By analogy with the theory surrounding the Ewens sampling formula in neutral population genetics, we ask whether there exists a natural one-parameter family of probability distributions on cladograms (``evolutionary trees'') which plays a central role in neutral evolutionary theory.
Unfortunately the answer seems to be "no''.

But we can embed the two most popular models into an interesting family which we call ``beta-splitting'' models. We briefly describe some mathematical results about this family, which exhibits qualitatively different behavior for different ranges of the parameter $\beta$.

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