# Dendrogram

Short description: Diagram representing a tree

Dendrogram of a hierarchical clustering (UPGMA) with the height of the nodes (adapted from bacterial 5S rRNA sequence data[1]).
A dendrogram of the Tree of Life. This phylogenetic tree is adapted from Woese et al. rRNA analysis.[3] The vertical line at bottom represents the last universal common ancestor (LUCA).
Heatmap of RNA-Seq data showing two dendrograms in the left and top margins.

A dendrogram is a diagram representing a tree. This diagrammatic representation is frequently used in different contexts:

The name dendrogram derives from the two ancient greek words δένδρον (déndron), meaning "tree", and γράμμα (grámma), meaning "drawing, mathematical figure".[7][8]

## Clustering example

For a clustering example, suppose that five taxa ($\displaystyle{ a }$ to $\displaystyle{ e }$) have been clustered by UPGMA based on a matrix of genetic distances. The hierarchical clustering dendrogram would show a column of five nodes representing the initial data (here individual taxa), and the remaining nodes represent the clusters to which the data belong, with the arrows representing the distance (dissimilarity). The distance between merged clusters is monotone, increasing with the level of the merger: the height of each node in the plot is proportional to the value of the intergroup dissimilarity between its two daughters (the nodes on the right representing individual observations all plotted at zero height).

## References

### Citations

1. Swofford, David L.; Olsen, Gary J.; Waddell, Peter J.; Hillis, David M. (1996). "Phylogenetic inference". Molecular Systematics, 2nd edition. Sunderland, MA: Sinauer. pp. 407–514. ISBN 9780878932825.
2. "Global Diversity of Sponges (Porifera)". PLOS ONE 7 (4): e35105. 2012. doi:10.1371/journal.pone.0035105. PMID 22558119. Bibcode2012PLoSO...735105V.
3. Woese, Carl R.; Kandler, O; Wheelis, M (1990). "Towards a natural system of organisms: proposal for the domains Archaea, Bacteria, and Eucarya". Proc Natl Acad Sci USA 87 (12): 4576–4579. doi:10.1073/pnas.87.12.4576. PMID 2112744. PMC 54159. Bibcode1990PNAS...87.4576W.
4. Everitt, Brian (1998). Dictionary of Statistics. Cambridge, UK: Cambridge University Press. p. 96. ISBN 0-521-59346-8.
5. Wilkinson, Leland; Friendly, Michael (May 2009). "The History of the Cluster Heat Map". The American Statistician 63 (2): 179–184. doi:10.1198/tas.2009.0033.
6. "Phylogenetic tree (biology)" (in en). Encyclopedia Britannica. Retrieved 2018-10-22.
7. Bailly, Anatole (1981-01-01). Abrégé du dictionnaire grec français. Paris: Hachette. ISBN 2010035283. OCLC 461974285.
8. Bailly, Anatole. "Greek-french dictionary online".