Phylogenetic tree
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# Overview
A phylogenetic tree, also called an evolutionary tree, is a tree showing the evolutionary relationships among various biological species or other entities that are believed to have a common ancestor.  In a phylogenetic tree, each node with descendants represents the most recent common ancestor of the descendants, and the edge lengths in some trees correspond to time estimates. Each node is called a taxonomic unit. Internal nodes are generally called hypothetical taxonomic units (HTUs) as they cannot be directly observed.

# History
Although the idea of a "tree of life" arose from ancient notions of a ladder-like progression from lower to higher forms of life (such as in the Great Chain of Being), Charles Darwin (1859) first illustrated and 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 the floral analogy effectively conveys the concept that speciation occurs through the adaptive and random splitting of lineages.  Over time, species classification has become less static and more dynamic.
Adolf Engler (1844 - 1930) and Karl A. E. Prantl (1849 - 1893) published a system of plant classification in their monograph Die Naturlichen Pflanzenfamilien. In it, they arranged the families and orders of flowering plants on the basis of complexity of floral morphology. Characters like a perianth with one whorl, unisexual flowers and pollination by wind were considered primitive as compared to perianth with two whorls, bisexual flowers and pollination by insects.
The plant kingdom is further divided into divisions, sub-divisions, classes, orders and families.  According to this system, monocotyledons are considered more primitive than dicotyledons. It also considers evolution of angiosperms from a single source and the sequence of orders and families show parallel evolution.

# Types
A rooted phylogenetic tree is a directed tree with a unique node corresponding to the (usually imputed) most recent common ancestor of all the entities at the leaves of the tree. The most common method for rooting trees is the use of an uncontroversial outgroup  close enough to allow inference from sequence or trait data, but far enough to be a clear outgroup.
Unrooted trees illustrate the relatedness of the leaf nodes without making assumptions about common ancestry. While unrooted trees can always be generated from rooted ones by simply omitting the root, a root cannot be inferred from an unrooted tree without some means of identifying ancestry; this is normally done by including an outgroup in the input data or introducing additional assumptions about the relative rates of evolution on each branch, such as an application of the molecular clock hypothesis. Figure 1 depicts an unrooted phylogenetic tree for myosin, a superfamily of proteins.
Both rooted and unrooted phylogenetic trees can be either bifurcating or multifurcating, and either labeled or unlabeled. A bifurcating tree has a maximum of two descendants arising from each interior node, while a multifurcating tree may have more than two. A labeled tree has specific values assigned to its leaves, while an unlabeled tree, sometimes called a tree shape, only defines a topology. 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
\frac{(2n-3)!}{2^{n-2}(n-2)!}
total rooted trees and
\frac{(2n-5)!}{2^{n-3}(n-3)!}
total unrooted trees, where n represents the number of leaf nodes. The number of unrooted trees for n input sequences or species is equal to the number of rooted trees for n-1 sequences.
A dendrogram is a broad term for the diagrammatic representation of a phylogenetic tree.
A cladogram is a tree formed using cladistic methods.  This type of tree only represents a branching pattern, i.e., its branch lengths do not represent time.
A phylogram is a phylogenetic tree that explicitly represents number of character changes through its branch lengths.
An ultrametric tree or chronogram is a phylogenetic tree that explicitly represents evolutionary time through its branch lengths.

# Construction
Phylogenetic trees among 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. Identifying the optimal tree using many of these techniques is NP-hard, 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:
- efficiency (how long does it take to compute the answer, how much memory does it need?)
- power (does it make good use of the data, or is information being wasted?)
- consistency (will it converge on the same answer repeatedly, if each time given different data for the same model problem?)
- robustness (does it cope well with violations of the assumptions of the underlying model?)
- falsifiability (does it alert us when it is not good to use, i.e. when assumptions are violated?)
Tree-building techniques have also gained the attention of mathematicians. Trees can also be built using T-theory. 

# Limitations
Although phylogenetic trees produced on the basis of sequenced genes or genomic data in different species can provide evolutionary insight, they have important limitations. They do not necessarily accurately represent the species evolutionary history. The data on which they are based is noisy; the analysis can be confounded by horizontal gene transfer,   hybridisation between species that were not nearest neighbors on the tree before hybridisation takes place, convergent evolution, and conserved sequences.  To avoid these limitations, one method of analysis, implemented in the program PhyloCode, does not assume a tree structure.
Also, there are problems in basing the 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 general, the output tree of a phylogenetic analysis is an estimate of the character'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.
When extinct species are included in a tree, they are terminal nodes, as it is unlikely that they are direct ancestors of any extant species. Scepticism must apply when extinct species are included in trees that are wholly or partly based on DNA sequence data, due to the fact that little useful "ancient DNA" is preserved for longer than 100,000 years, and except in the most unusual circumstances no DNA sequences long enough for use in phylogenetic analyses have yet been recovered from material over 1 million years old.
In some organisms, endosymbionts have an independent genetic history from the host.
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.