Editing Phylogenetic tree (section)

== Properties ==
=== Rooted tree ===
[[File:Phylogenetic treePureThickBraille.jpg|thumb|upright=1.35 |Rooted phylogenetic tree optimized for blind people. The lowest point of the tree is the root, which symbolizes the universal common ancestor to all living beings. The tree branches out into three main groups: Bacteria (left branch, letters a to i), Archea (middle branch, letters j to p) and Eukaryota (right branch, letters q to z). Each letter corresponds to a group of organisms, listed below this description. These letters and the description should be converted to Braille font, and printed using a Braille printer. The figure can be 3D printed by copying the png file and using Cura or other software to generate the Gcode for 3D printing.]]
A rooted phylogenetic [[Tree (data structure)|tree]] (see two graphics at top) is a [[directed graph|directed]] tree with a unique node — the root — corresponding to the (usually [[imputation (statistics)|imputed]]) most recent common ancestor of all the entities at the [[leaf node|leaves]] of the tree. The root node does not have a parent node, but serves as the parent of all other nodes in the tree. The root is therefore a node of [[Node (computer science)#Nodes and trees|degree]] 2, while other internal nodes have a minimum degree of 3 (where "degree" here refers to the total number of incoming and outgoing edges).{{citation needed|date=June 2024}}

The most common method for rooting trees is the use of an uncontroversial [[outgroup (cladistics)|outgroup]]—close enough to allow inference from trait data or molecular sequencing, but far enough to be a clear outgroup. Another method is midpoint rooting, or a tree can also be rooted by using a non-stationary [[substitution model]].<ref>{{cite journal |last1=Dang |first1=Cuong Cao |last2=Minh |first2=Bui Quang |last3=McShea |first3=Hanon |last4=Masel |first4=Joanna |last5=James |first5=Jennifer Eleanor |last6=Vinh |first6=Le Sy |last7=Lanfear |first7=Robert |title=nQMaker: Estimating Time Nonreversible Amino Acid Substitution Models |journal=Systematic Biology |date=9 February 2022 |volume=71 |issue=5 |pages=1110–1123 |doi=10.1093/sysbio/syac007|pmid=35139203 |pmc=9366462 }}</ref>

=== Unrooted tree ===
[[File:MyosinUnrootedTree.jpg|thumb|upright=1.35|An unrooted phylogenetic tree for [[myosin]], a [[gene family|superfamily]] of [[protein]]s<ref name=Hodge_2000>{{cite journal|vauthors=Hodge T, Cope M |title=A myosin family tree|journal=J Cell Sci|volume=113|issue=19|pages=3353–4|date=1 October 2000|doi=10.1242/jcs.113.19.3353|url=http://jcs.biologists.org/cgi/content/full/113/19/3353|pmid=10984423|url-status=live|archive-url=https://web.archive.org/web/20070930043742/http://jcs.biologists.org/cgi/content/full/113/19/3353|archive-date=30 September 2007}}</ref>]]

Unrooted trees illustrate the relatedness of the leaf nodes without making assumptions about ancestry. They do not require the ancestral root to be known or inferred.<ref>{{cite web |url=https://www.ncbi.nlm.nih.gov/Class/NAWBIS/Modules/Phylogenetics/phylo9.html |title="Tree" Facts: Rooted versus Unrooted Trees |access-date=2014-05-26 |url-status=live |archive-url=https://web.archive.org/web/20140414030413/http://www.ncbi.nlm.nih.gov/Class/NAWBIS/Modules/Phylogenetics/phylo9.html |archive-date=2014-04-14 }}</ref> Rooted trees can be generated from unrooted ones by inserting a root. Inferring the root of an unrooted tree requires some means of identifying ancestry. This is normally done by including an outgroup in the input data so that the root is necessarily between the outgroup and the rest of the taxa in the tree, or by introducing additional assumptions about the relative rates of evolution on each branch, such as an application of the [[molecular clock]] [[hypothesis]].<!--- THIS REF IS ____ <ref name=Maher_2002>{{cite journal |author=Maher BA |title=Uprooting the Tree of Life |journal=The Scientist |volume=16 |issue=2 |pages=90–95 |year=2002 |url=http://www.the-scientist.com/yr2002/sep/research1_020916.html |url-status=live |archive-url=https://web.archive.org/web/20031002231607/http://www.the-scientist.com/yr2002/sep/research1_020916.html |archive-date=2003-10-02 |bibcode=2000SciAm.282b..90D |doi=10.1038/scientificamerican0200-90 |pmid=10710791}}</ref> I HOPE THIS ONE IS BETTER---><ref>{{cite journal |author=W. Ford Doolittle |title=Uprooting the Tree of Life |journal=Scientific American |volume=282 |issue=2 |pages=90–95 |year=2002 |bibcode=2000SciAm.282b..90D |doi=10.1038/scientificamerican0200-90 |pmid=10710791 |quote=''No abstract available''}}</ref>

=== Bifurcating versus multifurcating ===
Both rooted and unrooted trees can be either [[bifurcation theory|bifurcating]] or multifurcating. A rooted bifurcating tree has exactly two descendants arising from each [[interior node]] (that is, it forms a [[binary tree]]), and an unrooted bifurcating tree takes the form of an [[unrooted binary tree]], a [[free tree]] with exactly three neighbors at each internal node. In contrast, a rooted multifurcating tree may have more than two children at some nodes and an unrooted multifurcating tree may have more than three neighbors at some nodes.{{citation needed|date=June 2024}}

=== Labeled versus unlabeled ===
Both rooted and unrooted trees can be either labeled or unlabeled. A labeled tree has specific values assigned to its leaves, while an unlabeled tree, sometimes called a tree shape, defines a topology only. Some sequence-based trees built from a small genomic locus, such as Phylotree,<ref>{{cite journal |last1=van Oven |first1=Mannis |last2=Kayser |first2=Manfred |title=Updated comprehensive phylogenetic tree of global human mitochondrial DNA variation |journal=Human Mutation |date=2009 |volume=30 |issue=2 |pages=E386–E394 |doi=10.1002/humu.20921 |pmid=18853457 |s2cid=27566749 |ref=phylotree|doi-access=free }}</ref> feature internal nodes labeled with inferred ancestral haplotypes.

=== Enumerating trees ===
[[File:Number of trees as a function of the number of leaves.svg|thumb|upright=1.35|Increase in the total number of phylogenetic trees as a function of the number of labeled leaves: unrooted binary trees (blue diamonds), rooted binary trees (red circles), and rooted multifurcating or binary trees (green: triangles). The Y-axis scale is [[Logarithmic scale|logarithmic]].]]
The number of possible trees for a given number of leaf nodes depends on the specific type of tree, but there are always more labeled than unlabeled trees, more multifurcating than bifurcating trees, and more rooted than unrooted trees. The last distinction is the most biologically relevant; it arises because there are many places on an unrooted tree to put the root. For bifurcating labeled trees, the total number of rooted trees is:

:<math> (2n-3)!! = \frac{(2n-3)!}{2^{n-2}(n-2)!} </math> for <math>n \ge 2</math>, <math>n</math> represents the number of leaf nodes.<ref name="Felsenstein1978">{{Cite journal |last=Felsenstein |first=Joseph |date=1978-03-01 |title=The Number of Evolutionary Trees |url=https://academic.oup.com/sysbio/article/27/1/27/1626689 |journal=Systematic Biology |language=en |volume=27 |issue=1 |pages=27–33 |doi=10.2307/2412810 |issn=1063-5157 |jstor=2412810}}</ref>

For bifurcating labeled trees, the total number of unrooted trees is:<ref name="Felsenstein1978"/>

:<math> (2n-5)!! = \frac{(2n-5)!}{2^{n-3}(n-3)!} </math> for <math>n \ge 3</math>.

Among labeled bifurcating trees, the number of unrooted trees with <math>n</math> leaves is equal to the number of rooted trees with <math>n-1</math> leaves.<ref name="Felsenstein"/>

The number of rooted trees grows quickly as a function of the number of tips. For 10 tips, there are more than <math>34 \times 10^6</math> possible bifurcating trees, and the number of multifurcating trees rises faster, with ca. 7 times as many of the latter as of the former.

{| class=wikitable sortable style=text-align:right
|+ Counting trees.<ref name="Felsenstein1978"/>
! Labeled<br>leaves !! Binary<br>unrooted trees !! Binary<br>rooted trees !! Multifurcating<br>rooted trees !! All possible<br>rooted trees
|-
| 1 || 1 || 1 || 0 || 1
|-
| 2 || 1 || 1 || 0 || 1
|-
| 3 || 1 || 3 || 1 || 4
|-
| 4 || 3 || 15 || 11 || 26
|-
| 5 || 15 || 105 || 131 || 236
|-
| 6 || 105 || 945 || 1,807 || 2,752
|-
| 7 || 945 || 10,395 || 28,813 || 39,208
|-
| 8 || 10,395 || 135,135 || 524,897 || 660,032
|-
| 9 || 135,135 || 2,027,025 || 10,791,887 || 12,818,912
|-
| 10 || 2,027,025 || 34,459,425 || 247,678,399 || 282,137,824
|-
|}