STATISTICAL TESTS FOR DISCRETE CROSS-SPECIES DATA

Four methods have been proposed that can be used to test for associati ons between the states of discrete characters in cross-species data an d that do not suffer from non-independence due to overcounting of data points. The tests are those of Ridley (1983), Burt (1989), Grafen (19 89), and a new test called the ICDE test. The aim of the paper is to m easure the Type I error rates for these methods with simulated null di stributions of discrete characters. The null data is generated by a mo del of discrete character evolution, using three shapes of phylogeny: tetratomous, dichotomous, and realistic. Ridley's and Burt's tests are both reasonably valid with the realistic phylogeny but biased with th e tetratomous and dichotomous phylogenies. Grafen's phylogenetic regre ssion is reasonably valid with all tree shapes. One version of the ICD E test was valid, the other less so. The invalid results are explained in terms of two kinds of statistical non-independence that arise in d iscrete data: non-independence due to the reconstruction of character states by parsimony, and the ''family problem'' in which similar patte rns are found in null data in many separate radiations because all the radiations began from the same ancestral state. (C) 1996 Academic Pre ss Limited