model is computed with a rate estimated from the data. Alternatively, the user may specify an expected cumulative density function (z): in this case, x and z must be of the same length.

Usage

diversi.gof(x, null = "exponential", z = NULL)

Arguments

a numeric vector with the branching times.

null

a character string specifying the null distribution for the branching times. Only two choices are possible: either "exponential", or "user".

used if null = "user"; gives the expected distribution under the model.

Value

A NULL value is returned, the results are simply printed.

Details

The Cram�r-von Mises and Anderson-Darling tests compare the empirical density function (EDF) of the observations to an expected cumulative density function. By contrast to the Kolmogorov--Smirnov test where the greatest difference between these two functions is used, in both tests all differences are taken into account. The distributions of both test statistics depend on the null hypothesis, and on whether or not some parameters were estimated from the data. However, these distributions are not known precisely and critical values were determined by Stephens (1974) using simulations. These critical values were used for the present function.

References

Paradis, E. (1998) Testing for constant diversification rates using molecular phylogenies: a general approach based on statistical tests for goodness of fit. Molecular Biology and Evolution, 15, 476--479. Stephens, M. A. (1974) EDF statistics for goodness of fit and some comparisons. Journal of American Statistical Association, 69, 730--737.