This widget shows how trees project into the space of relative pattern frequencies for the parsimony patterns only. The distance from the bottom of the triangle is proportional to the fraction of parsimony informative sites that support the tree AB|CD. The relative fraction of sites that support AC|BD is the distance from the right side of the triangle. et cetera.

The pale green, blue, and red regions correspond to parts of the pattern frequency space that correspond to the tree of that color. This means, for example, that any dataset with pattern frequencies that place it in the green region of the space will favor the green tree (AB|CD).


  1. Think about how changing a branch length would affect the frequency of a patterns for that tree.
  2. Grab one of the nodes attached to the branch, and stretch or shrink the branch (Note: the left internal node of each tree cannot move)
  3. See how the dot of the same color moves

Note: the branch lengths are the probability of change in a two-state model, so they are in the range [0, 0.5]. Most model-based phylogenetics uses branch lengths in terms of the expected number of changes per site (a transformation of these branch lengths).

Note: If a node is highlighted (from being clicked), the arrow keys will move it and TAB will advance the focus to another node in that tree.

Further Reading

See Kim (2000) for a great introduction to thinking about pattern frequency space

Kim, Junhyong. "Slicing hyperdimensional oranges: the geometry of phylogenetic estimation." Molecular phylogenetics and evolution 17.1 (2000): 58-75.

Further information on toplogical testing will be available in a forthcoming "Encyclopedia of Evolution" article by Emily Jane B. McTavish and Mark T. Holder.

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Source code at

Thanks to the U.S. National Science Foundation and the Heidelberg Institute for Theoretical Studies for support.