Evolutionary Trees and Ordinal Assertions

Sequence data for a group of species is often summarized by a distance matrix M where M[s,t] is the dissimilarity between the sequences of species s and t . An ordinal assertion is a statement of the form ``species a and b are as similar as species c and d '' and is supported by distance matrix M if M[a,b] ≤ M[c,d] . Recent preliminary research suggests that ordinal assertions can be used to reconstruct the evolutionary history of a group of species effectively. However, further research on the mathematical and algorithmic properties of ordinal assertions is needed to facilitate the development and assessment of inference methods that utilize ordinal assertions for reconstructing evolutionary histories.