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A `!dendrogram`! is a `F33f`_`[diagram`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Diagram]`_`f representing a `F33f`_`[tree graph`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Tree_(graph_theory)]`_`f and a `F33f`_`[similarity metric`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Similarity_measure]`_`f, based on `F33f`_`[numerical taxonomy`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Numerical_taxonomy]`_`f methods. This diagrammatic representation is frequently used in different contexts:

• in `F33f`_`[hierarchical clustering`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Hierarchical_clustering]`_`f, it illustrates the arrangement of the clusters produced by the corresponding analyses.`:cite-ref-2[`F5bf`_`[2`#cite-note-2]`_`f]

• in `F33f`_`[computational biology`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Computational_biology]`_`f, it shows the clustering of `F33f`_`[genes`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Gene]`_`f or samples, sometimes in the margins of `F33f`_`[heatmaps`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Heat_map]`_`f.`:cite-ref-wilkinson2009-3-0[`F5bf`_`[3`#cite-note-wilkinson2009-3]`_`f]

• in `F33f`_`[phylogenetics`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Phylogenetics]`_`f, it displays the `F33f`_`[evolutionary`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Evolution]`_`f relationships among various biological `F33f`_`[taxa`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Taxa]`_`f. In this case, the dendrogram is also called a `F33f`_`[phylogenetic tree`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Phylogenetic_tree]`_`f.`:cite-ref-4[`F5bf`_`[4`#cite-note-4]`_`f]

The name `*dendrogram`* derives from the two `F33f`_`[ancient greek`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Ancient_greek]`_`f words δένδρον (`*déndron`*), meaning "tree", and γράμμα (`*grámma`*), meaning "drawing, mathematical figure".`:cite-ref-5[`F5bf`_`[5`#cite-note-5]`_`f]`:cite-ref-6[`F5bf`_`[6`#cite-note-6]`_`f] Below a typical one:

The figure is a dendrogram output for hierarchical clustering of marine provinces using presence / absence of sponge species.`:cite-ref-vansoest2012-7-0[`F5bf`_`[7`#cite-note-vansoest2012-7]`_`f]

>>Contents

• `F0af`_`[History and methods`#history-and-methods]`_`f

• `F0af`_`[Other examples`#other-examples]`_`f

• `F0af`_`[Phylogenetic`#phylogenetic]`_`f

• `F0af`_`[Clustering`#clustering]`_`f

• `F0af`_`[See also`#see-also]`_`f

• `F0af`_`[References`#references]`_`f

• `F0af`_`[Citations`#citations]`_`f

• `F0af`_`[Sources`#sources]`_`f

• `F0af`_`[External links`#external-links]`_`f

-─

>>History and methods

The diagrams were popularized and methods refined by `F33f`_`[Robert R. Sokal`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Robert_R._Sokal]`_`f and `F33f`_`[Peter H. A. Sneath`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Peter_H._A._Sneath]`_`f in the 1960s, as part of the `F33f`_`[numerical taxonomy`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Numerical_taxonomy]`_`f tools. Despite having been born out of a demand from `F33f`_`[biological taxonomy`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Taxonomy_(biology)]`_`f, it was adopted as a method of `F33f`_`[data visualization`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Data_visualization]`_`f in statistics, with `F33f`_`[cluster analysis`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Cluster_analysis]`_`f.

Nowadays dendrograms are key tools in `F33f`_`[hierarchical clustering`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Hierarchical_clustering]`_`f, and their methods are known as `F33f`_`[cluster linkage`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Hierarchical_clustering]`_`f.

>>Other examples

Diagram variations.

>>Phylogenetic

A dendrogram of the `F33f`_`[Tree of Life`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Tree_of_Life]`_`f. The figure does not use a metric axis, only the approximate distance on the tree, to show evolutionary order.

This phylogenetic tree is adapted from Woese et al. rRNA analysis.`:cite-ref-woese-1990-8-0[`F5bf`_`[8`#cite-note-woese-1990-8]`_`f] The vertical line at bottom represents the `F33f`_`[last universal common ancestor`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Last_universal_common_ancestor]`_`f (LUCA).

>>Clustering

For a clustering example, suppose that five taxa ( a {\\displaystyle a} to e {\\displaystyle e} ) have been clustered by `F33f`_`[UPGMA`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=UPGMA]`_`f based on a matrix of `F33f`_`[genetic distances`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Genetic_distances]`_`f. The matrix is showed as a `F33f`_`[heatmap`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Heatmap]`_`f of `F33f`_`[RNA-Seq`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=RNA-Seq]`_`f, with data showing two dendrograms in the left and top margins.

The `F33f`_`[hierarchical clustering`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Hierarchical_clustering]`_`f 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).

>>See also

• `F33f`_`[Cladogram`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Cladogram]`_`f

• `F33f`_`[Distance matrices in phylogeny`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Distance_matrices_in_phylogeny]`_`f

• `F33f`_`[Hierarchical clustering`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Hierarchical_clustering]`_`f

• `F33f`_`[MEGA`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=MEGA,_Molecular_Evolutionary_Genetics_Analysis]`_`f, a `F33f`_`[freeware`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Freeware]`_`f for drawing dendrograms

• `F33f`_`[yEd`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=YEd]`_`f, a freeware for drawing and automatically arranging dendrograms

• `F33f`_`[Taxonomy`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Taxonomy]`_`f

• `F33f`_`[Numerical taxonomy`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Numerical_taxonomy]`_`f

>>References

>>>Citations

`:cite-note-swofford1996-1`!1.`! `:citerefswoffordolsenwaddellhillis1996`aSwofford DL, Olsen GJ, Waddell PJ, Hillis DM (1996). "Phylogenetic inference". In Hillis DM, Moritz C, Mable BK (eds.). `*Molecular Systematics, 2nd edition`*. Sunderland, MA: Sinauer. pp. 407–514. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 9780878932825.

`:cite-note-2`!2.`! `F0af`_`[↑`#cite-ref-2]`_`f `:citerefeveritt1998`aEveritt, Brian (1998). `*Dictionary of Statistics`*. Cambridge, UK: Cambridge University Press. p. 96. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 0-521-59346-8.

`:cite-note-wilkinson2009-3`!3.`! `F0af`_`[↑`#cite-ref-wilkinson2009-3-0]`_`f `:citerefwilkinsonfriendly2009`aWilkinson, Leland; Friendly, Michael (May 2009). "The History of the Cluster Heat Map". `*The American Statistician`*. `!63`! (2): 179–184. `F33f`_`[CiteSeerX`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=CiteSeerX_(identifier)]`_`f 10.1.1.165.7924. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1198/tas.2009.0033. `F33f`_`[S2CID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=S2CID_(identifier)]`_`f 122792460.

`:cite-note-4`!4.`! `F0af`_`[↑`#cite-ref-4]`_`f "Phylogenetic tree (biology)". `*Encyclopedia Britannica`*. Retrieved 2018-10-22.

`:cite-note-5`!5.`! `F0af`_`[↑`#cite-ref-5]`_`f `:citerefbailly1981`aBailly, Anatole (1981-01-01). `*Abrégé du dictionnaire grec français`*. Paris: Hachette. `F33f`_`[ISBN`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ISBN_(identifier)]`_`f 2010035283. `F33f`_`[OCLC`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=OCLC_(identifier)]`_`f 461974285.

`:cite-note-6`!6.`! `F0af`_`[↑`#cite-ref-6]`_`f `:citerefbailly`aBailly, Anatole. "Greek-french dictionary online". `*www.tabularium.be`*. Retrieved October 20, 2018.

`:cite-note-vansoest2012-7`!7.`! `F0af`_`[↑`#cite-ref-vansoest2012-7-0]`_`f `:citerefvan-soestboury-esnaultvaceletdohrmann2012`aVan Soest R, Boury-Esnault N, Vacelet J, Dohrmann M, Erpenbeck D, De Voogd N, Santodomingo N, Vanhoorne B, Kelly M, Hooper J (2012). "Global Diversity of Sponges (Porifera)". `*PLOS ONE`*. `!7`! (4): e35105. `F33f`_`[Bibcode`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bibcode_(identifier)]`_`f:2012PLoSO...735105V. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1371/journal.pone.0035105. `F33f`_`[PMC`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=PMC_(identifier)]`_`f 3338747. `F33f`_`[PMID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=PMID_(identifier)]`_`f 22558119.

`:cite-note-woese-1990-8`!8.`! `F0af`_`[↑`#cite-ref-woese-1990-8-0]`_`f `:citerefwoesekandlerwheelis1990`a`F33f`_`[Woese, Carl R.`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Carl_Woese]`_`f; `F33f`_`[Kandler, O`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Otto_Kandler]`_`f; Wheelis, M (1990). "Towards a natural system of organisms: proposal for the domains Archaea, Bacteria, and Eucarya" (PDF). `*Proc Natl Acad Sci USA`*. `!87`! (12): 4576–4579. `F33f`_`[Bibcode`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bibcode_(identifier)]`_`f:1990PNAS...87.4576W. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1073/pnas.87.12.4576. `F33f`_`[PMC`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=PMC_(identifier)]`_`f 54159. `F33f`_`[PMID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=PMID_(identifier)]`_`f 2112744.

>>>Sources

• `:citerefgalili2015`aGalili, T. (2015). "dendextend: an R package for visualizing, adjusting and comparing trees of hierarchical clustering". `*Bioinformatics`*. `!31`! (22): 3718–3720. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1093/bioinformatics/btv428. `F33f`_`[PMC`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=PMC_(identifier)]`_`f 4817050. `F33f`_`[PMID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=PMID_(identifier)]`_`f 26209431.

>>External links

• Iris dendrogram - Example of using a dendrogram to visualize the 3 clusters from `F33f`_`[hierarchical clustering`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Hierarchical_clustering]`_`f using the "complete" method vs the real species category (using `F33f`_`[R`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=R_(programming_language)]`_`f).

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