Additive vs ultrametric: triangle inequality Additive vs ultrametric ...

Cluster analyses
http://www.biomedcentral.com/1471-2105/9/90/figure/F5
Distances are always estimates
• Pairwise distance values are never exact:
– Complete phylogenetic record of all
genetic/phenotypic events would constitute set of
distances that are completely:
• Additive.
• Mutually consistent across all taxa.
– Observed distances are approximations:
• Comprise ‘true’ distances, plus error.
• Don’t display complete additivity and mutual
consistency.
– Additivity (metricity) and ultrametricity are properties
of a distance matrix.
• Can be tested statistically.
– Q: to what extent do methods recover ‘true’
distances, in presence of error.
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