A phylogenetic tree or evolutionary tree is a branching diagram or "tree" showing the evolutionary relationships among various biological species or other entities—their phylogeny (/faɪˈlɒdʒəni/)—based upon similarities and differences in their physical or genetic characteristics. All life on Earth is part of a single phylogenetic tree, indicating common ancestry.

In a rooted phylogenetic tree, each node with descendants represents the inferred most recent common ancestor of those descendants, and the edge lengths in some trees may be interpreted as time estimates. Each node is called a taxonomic unit. Internal nodes are generally called hypothetical taxonomic units, as they cannot be directly observed. Trees are useful in fields of biology such as bioinformatics, systematics, and phylogenetics. Unrooted trees illustrate only the relatedness of the leaf nodes and do not require the ancestral root to be known or inferred.

The idea of a "tree of life" arose from ancient notions of a ladder-like progression from lower into higher forms of life (such as in the Great Chain of Being). Early representations of "branching" phylogenetic trees include a "paleontological chart" showing the geological relationships among plants and animals in the book Elementary Geology, by Edward Hitchcock (first edition: 1840).

Charles Darwin (1859) also produced one of the first illustrations and crucially popularized the notion of an evolutionary "tree" in his seminal book The Origin of Species. Over a century later, evolutionary biologists still use tree diagrams to depict evolution because such diagrams effectively convey the concept that speciation occurs through the adaptive and semirandom splitting of lineages. Over time, species classification has become less static and more dynamic.

The term phylogenetic, or phylogeny, derives from the two ancient greek words φῦλον (phûlon), meaning "race, lineage", and γένεσις (génesis), meaning "origin, source".^[3][4]

A rooted phylogenetic tree (see two graphics at top) is a directed tree with a unique node — the root — corresponding to the (usually imputed) most recent common ancestor of all the entities at the 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 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).

The most common method for rooting trees is the use of an uncontroversial outgroup—close enough to allow inference from trait data or molecular sequencing, but far enough to be a clear outgroup.

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.^[6] Unrooted trees can always be generated from rooted ones by simply omitting the root. By contrast, 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.^[7]

Both rooted and unrooted phylogenetic trees can be either bifurcating or multifurcating, and either labeled or unlabeled. 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. A labeled tree has specific values assigned to its leaves, while an unlabeled tree, sometimes called a tree shape, defines a topology only. The number of possible trees for a given number of leaf nodes depends on the specific type of tree, but there are always more multifurcating than bifurcating trees, more labeled than unlabeled 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 labeled bifurcating trees, there are:

total rooted trees and

Darwin^[9] also mentioned that the coral may be a more suitable metaphor than the tree. Indeed, phylogenetic corals are useful for portraying past and present life, and they have some advantages over trees (anastomoses allowed, etc).^[10]

Phylogenetic trees composed with a nontrivial number of input sequences are constructed using computational phylogenetics methods. Distance-matrix methods such as neighbor-joining or UPGMA, which calculate genetic distance from multiple sequence alignments, are simplest to implement, but do not invoke an evolutionary model. Many sequence alignment methods such as ClustalW also create trees by using the simpler algorithms (i.e. those based on distance) of tree construction. Maximum parsimony is another simple method of estimating phylogenetic trees, but implies an implicit model of evolution (i.e. parsimony). More advanced methods use the optimality criterion of maximum likelihood, often within a Bayesian framework, and apply an explicit model of evolution to phylogenetic tree estimation.^[8] Identifying the optimal tree using many of these techniques is NP-hard,^[8] so heuristic search and optimization methods are used in combination with tree-scoring functions to identify a reasonably good tree that fits the data.

Tree-building methods can be assessed on the basis of several criteria:^[15]

Tree-building techniques have also gained the attention of mathematicians. Trees can also be built using T-theory.^[16]

Although phylogenetic trees produced on the basis of sequenced genes or genomic data in different species can provide evolutionary insight, these analyses have important limitations. Most importantly, the trees that they generate are not necessarily correct – they do not necessarily accurately represent the evolutionary history of the included taxa. As with any scientific result, they are subject to falsification by further study (e.g., gathering of additional data, analyzing the existing data with improved methods). The data on which they are based may be noisy;^[17] the analysis can be confounded by genetic recombination,^[18] horizontal gene transfer,^[19] hybridisation between species that were not nearest neighbors on the tree before hybridisation takes place, convergent evolution, and conserved sequences.

Also, there are problems in basing an analysis on a single type of character, such as a single gene or protein or only on morphological analysis, because such trees constructed from another unrelated data source often differ from the first, and therefore great care is needed in inferring phylogenetic relationships among species. This is most true of genetic material that is subject to lateral gene transfer and recombination, where different haplotype blocks can have different histories. In these types of analysis, the output tree of a phylogenetic analysis of a single gene is an estimate of the gene's phylogeny (i.e. a gene tree) and not the phylogeny of the taxa (i.e. species tree) from which these characters were sampled, though ideally, both should be very close. For this reason, serious phylogenetic studies generally use a combination of genes that come from different genomic sources (e.g., from mitochondrial or plastid vs. nuclear genomes)^[20], or genes that would be expected to evolve under different selective regimes, so that homoplasy (false homology) would be unlikely to result from natural selection.

When extinct species are included as terminal nodes in an analysis (rather than, for example, to constrain internal nodes), they are considered not to represent direct ancestors of any extant species. Extinct species do not typically contain high-quality DNA.

The range of useful DNA materials has expanded with advances in extraction and sequencing technologies. Development of technologies able to infer sequences from smaller fragments, or from spatial patterns of DNA degradation products, would further expand the range of DNA considered useful.

Phylogenetic trees can also be inferred from a range of other data types, including morphology, the presence or absence of particular types of genes, insertion and deletion events – and any other observation thought to contain an evolutionary signal.

Phylogenetic networks are used when bifurcating trees are not suitable, due to these complications which suggest a more reticulate evolutionary history of the organisms sampled.