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<title>Dendrogram</title>

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</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="Dendrogramma" title="Dendrogramma">Dendrogramma</a>.</div>

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<p>A <b>dendrogram</b> is a <a href="Diagram" title="Diagram">diagram</a> representing a <a href="Tree_(graph_theory)" title="Tree (graph theory)">tree graph</a> and a <a href="Similarity_measure" title="Similarity measure">similarity metric</a>, based on <a href="Numerical_taxonomy" title="Numerical taxonomy">numerical taxonomy</a> methods. This diagrammatic representation is frequently used in different contexts:

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<ul><li>in <a href="Hierarchical_clustering" title="Hierarchical clustering">hierarchical clustering</a>, it illustrates the arrangement of the clusters produced by the corresponding analyses.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li>

<li>in <a href="Computational_biology" title="Computational biology">computational biology</a>, it shows the clustering of <a href="Gene" title="Gene">genes</a> or samples, sometimes in the margins of <a href="Heat_map" title="Heat map">heatmaps</a>.<sup id="cite_ref-Wilkinson2009_3-0" class="reference"><a href="#cite_note-Wilkinson2009-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li>

<li>in <a href="Phylogenetics" title="Phylogenetics">phylogenetics</a>, it displays the <a href="Evolution" title="Evolution">evolutionary</a> relationships among various biological <a href="Taxa" class="mw-redirect" title="Taxa">taxa</a>. In this case, the dendrogram is also called a <a href="Phylogenetic_tree" title="Phylogenetic tree">phylogenetic tree</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li></ul>

<p>The name <i>dendrogram</i> derives from the two <a href="Ancient_greek" class="mw-redirect" title="Ancient greek">ancient greek</a> words <span lang="grc"><a href="https://en.wiktionary.org/wiki/%CE%B4%CE%AD%CE%BD%CE%B4%CF%81%CE%BF%CE%BD#Ancient_Greek" class="extiw external" title="wikt:δένδρον">δένδρον</a></span> (<span title="Ancient Greek transliteration" lang="grc-Latn"><i>déndron</i></span>), meaning "tree", and <span lang="grc"><a href="https://en.wiktionary.org/wiki/%CE%B3%CF%81%CE%AC%CE%BC%CE%BC%CE%B1#Ancient_Greek" class="extiw external" title="wikt:γράμμα">γράμμα</a></span> (<span title="Ancient Greek transliteration" lang="grc-Latn"><i>grámma</i></span>), meaning "drawing, mathematical figure".<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Below a typical one:

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<p>The figure is a dendrogram output for hierarchical clustering of marine provinces using presence / absence of sponge species.<sup id="cite_ref-VanSoest2012_7-0" class="reference"><a href="#cite_note-VanSoest2012-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="History_and_methods">History and methods</h2></div>

<p>The diagrams were popularized and methods refined by <a href="Robert_R._Sokal" title="Robert R. Sokal">Robert R. Sokal</a> and <a href="Peter_H._A._Sneath" class="mw-redirect" title="Peter H. A. Sneath">Peter H. A. Sneath</a> in the 1960s, as part of the <a href="Numerical_taxonomy" title="Numerical taxonomy">numerical taxonomy</a> tools. Despite having been born out of a demand from <a href="Taxonomy_(biology)" title="Taxonomy (biology)">biological taxonomy</a>, it was adopted as a method of <a href="Data_visualization" class="mw-redirect" title="Data visualization">data visualization</a> in statistics, with <a href="Cluster_analysis" title="Cluster analysis">cluster analysis</a>.

</p><p>Nowadays dendrograms are key tools in <a href="Hierarchical_clustering" title="Hierarchical clustering">hierarchical clustering</a>, and their methods are known as <a href="Hierarchical_clustering#Cluster_Linkage" title="Hierarchical clustering">cluster linkage</a>.

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<div class="mw-heading mw-heading2"><h2 id="Other_examples">Other examples</h2></div>

<p>Diagram variations.

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<div class="mw-heading mw-heading2"><h2 id="Phylogenetic">Phylogenetic</h2></div>

<p>A dendrogram of the <a href="Tree_of_Life" class="mw-redirect" title="Tree of Life">Tree of Life</a>. The figure does not use a metric axis, only the approximate distance on the tree, to show evolutionary order.

</p>

<p>This phylogenetic tree is adapted from Woese et al. rRNA analysis.<sup id="cite_ref-Woese_1990_8-0" class="reference"><a href="#cite_note-Woese_1990-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The vertical line at bottom represents the <a href="Last_universal_common_ancestor" title="Last universal common ancestor">last universal common ancestor</a> (LUCA).

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<div class="mw-heading mw-heading2"><h2 id="Clustering">Clustering</h2></div>

<p>For a clustering example, suppose that five taxa (<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}">

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<p>The <a href="Hierarchical_clustering" title="Hierarchical clustering">hierarchical clustering</a> 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).

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<ul><li><a href="Cladogram" title="Cladogram">Cladogram</a></li>

<li><a href="Distance_matrices_in_phylogeny" title="Distance matrices in phylogeny">Distance matrices in phylogeny</a></li>

<li><a href="Hierarchical_clustering" title="Hierarchical clustering">Hierarchical clustering</a></li>

<li><a href="MEGA%2C_Molecular_Evolutionary_Genetics_Analysis" class="mw-redirect" title="MEGA, Molecular Evolutionary Genetics Analysis">MEGA</a>, a <a href="Freeware" title="Freeware">freeware</a> for drawing dendrograms</li>

<li><a href="YEd" title="YEd">yEd</a>, a freeware for drawing and automatically arranging dendrograms</li>

<li><a href="Taxonomy" title="Taxonomy">Taxonomy</a></li>

<li><a href="Numerical_taxonomy" title="Numerical taxonomy">Numerical taxonomy</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3></div>

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</style><cite id="CITEREFSwoffordOlsenWaddellHillis1996" class="citation book cs1">Swofford DL, Olsen GJ, Waddell PJ, Hillis DM (1996). "Phylogenetic inference". In Hillis DM, Moritz C, Mable BK (eds.). <i>Molecular Systematics, 2nd edition</i>. Sunderland, MA: Sinauer. pp. <span class="nowrap">407–</span>514. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780878932825</bdi>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFEveritt1998" class="citation book cs1">Everitt, Brian (1998). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/cambridgediction00ever_0/page/96"><i>Dictionary of Statistics</i></a></span>. Cambridge, UK: Cambridge University Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/cambridgediction00ever_0/page/96">96</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-521-59346-8</bdi>.</cite></span>

</li>

<li id="cite_note-Wilkinson2009-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Wilkinson2009_3-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFWilkinsonFriendly2009" class="citation journal cs1">Wilkinson, Leland; Friendly, Michael (May 2009). "The History of the Cluster Heat Map". <i>The American Statistician</i>. <b>63</b> (2): <span class="nowrap">179–</span>184. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.165.7924">10.1.1.165.7924</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1198%2Ftas.2009.0033">10.1198/tas.2009.0033</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:122792460">122792460</a>.</cite></span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="https://www.britannica.com/science/phylogenetic-tree">"Phylogenetic tree (biology)"</a>. <i>Encyclopedia Britannica</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2018-10-22</span></span>.</cite></span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite id="CITEREFBailly1981" class="citation book cs1">Bailly, Anatole (1981-01-01). <i>Abrégé du dictionnaire grec français</i>. Paris: Hachette. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>2010035283</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/461974285">461974285</a>.</cite></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFBailly" class="citation web cs1">Bailly, Anatole. <a rel="nofollow" class="external text" href="http://www.tabularium.be/bailly/">"Greek-french dictionary online"</a>. <i>www.tabularium.be</i><span class="reference-accessdate">. Retrieved <span class="nowrap">October 20,</span> 2018</span>.</cite></span>

</li>

<li id="cite_note-VanSoest2012-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-VanSoest2012_7-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFVan_SoestBoury-EsnaultVaceletDohrmann2012" class="citation journal cs1">Van Soest R, Boury-Esnault N, Vacelet J, Dohrmann M, Erpenbeck D, De Voogd N, Santodomingo N, Vanhoorne B, Kelly M, Hooper J (2012). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3338747">"Global Diversity of Sponges (Porifera)"</a>. <i>PLOS ONE</i>. <b>7</b> (4): e35105. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2012PLoSO...735105V">2012PLoSO...735105V</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1371%2Fjournal.pone.0035105">10.1371/journal.pone.0035105</a></span>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3338747">3338747</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/22558119">22558119</a>.</cite></span>

</li>

<li id="cite_note-Woese_1990-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Woese_1990_8-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFWoeseKandlerWheelis1990" class="citation journal cs1"><a href="Carl_Woese" title="Carl Woese">Woese, Carl R.</a>; <a href="Otto_Kandler" title="Otto Kandler">Kandler, O</a>; Wheelis, M (1990). <a rel="nofollow" class="external text" href="http://www.pnas.org/content/87/12/4576.full.pdf">"Towards a natural system of organisms: proposal for the domains Archaea, Bacteria, and Eucarya"</a> <span class="cs1-format">(PDF)</span>. <i>Proc Natl Acad Sci USA</i>. <b>87</b> (12): <span class="nowrap">4576–</span>4579. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1990PNAS...87.4576W">1990PNAS...87.4576W</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.87.12.4576">10.1073/pnas.87.12.4576</a></span>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC54159">54159</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/2112744">2112744</a>.</cite></span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3></div>

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<ul><li><cite id="CITEREFGalili2015" class="citation journal cs1">Galili, T. (2015). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4817050">"dendextend: an R package for visualizing, adjusting and comparing trees of hierarchical clustering"</a>. <i>Bioinformatics</i>. <b>31</b> (22): <span class="nowrap">3718–</span>3720. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fbioinformatics%2Fbtv428">10.1093/bioinformatics/btv428</a>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4817050">4817050</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26209431">26209431</a>.</cite></li></ul>

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<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="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</a> - Example of using a dendrogram to visualize the 3 clusters from <a href="Hierarchical_clustering" title="Hierarchical clustering">hierarchical clustering</a> using the "complete" method vs the real species category (using <a href="R_(programming_language)" title="R (programming language)">R</a>).</li></ul></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-08-05" href="https://en.wikipedia.org/wiki/?title=Dendrogram&oldid=1304380902">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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