Editing Dendrogram

{{Distinguish|Dendrogramma}}
{{short description|Diagram with a treelike structure}}
{{More citations needed|date=January 2017}}

{{merge to|Tree structure|date=May 2025}}

[[File:UPGMA Dendrogram Hierarchical.svg|thumb|Dendrogram of a hierarchical clustering (UPGMA) with the height of the nodes (adapted from bacterial 5S rRNA sequence data<ref name="Swofford1996">{{cite book|title=Molecular Systematics, 2nd edition|last1=Swofford|first1=David L.|last2=Olsen|first2=Gary J.|last3=Waddell|first3=Peter J.|last4=Hillis|first4=David M. | name-list-style = vanc |year=1996|isbn=9780878932825|editor-last1=Hillis|editor-first1=David M.|editor-last2=Moritz|editor-first2=Craig|editor-last3=Mable|editor-first3=Barbara K.|publisher=Sinauer|location=Sunderland, MA|pages=407–514|chapter=Phylogenetic inference}}</ref>).]]
[[File:Global-Diversity-of-Sponges-(Porifera)-pone.0035105.s008.tif|thumb|Dendrogram output for hierarchical clustering of marine provinces using presence / absence of sponge species.<ref name="VanSoest2012">{{Cite journal |vauthors=Van Soest R, Boury-Esnault N, Vacelet J, Dohrmann M, Erpenbeck D, De Voogd N, Santodomingo N, Vanhoorne B, Kelly M, Hooper J| title = Global Diversity of Sponges (Porifera) | doi = 10.1371/journal.pone.0035105 | journal = PLOS ONE | volume = 7 | issue = 4 | pages = e35105 | year = 2012 | pmid = 22558119 | pmc = 3338747 | bibcode = 2012PLoSO...735105V| doi-access = free }}
</ref>]]
[[File:Phylogenetic tree.svg|thumb|A dendrogram of the [[Tree of Life]]. This phylogenetic tree is adapted from Woese et al. rRNA analysis.<ref name="Woese_1990">{{cite journal | last1 = Woese | first1 = Carl R.| author-link1 = Carl Woese | last2 =  Kandler | first2 = O | last3 = Wheelis | first3= M | title = Towards a natural system of organisms: proposal for the domains Archaea, Bacteria, and Eucarya | url=http://www.pnas.org/content/87/12/4576.full.pdf | journal = Proc Natl Acad Sci USA | volume = 87 | issue = 12 | pages = 4576–4579 | year = 1990 | pmid = 2112744 | doi = 10.1073/pnas.87.12.4576 | pmc = 54159 | bibcode=1990PNAS...87.4576W| author2-link = Otto Kandler| doi-access = free}}</ref> The vertical line at bottom represents the [[last universal common ancestor]] (LUCA).]]
[[File:Heatmap RNAseqV2 1.png|thumb|Heatmap of [[RNA-Seq]] data showing two dendrograms in the left and top margins.]]

A '''dendrogram''' is a [[diagram]] representing a [[Tree (graph theory)|tree graph]]. This diagrammatic representation is frequently used in different contexts:
* in [[hierarchical clustering]], it illustrates the arrangement of the clusters produced by the corresponding analyses.<ref>{{cite book |last= Everitt |first= Brian |date= 1998 |title= Dictionary of Statistics |location= Cambridge, UK |publisher= Cambridge University Press |page= [https://archive.org/details/cambridgediction00ever_0/page/96 96] |isbn= 0-521-59346-8 |url-access= registration |url= https://archive.org/details/cambridgediction00ever_0/page/96 }}</ref>
* in [[computational biology]], it shows the clustering of [[gene]]s or samples, sometimes in the margins of [[heat map|heatmaps]].<ref name="Wilkinson2009">{{cite journal|last1=Wilkinson|first1=Leland|last2=Friendly|first2=Michael|title=The History of the Cluster Heat Map|journal=The American Statistician|date=May 2009|volume=63|issue=2|pages=179–184|doi=10.1198/tas.2009.0033|s2cid=122792460|citeseerx=10.1.1.165.7924}}</ref>
* in [[phylogenetics]], it displays the [[evolution]]ary relationships among various biological [[taxa]]. In this case, the dendrogram is also called a [[phylogenetic tree]].<ref>{{Cite encyclopedia|url=https://www.britannica.com/science/phylogenetic-tree|title=Phylogenetic tree (biology)|encyclopedia=Encyclopedia Britannica|access-date=2018-10-22|language=en}}</ref>

The name ''dendrogram'' derives from the two [[ancient greek]] words {{wikt-lang|grc|δένδρον}} ({{grc-transl|δένδρον}}), meaning "tree", and {{wikt-lang|grc|γράμμα}} ({{grc-transl|γράμμα}}), meaning "drawing, mathematical figure".<ref>{{Cite book |title=Abrégé du dictionnaire grec français |last=Bailly |first=Anatole |date=1981-01-01 |publisher=Hachette |isbn=2010035283 |location=Paris |oclc=461974285 }}</ref><ref>{{Cite web |url=http://www.tabularium.be/bailly/ |title=Greek-french dictionary online |last=Bailly |first=Anatole |website=www.tabularium.be |access-date=October 20, 2018}}</ref>

== Clustering example ==

For a clustering example, suppose that five taxa (<math>a</math> to <math>e</math>) 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).

== See also ==
* [[Cladogram]]
* [[Distance matrices in phylogeny]]
* [[Hierarchical clustering]]
* [[MEGA, Molecular Evolutionary Genetics Analysis|MEGA]], a [[freeware]] for drawing dendrograms
* [[yEd]], a freeware for drawing and automatically arranging dendrograms
* [[Taxonomy]]

== References ==
=== Citations ===
{{Reflist}}

=== Sources ===
{{refbegin}}
* {{cite journal | last = Galili | first = T. | year = 2015 | title = dendextend: an R package for visualizing, adjusting and comparing trees of hierarchical clustering | doi = 10.1093/bioinformatics/btv428 | journal = Bioinformatics | volume =  31 | issue = 22 | pages =  3718–3720 | pmid = 26209431 | pmc = 4817050 }}
{{refend}}

== External links ==
* [https://cran.r-project.org/web/packages/dendextend/vignettes/Cluster_Analysis.html#the-3-clusters-from-the-complete-method-vs-the-real-species-category Iris dendrogram] - Example of using a dendrogram to visualize the 3 clusters from [[hierarchical clustering]] using the "complete" method vs the real species category (using [[R (programming language)|R]]).

[[Category:Trees (data structures)]]
[[Category:Statistical charts and diagrams]]
[[Category:Graph drawing]]
[[Category:Cluster analysis]]