RANDOM DENDROGRAMS AND NULL HYPOTHESES IN CLADISTIC BIOGEOGRAPHY

Simberloff et al. (1981, pages 40-63 in Vicariance biogeography: A critique [G. Nelson and D. E. Rosen, eds.], Columbia Univ. Press, New York) proposed three different sampling distributions of trees for testing cladistic biogeographic hypotheses. Two of these distributions involved sampling from a uniform distribution of cladograms (either labeled or unlabeled), whereas the third distribution was calculated by a simple Markovian model. This paper presents a proof that the third distribution of cladograms is identical to the uniform distribution of dendrograms (rooted trees with internal nodes ranked). Hence, all three sampling distributions are uniform distributions that differ solely in the kind of tree being sampled. The paper concludes by suggesting ways of constructing nonuniform tree distributions.