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Computational phylogenetics is the application of computational
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
s, methods, and programs to
phylogenetic In biology, phylogenetics (; from Greek φυλή/ φῦλον [] "tribe, clan, race", and wikt:γενετικός, γενετικός [] "origin, source, birth") is the study of the evolutionary history and relationships among or within groups o ...
analyses. The goal is to assemble a
phylogenetic tree A phylogenetic tree (also phylogeny or evolutionary tree Felsenstein J. (2004). ''Inferring Phylogenies'' Sinauer Associates: Sunderland, MA.) is a branching diagram or a tree showing the evolutionary relationships among various biological spec ...
representing a hypothesis about the evolutionary ancestry of a set of
gene In biology, the word gene (from , ; "...Wilhelm Johannsen coined the word gene to describe the Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanings. The Mendelian gene is a ba ...
s,
species In biology, a species is the basic unit of Taxonomy (biology), classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of ...
, or other
taxa In biology, a taxon (back-formation from ''taxonomy''; plural taxa) is a group of one or more populations of an organism or organisms seen by taxonomists to form a unit. Although neither is required, a taxon is usually known by a particular nam ...
. For example, these techniques have been used to explore the family tree of
hominid The Hominidae (), whose members are known as the great apes or hominids (), are a taxonomic family of primates that includes eight extant species in four genera: '' Pongo'' (the Bornean, Sumatran and Tapanuli orangutan); ''Gorilla'' (the eas ...
species and the relationships between specific genes shared by many types of organisms. Traditional phylogenetics relies on morphological data obtained by measuring and quantifying the phenotypic properties of representative organisms, while the more recent field of molecular phylogenetics uses
nucleotide Nucleotides are organic molecules consisting of a nucleoside and a phosphate. They serve as monomeric units of the nucleic acid polymers – deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), both of which are essential biomolecules with ...
sequences encoding genes or
amino acid Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although hundreds of amino acids exist in nature, by far the most important are the alpha-amino acids, which comprise proteins. Only 22 alpha am ...
sequences encoding proteins as the basis for classification. Many forms of molecular phylogenetics are closely related to and make extensive use of
sequence alignment In bioinformatics, a sequence alignment is a way of arranging the sequences of DNA, RNA, or protein to identify regions of similarity that may be a consequence of functional, structural, or evolutionary relationships between the sequences. Ali ...
in constructing and refining phylogenetic trees, which are used to classify the evolutionary relationships between homologous
gene In biology, the word gene (from , ; "...Wilhelm Johannsen coined the word gene to describe the Mendelian units of heredity..." meaning ''generation'' or ''birth'' or ''gender'') can have several different meanings. The Mendelian gene is a ba ...
s represented in the
genome In the fields of molecular biology and genetics, a genome is all the genetic information of an organism. It consists of nucleotide sequences of DNA (or RNA in RNA viruses). The nuclear genome includes protein-coding genes and non-coding gen ...
s of divergent species. The phylogenetic trees constructed by computational methods are unlikely to perfectly reproduce the
evolutionary tree A phylogenetic tree (also phylogeny or evolutionary tree Felsenstein J. (2004). ''Inferring Phylogenies'' Sinauer Associates: Sunderland, MA.) is a branching diagram or a tree showing the evolutionary relationships among various biological spec ...
that represents the historical relationships between the species being analyzed. The historical species tree may also differ from the historical tree of an individual homologous gene shared by those species.


Types of phylogenetic trees and networks

Phylogenetic tree A phylogenetic tree (also phylogeny or evolutionary tree Felsenstein J. (2004). ''Inferring Phylogenies'' Sinauer Associates: Sunderland, MA.) is a branching diagram or a tree showing the evolutionary relationships among various biological spec ...
s generated by computational phylogenetics can be either ''rooted'' or ''unrooted'' depending on the input data and the algorithm used. A rooted tree is a
directed graph In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. Definition In formal terms, a directed graph is an ordered pa ...
that explicitly identifies a
most recent common ancestor In biology and genetic genealogy, the most recent common ancestor (MRCA), also known as the last common ancestor (LCA) or concestor, of a set of organisms is the most recent individual from which all the organisms of the set are descended. The ...
(MRCA), usually an inputted sequence that is not represented in the input. Genetic distance measures can be used to plot a tree with the input sequences as
leaf node In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be co ...
s and their distances from the root proportional to their
genetic distance Genetic distance is a measure of the genetic divergence between species or between populations within a species, whether the distance measures time from common ancestor or degree of differentiation. Populations with many similar alleles have s ...
from the hypothesized MRCA. Identification of a root usually requires the inclusion in the input data of at least one "outgroup" known to be only distantly related to the sequences of interest. By contrast, unrooted trees plot the distances and relationships between input sequences without making assumptions regarding their descent. An unrooted tree can always be produced from a rooted tree, but a root cannot usually be placed on an unrooted tree without additional data on divergence rates, such as the assumption of the
molecular clock The molecular clock is a figurative term for a technique that uses the mutation rate of biomolecules to deduce the time in prehistory when two or more life forms diverged. The biomolecular data used for such calculations are usually nucleotid ...
hypothesis. The set of all possible phylogenetic trees for a given group of input sequences can be conceptualized as a discretely defined multidimensional "tree space" through which search paths can be traced by
optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
algorithms. Although counting the total number of trees for a nontrivial number of input sequences can be complicated by variations in the definition of a tree topology, it is always true that there are more rooted than unrooted trees for a given number of inputs and choice of parameters. Both rooted and unrooted phylogenetic trees can be further generalized to rooted or unrooted
phylogenetic network A phylogenetic network is any graph used to visualize evolutionary relationships (either abstractly or explicitly) between nucleotide sequences, genes, chromosomes, genomes, or species. They are employed when reticulation events such as hybridi ...
s, which allow for the modeling of evolutionary phenomena such as
hybridization Hybridization (or hybridisation) may refer to: *Hybridization (biology), the process of combining different varieties of organisms to create a hybrid *Orbital hybridization, in chemistry, the mixing of atomic orbitals into new hybrid orbitals *Nu ...
or
horizontal gene transfer Horizontal gene transfer (HGT) or lateral gene transfer (LGT) is the movement of genetic material between unicellular and/or multicellular organisms other than by the ("vertical") transmission of DNA from parent to offspring (reproduction). HG ...
.


Coding characters and defining homology


Morphological analysis

The basic problem in morphological phylogenetics is the assembly of a
matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** ''The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...
representing a mapping from each of the taxa being compared to representative measurements for each of the phenotypic characteristics being used as a classifier. The types of phenotypic data used to construct this matrix depend on the taxa being compared; for individual species, they may involve measurements of average body size, lengths or sizes of particular bones or other physical features, or even behavioral manifestations. Of course, since not every possible phenotypic characteristic could be measured and encoded for analysis, the selection of which features to measure is a major inherent obstacle to the method. The decision of which traits to use as a basis for the matrix necessarily represents a hypothesis about which traits of a species or higher taxon are evolutionarily relevant. Morphological studies can be confounded by examples of convergent evolution of phenotypes. A major challenge in constructing useful classes is the high likelihood of inter-taxon overlap in the distribution of the phenotype's variation. The inclusion of extinct taxa in morphological analysis is often difficult due to absence of or incomplete
fossil A fossil (from Classical Latin , ) is any preserved remains, impression, or trace of any once-living thing from a past geological age. Examples include bones, shells, exoskeletons, stone imprints of animals or microbes, objects preserved in ...
records, but has been shown to have a significant effect on the trees produced; in one study only the inclusion of extinct species of
ape Apes (collectively Hominoidea ) are a clade of Old World simians native to sub-Saharan Africa and Southeast Asia (though they were more widespread in Africa, most of Asia, and as well as Europe in prehistory), which together with its sister g ...
s produced a morphologically derived tree that was consistent with that produced from molecular data. Some phenotypic classifications, particularly those used when analyzing very diverse groups of taxa, are discrete and unambiguous; classifying organisms as possessing or lacking a tail, for example, is straightforward in the majority of cases, as is counting features such as eyes or vertebrae. However, the most appropriate representation of continuously varying phenotypic measurements is a controversial problem without a general solution. A common method is simply to sort the measurements of interest into two or more classes, rendering continuous observed variation as discretely classifiable (e.g., all examples with humerus bones longer than a given cutoff are scored as members of one state, and all members whose humerus bones are shorter than the cutoff are scored as members of a second state). This results in an easily manipulated
data set A data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of th ...
but has been criticized for poor reporting of the basis for the class definitions and for sacrificing information compared to methods that use a continuous weighted distribution of measurements. Because morphological data is extremely labor-intensive to collect, whether from literature sources or from field observations, reuse of previously compiled data matrices is not uncommon, although this may propagate flaws in the original matrix into multiple derivative analyses.


Molecular analysis

The problem of character coding is very different in molecular analyses, as the characters in biological sequence data are immediate and discretely defined - distinct
nucleotide Nucleotides are organic molecules consisting of a nucleoside and a phosphate. They serve as monomeric units of the nucleic acid polymers – deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), both of which are essential biomolecules with ...
s in DNA or
RNA Ribonucleic acid (RNA) is a polymeric molecule essential in various biological roles in coding, decoding, regulation and expression of genes. RNA and deoxyribonucleic acid ( DNA) are nucleic acids. Along with lipids, proteins, and carbohyd ...
sequences and distinct
amino acid Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although hundreds of amino acids exist in nature, by far the most important are the alpha-amino acids, which comprise proteins. Only 22 alpha am ...
s in protein sequences. However, defining homology can be challenging due to the inherent difficulties of
multiple sequence alignment Multiple sequence alignment (MSA) may refer to the process or the result of sequence alignment of three or more biological sequences, generally protein, DNA, or RNA. In many cases, the input set of query sequences are assumed to have an evoluti ...
. For a given gapped MSA, several rooted phylogenetic trees can be constructed that vary in their interpretations of which changes are "
mutation In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, mitos ...
s" versus ancestral characters, and which events are insertion mutations or deletion mutations. For example, given only a pairwise alignment with a gap region, it is impossible to determine whether one sequence bears an insertion mutation or the other carries a deletion. The problem is magnified in MSAs with unaligned and nonoverlapping gaps. In practice, sizable regions of a calculated alignment may be discounted in phylogenetic tree construction to avoid integrating noisy data into the tree calculation.


Distance-matrix methods

Distance-matrix methods of phylogenetic analysis explicitly rely on a measure of "genetic distance" between the sequences being classified, and therefore, they require an MSA as an input. Distance is often defined as the fraction of mismatches at aligned positions, with gaps either ignored or counted as mismatches. Distance methods attempt to construct an all-to-all matrix from the sequence query set describing the distance between each sequence pair. From this is constructed a phylogenetic tree that places closely related sequences under the same
interior node In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be co ...
and whose branch lengths closely reproduce the observed distances between sequences. Distance-matrix methods may produce either rooted or unrooted trees, depending on the algorithm used to calculate them. They are frequently used as the basis for progressive and iterative types of
multiple sequence alignment Multiple sequence alignment (MSA) may refer to the process or the result of sequence alignment of three or more biological sequences, generally protein, DNA, or RNA. In many cases, the input set of query sequences are assumed to have an evoluti ...
s. The main disadvantage of distance-matrix methods is their inability to efficiently use information about local high-variation regions that appear across multiple subtrees.


UPGMA and WPGMA

The
UPGMA UPGMA (unweighted pair group method with arithmetic mean) is a simple agglomerative (bottom-up) hierarchical clustering method. The method is generally attributed to Sokal and Michener. The UPGMA method is similar to its ''weighted'' variant, the ...
(''Unweighted Pair Group Method with Arithmetic mean'') and
WPGMA WPGMA (Weighted Pair Group Method with Arithmetic Mean) is a simple agglomerative (bottom-up) hierarchical clustering method, generally attributed to Sokal and Michener. The WPGMA method is similar to its ''unweighted'' variant, the UPGMA method. ...
(''Weighted Pair Group Method with Arithmetic mean'') methods produce rooted trees and require a constant-rate assumption - that is, it assumes an
ultrametric In mathematics, an ultrametric space is a metric space in which the triangle inequality is strengthened to d(x,z)\leq\max\left\. Sometimes the associated metric is also called a non-Archimedean metric or super-metric. Although some of the theorems ...
tree in which the distances from the root to every branch tip are equal.


Neighbor-joining

Neighbor-joining methods apply general
cluster analysis Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of ...
techniques to sequence analysis using genetic distance as a clustering metric. The simple
neighbor-joining In bioinformatics, neighbor joining is a bottom-up (agglomerative) clustering method for the creation of phylogenetic trees, created by Naruya Saitou and Masatoshi Nei in 1987. Usually based on DNA or protein sequence data, the algorithm requir ...
method produces unrooted trees, but it does not assume a constant rate of evolution (i.e., a
molecular clock The molecular clock is a figurative term for a technique that uses the mutation rate of biomolecules to deduce the time in prehistory when two or more life forms diverged. The biomolecular data used for such calculations are usually nucleotid ...
) across lineages.


Fitch–Margoliash method

The Fitch–Margoliash method uses a weighted
least squares The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the re ...
method for clustering based on genetic distance. Closely related sequences are given more weight in the tree construction process to correct for the increased inaccuracy in measuring distances between distantly related sequences. The distances used as input to the algorithm must be normalized to prevent large artifacts in computing relationships between closely related and distantly related groups. The distances calculated by this method must be
linear Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear r ...
; the linearity criterion for distances requires that the
expected value In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a ...
s of the branch lengths for two individual branches must equal the expected value of the sum of the two branch distances - a property that applies to biological sequences only when they have been corrected for the possibility of back mutations at individual sites. This correction is done through the use of a
substitution matrix In bioinformatics and evolutionary biology, a substitution matrix describes the frequency at which a character in a nucleotide sequence or a protein sequence changes to other character states over evolutionary time. The information is often in t ...
such as that derived from the Jukes-Cantor model of DNA evolution. The distance correction is only necessary in practice when the evolution rates differ among branches. Another modification of the algorithm can be helpful, especially in case of concentrated distances (please report to
concentration of measure In mathematics, concentration of measure (about a median) is a principle that is applied in measure theory, probability and combinatorics, and has consequences for other fields such as Banach space theory. Informally, it states that "A random var ...
phenomenon and
curse of dimensionality The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The ...
): that modification, described in, has been shown to improve the efficiency of the algorithm and its robustness. The least-squares criterion applied to these distances is more accurate but less efficient than the neighbor-joining methods. An additional improvement that corrects for correlations between distances that arise from many closely related sequences in the data set can also be applied at increased computational cost. Finding the optimal least-squares tree with any correction factor is
NP-complete In computational complexity theory, a problem is NP-complete when: # it is a problem for which the correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by tryi ...
, so
heuristic A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, ...
search methods like those used in maximum-parsimony analysis are applied to the search through tree space.


Using outgroups

Independent information about the relationship between sequences or groups can be used to help reduce the tree search space and root unrooted trees. Standard usage of distance-matrix methods involves the inclusion of at least one
outgroup Outgroup may refer to: * Outgroup (cladistics), an evolutionary-history concept * Outgroup (sociology) In sociology and social psychology, an in-group is a social group to which a person psychologically identifies as being a member. By contras ...
sequence known to be only distantly related to the sequences of interest in the query set. This usage can be seen as a type of
experimental control A scientific control is an experiment or observation designed to minimize the effects of variables other than the independent variable (i.e. confounding variables). This increases the reliability of the results, often through a comparison betwe ...
. If the outgroup has been appropriately chosen, it will have a much greater
genetic distance Genetic distance is a measure of the genetic divergence between species or between populations within a species, whether the distance measures time from common ancestor or degree of differentiation. Populations with many similar alleles have s ...
and thus a longer branch length than any other sequence, and it will appear near the root of a rooted tree. Choosing an appropriate outgroup requires the selection of a sequence that is moderately related to the sequences of interest; too close a relationship defeats the purpose of the outgroup and too distant adds
noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference aris ...
to the analysis. Care should also be taken to avoid situations in which the species from which the sequences were taken are distantly related, but the gene encoded by the sequences is highly conserved across lineages.
Horizontal gene transfer Horizontal gene transfer (HGT) or lateral gene transfer (LGT) is the movement of genetic material between unicellular and/or multicellular organisms other than by the ("vertical") transmission of DNA from parent to offspring (reproduction). HG ...
, especially between otherwise divergent bacteria, can also confound outgroup usage.


Maximum parsimony

Maximum parsimony In phylogenetics, maximum parsimony is an optimality criterion under which the phylogenetic tree that minimizes the total number of character-state changes (or miminizes the cost of differentially weighted character-state changes) is preferred. ...
(MP) is a method of identifying the potential phylogenetic tree that requires the smallest total number of
evolution Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...
ary events to explain the observed sequence data. Some ways of scoring trees also include a "cost" associated with particular types of evolutionary events and attempt to locate the tree with the smallest total cost. This is a useful approach in cases where not every possible type of event is equally likely - for example, when particular
nucleotide Nucleotides are organic molecules consisting of a nucleoside and a phosphate. They serve as monomeric units of the nucleic acid polymers – deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), both of which are essential biomolecules with ...
s or
amino acid Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although hundreds of amino acids exist in nature, by far the most important are the alpha-amino acids, which comprise proteins. Only 22 alpha am ...
s are known to be more mutable than others. The most naive way of identifying the most parsimonious tree is simple enumeration - considering each possible tree in succession and searching for the tree with the smallest score. However, this is only possible for a relatively small number of sequences or species because the problem of identifying the most parsimonious tree is known to be
NP-hard In computational complexity theory, NP-hardness ( non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard p ...
; consequently a number of
heuristic A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, ...
search methods for
optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
have been developed to locate a highly parsimonious tree, if not the best in the set. Most such methods involve a
steepest descent In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of th ...
-style minimization mechanism operating on a tree rearrangement criterion.


Branch and bound

The
branch and bound Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutio ...
algorithm is a general method used to increase the efficiency of searches for near-optimal solutions of
NP-hard In computational complexity theory, NP-hardness ( non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard p ...
problems first applied to phylogenetics in the early 1980s. Branch and bound is particularly well suited to phylogenetic tree construction because it inherently requires dividing a problem into a tree structure as it subdivides the problem space into smaller regions. As its name implies, it requires as input both a branching rule (in the case of phylogenetics, the addition of the next species or sequence to the tree) and a bound (a rule that excludes certain regions of the search space from consideration, thereby assuming that the optimal solution cannot occupy that region). Identifying a good bound is the most challenging aspect of the algorithm's application to phylogenetics. A simple way of defining the bound is a maximum number of assumed evolutionary changes allowed per tree. A set of criteria known as Zharkikh's rules severely limit the search space by defining characteristics shared by all candidate "most parsimonious" trees. The two most basic rules require the elimination of all but one redundant sequence (for cases where multiple observations have produced identical data) and the elimination of character sites at which two or more states do not occur in at least two species. Under ideal conditions these rules and their associated algorithm would completely define a tree.


Sankoff-Morel-Cedergren algorithm

The Sankoff-Morel-Cedergren algorithm was among the first published methods to simultaneously produce an MSA and a phylogenetic tree for nucleotide sequences. The method uses a
maximum parsimony In phylogenetics, maximum parsimony is an optimality criterion under which the phylogenetic tree that minimizes the total number of character-state changes (or miminizes the cost of differentially weighted character-state changes) is preferred. ...
calculation in conjunction with a scoring function that penalizes gaps and mismatches, thereby favoring the tree that introduces a minimal number of such events (an alternative view holds that the trees to be favored are those that maximize the amount of sequence similarity that can be interpreted as homology, a point of view that may lead to different optimal trees ). The imputed sequences at the
interior node In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be co ...
s of the tree are scored and summed over all the nodes in each possible tree. The lowest-scoring tree sum provides both an optimal tree and an optimal MSA given the scoring function. Because the method is highly computationally intensive, an approximate method in which initial guesses for the interior alignments are refined one node at a time. Both the full and the approximate version are in practice calculated by dynamic programming.


MALIGN and POY

More recent phylogenetic tree/MSA methods use heuristics to isolate high-scoring, but not necessarily optimal, trees. The MALIGN method uses a maximum-parsimony technique to compute a multiple alignment by maximizing a
cladogram A cladogram (from Greek ''clados'' "branch" and ''gramma'' "character") is a diagram used in cladistics to show relations among organisms. A cladogram is not, however, an evolutionary tree because it does not show how ancestors are related to ...
score, and its companion POY uses an iterative method that couples the optimization of the phylogenetic tree with improvements in the corresponding MSA. However, the use of these methods in constructing evolutionary hypotheses has been criticized as biased due to the deliberate construction of trees reflecting minimal evolutionary events. This, in turn, has been countered by the view that such methods should be seen as heuristic approaches to find the trees that maximize the amount of sequence similarity that can be interpreted as homology.


Maximum likelihood

The
maximum likelihood In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statis ...
method uses standard statistical techniques for inferring
probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon ...
s to assign probabilities to particular possible phylogenetic trees. The method requires a
substitution model In biology, a substitution model, also called models of DNA sequence evolution, are Markov models that describe changes over evolutionary time. These models describe evolutionary changes in macromolecules (e.g., DNA sequences) represented as seque ...
to assess the probability of particular
mutation In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, mitos ...
s; roughly, a tree that requires more mutations at interior nodes to explain the observed phylogeny will be assessed as having a lower probability. This is broadly similar to the maximum-parsimony method, but maximum likelihood allows additional statistical flexibility by permitting varying rates of evolution across both lineages and sites. In fact, the method requires that evolution at different sites and along different lineages must be statistically independent. Maximum likelihood is thus well suited to the analysis of distantly related sequences, but it is believed to be computationally intractable to compute due to its NP-hardness. The "pruning" algorithm, a variant of
dynamic programming Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. ...
, is often used to reduce the search space by efficiently calculating the likelihood of subtrees. The method calculates the likelihood for each site in a "linear" manner, starting at a node whose only descendants are leaves (that is, the tips of the tree) and working backwards toward the "bottom" node in nested sets. However, the trees produced by the method are only rooted if the substitution model is irreversible, which is not generally true of biological systems. The search for the maximum-likelihood tree also includes a branch length optimization component that is difficult to improve upon algorithmically; general
global optimization Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the max ...
tools such as the Newton–Raphson method are often used. Some tools that use maximum likelihood to infer phylogenetic trees from variant allelic frequency data (VAFs) include AncesTree and CITUP.


Bayesian inference

Bayesian inference Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and ...
can be used to produce phylogenetic trees in a manner closely related to the maximum likelihood methods. Bayesian methods assume a prior
probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon ...
of the possible trees, which may simply be the probability of any one tree among all the possible trees that could be generated from the data, or may be a more sophisticated estimate derived from the assumption that divergence events such as
speciation Speciation is the evolutionary process by which populations evolve to become distinct species. The biologist Orator F. Cook coined the term in 1906 for cladogenesis, the splitting of lineages, as opposed to anagenesis, phyletic evolution within ...
occur as
stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...
es. The choice of prior distribution is a point of contention among users of Bayesian-inference phylogenetics methods. Implementations of Bayesian methods generally use
Markov chain Monte Carlo In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a ...
sampling algorithms, although the choice of move set varies; selections used in Bayesian phylogenetics include circularly permuting leaf nodes of a proposed tree at each step and swapping descendant subtrees of a random
internal node In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be c ...
between two related trees. The use of Bayesian methods in phylogenetics has been controversial, largely due to incomplete specification of the choice of move set, acceptance criterion, and prior distribution in published work. Bayesian methods are generally held to be superior to parsimony-based methods; they can be more prone to long-branch attraction than maximum likelihood techniques, although they are better able to accommodate missing data. Whereas likelihood methods find the tree that maximizes the probability of the data, a Bayesian approach recovers a tree that represents the most likely clades, by drawing on the posterior distribution. However, estimates of the posterior probability of clades (measuring their 'support') can be quite wide of the mark, especially in clades that aren't overwhelmingly likely. As such, other methods have been put forwards to estimate posterior probability. Some tools that use Bayesian inference to infer phylogenetic trees from variant allelic frequency data (VAFs) include Canopy, EXACT, and PhyloWGS.


Model selection

Molecular phylogenetics methods rely on a defined
substitution model In biology, a substitution model, also called models of DNA sequence evolution, are Markov models that describe changes over evolutionary time. These models describe evolutionary changes in macromolecules (e.g., DNA sequences) represented as seque ...
that encodes a hypothesis about the relative rates of
mutation In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, mitos ...
at various sites along the gene or amino acid sequences being studied. At their simplest, substitution models aim to correct for differences in the rates of transitions and
transversion Transversion, in molecular biology, refers to a point mutation in DNA in which a single (two ring) purine ( A or G) is changed for a (one ring) pyrimidine ( T or C), or vice versa. A transversion can be spontaneous, or it can be caused by ioni ...
s in nucleotide sequences. The use of substitution models is necessitated by the fact that the
genetic distance Genetic distance is a measure of the genetic divergence between species or between populations within a species, whether the distance measures time from common ancestor or degree of differentiation. Populations with many similar alleles have s ...
between two sequences increases linearly only for a short time after the two sequences diverge from each other (alternatively, the distance is linear only shortly before
coalescence Coalescence may refer to: * Coalescence (chemistry), the process by which two or more separate masses of miscible substances seem to "pull" each other together should they make the slightest contact * Coalescence (computer science), the merging o ...
). The longer the amount of time after divergence, the more likely it becomes that two mutations occur at the same nucleotide site. Simple genetic distance calculations will thus undercount the number of mutation events that have occurred in evolutionary history. The extent of this undercount increases with increasing time since divergence, which can lead to the phenomenon of
long branch attraction In phylogenetics, long branch attraction (LBA) is a form of systematic error whereby distantly related lineages are incorrectly inferred to be closely related. LBA arises when the amount of molecular or morphological change accumulated within a lin ...
, or the misassignment of two distantly related but convergently evolving sequences as closely related. The maximum parsimony method is particularly susceptible to this problem due to its explicit search for a tree representing a minimum number of distinct evolutionary events.


Types of models

All substitution models assign a set of weights to each possible change of state represented in the sequence. The most common model types are implicitly reversible because they assign the same weight to, for example, a G>C nucleotide mutation as to a C>G mutation. The simplest possible model, the Jukes-Cantor model, assigns an equal probability to every possible change of state for a given nucleotide base. The rate of change between any two distinct nucleotides will be one-third of the overall substitution rate. More advanced models distinguish between transitions and
transversion Transversion, in molecular biology, refers to a point mutation in DNA in which a single (two ring) purine ( A or G) is changed for a (one ring) pyrimidine ( T or C), or vice versa. A transversion can be spontaneous, or it can be caused by ioni ...
s. The most general possible time-reversible model, called the GTR model, has six mutation rate parameters. An even more generalized model known as the general 12-parameter model breaks time-reversibility, at the cost of much additional complexity in calculating genetic distances that are consistent among multiple lineages. One possible variation on this theme adjusts the rates so that overall GC content - an important measure of DNA double helix stability - varies over time. Models may also allow for the variation of rates with positions in the input sequence. The most obvious example of such variation follows from the arrangement of nucleotides in protein-coding genes into three-base
codon The genetic code is the set of rules used by living cells to translate information encoded within genetic material ( DNA or RNA sequences of nucleotide triplets, or codons) into proteins. Translation is accomplished by the ribosome, which links p ...
s. If the location of the
open reading frame In molecular biology, open reading frames (ORFs) are defined as spans of DNA sequence between the start and stop codons. Usually, this is considered within a studied region of a prokaryotic DNA sequence, where only one of the six possible readin ...
(ORF) is known, rates of mutation can be adjusted for position of a given site within a codon, since it is known that
wobble base pair A wobble base pair is a pairing between two nucleotides in RNA molecules that does not follow Watson-Crick base pair rules. The four main wobble base pairs are guanine-uracil (G-U), hypoxanthine-uracil (I-U), hypoxanthine-adenine (I-A), and hypox ...
ing can allow for higher mutation rates in the third nucleotide of a given codon without affecting the codon's meaning in the
genetic code The genetic code is the set of rules used by living cells to translate information encoded within genetic material ( DNA or RNA sequences of nucleotide triplets, or codons) into proteins. Translation is accomplished by the ribosome, which links ...
. A less hypothesis-driven example that does not rely on ORF identification simply assigns to each site a rate randomly drawn from a predetermined distribution, often the
gamma distribution In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-square distribution are special cases of the gamma distr ...
or
log-normal distribution In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a normal ...
. Finally, a more conservative estimate of rate variations known as the covarion method allows autocorrelated variations in rates, so that the mutation rate of a given site is correlated across sites and lineages.


Choosing the best model

The selection of an appropriate model is critical for the production of good phylogenetic analyses, both because underparameterized or overly restrictive models may produce aberrant behavior when their underlying assumptions are violated, and because overly complex or overparameterized models are computationally expensive and the parameters may be overfit. The most common method of model selection is the
likelihood ratio test In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models based on the ratio of their likelihoods, specifically one found by maximization over the entire parameter space and another found after im ...
(LRT), which produces a likelihood estimate that can be interpreted as a measure of "
goodness of fit The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measure ...
" between the model and the input data. However, care must be taken in using these results, since a more complex model with more parameters will always have a higher likelihood than a simplified version of the same model, which can lead to the naive selection of models that are overly complex. For this reason model selection computer programs will choose the simplest model that is not significantly worse than more complex substitution models. A significant disadvantage of the LRT is the necessity of making a series of pairwise comparisons between models; it has been shown that the order in which the models are compared has a major effect on the one that is eventually selected. An alternative model selection method is the
Akaike information criterion The Akaike information criterion (AIC) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to e ...
(AIC), formally an estimate of the
Kullback–Leibler divergence In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted D_\text(P \parallel Q), is a type of statistical distance: a measure of how one probability distribution ''P'' is different fro ...
between the true model and the model being tested. It can be interpreted as a likelihood estimate with a correction factor to penalize overparameterized models. The AIC is calculated on an individual model rather than a pair, so it is independent of the order in which models are assessed. A related alternative, the
Bayesian information criterion In statistics, the Bayesian information criterion (BIC) or Schwarz information criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models; models with lower BIC are generally preferred. It is based, in part, on ...
(BIC), has a similar basic interpretation but penalizes complex models more heavily. Determining the most suitable model for phylogeny reconstruction constitutes a fundamental step in numerous evolutionary studies. However, various criteria for model selection are leading to debate over which criterion is preferable. It has recently been shown that, when topologies and ancestral sequence reconstruction are the desired output, choosing one criterion over another is not crucial. Instead, using the most complex nucleotide substitution model, GTR+I +G, leads to similar results for the inference of tree topology and ancestral sequences. A comprehensive step-by-step protocol on constructing phylogenetic trees, including DNA/Amino Acid contiguous sequence assembly, multiple sequence alignment, model-test (testing best-fitting substitution models) and phylogeny reconstruction using Maximum Likelihood and Bayesian Inference, is available at ''Protocol Exchange'' A non traditional way of evaluating the phylogenetic tree is to compare it with clustering result. One can use a Multidimensional Scaling technique, so called Interpolative Joining to do dimensionality reduction to visualize the clustering result for the sequences in 3D, and then map the phylogenetic tree onto the clustering result. A better tree usually has a higher correlation with the clustering result.


Evaluating tree support

As with all statistical analysis, the estimation of phylogenies from character data requires an evaluation of confidence. A number of methods exist to test the amount of support for a phylogenetic tree, either by evaluating the support for each sub-tree in the phylogeny (nodal support) or evaluating whether the phylogeny is significantly different from other possible trees (alternative tree hypothesis tests).


Nodal support

The most common method for assessing tree support is to evaluate the statistical support for each node on the tree. Typically, a node with very low support is not considered valid in further analysis, and visually may be collapsed into a
polytomy An internal node of a phylogenetic tree is described as a polytomy or multifurcation if (i) it is in a rooted tree and is linked to three or more child subtrees or (ii) it is in an unrooted tree and is attached to four or more branches. A tr ...
to indicate that relationships within a clade are unresolved.


Consensus tree

Many methods for assessing nodal support involve consideration of multiple phylogenies. The consensus tree summarizes the nodes that are shared among a set of trees. In a *strict consensus,* only nodes found in every tree are shown, and the rest are collapsed into an unresolved
polytomy An internal node of a phylogenetic tree is described as a polytomy or multifurcation if (i) it is in a rooted tree and is linked to three or more child subtrees or (ii) it is in an unrooted tree and is attached to four or more branches. A tr ...
. Less conservative methods, such as the *majority-rule consensus* tree, consider nodes that are supported by a given percentage of trees under consideration (such as at least 50%). For example, in maximum parsimony analysis, there may be many trees with the same parsimony score. A strict consensus tree would show which nodes are found in all equally parsimonious trees, and which nodes differ. Consensus trees are also used to evaluate support on phylogenies reconstructed with Bayesian inference (see below).


Bootstrapping and jackknifing

In statistics, the bootstrap is a method for inferring the variability of data that has an unknown distribution using pseudoreplications of the original data. For example, given a set of 100 data points, a pseudoreplicate is a data set of the same size (100 points) randomly sampled from the original data, with replacement. That is, each original data point may be represented more than once in the pseudoreplicate, or not at all. Statistical support involves evaluation of whether the original data has similar properties to a large set of pseudoreplicates. In phylogenetics, bootstrapping is conducted using the columns of the character matrix. Each pseudoreplicate contains the same number of species (rows) and characters (columns) randomly sampled from the original matrix, with replacement. A phylogeny is reconstructed from each pseudoreplicate, with the same methods used to reconstruct the phylogeny from the original data. For each node on the phylogeny, the nodal support is the percentage of pseudoreplicates containing that node. The statistical rigor of the bootstrap test has been empirically evaluated using viral populations with known evolutionary histories, finding that 70% bootstrap support corresponds to a 95% probability that the clade exists. However, this was tested under ideal conditions (e.g. no change in evolutionary rates, symmetric phylogenies). In practice, values above 70% are generally supported and left to the researcher or reader to evaluate confidence. Nodes with support lower than 70% are typically considered unresolved. Jackknifing in phylogenetics is a similar procedure, except the columns of the matrix are sampled without replacement. Pseudoreplicates are generated by randomly subsampling the data—for example, a "10% jackknife" would involve randomly sampling 10% of the matrix many times to evaluate nodal support.


Posterior probability

Reconstruction of phylogenies using
Bayesian inference Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and ...
generates a posterior distribution of highly probable trees given the data and evolutionary model, rather than a single "best" tree. The trees in the posterior distribution generally have many different topologies. When the input data is variant allelic frequency data (VAF), the tool EXACT can compute the probabilities of trees exactly, for small, biologically relevant tree sizes, by exhaustively searching the entire tree space. Most Bayesian inference methods utilize a Markov-chain Monte Carlo iteration, and the initial steps of this chain are not considered reliable reconstructions of the phylogeny. Trees generated early in the chain are usually discarded as
burn-in Burn-in is the process by which components of a system are exercised before being placed in service (and often, before the system being completely assembled from those components). This testing process will force certain failures to occur under ...
. The most common method of evaluating nodal support in a Bayesian phylogenetic analysis is to calculate the percentage of trees in the posterior distribution (post-burn-in) which contain the node. The statistical support for a node in Bayesian inference is expected to reflect the probability that a clade really exists given the data and evolutionary model. Therefore, the threshold for accepting a node as supported is generally higher than for bootstrapping.


Step counting methods

Bremer support counts the number of extra steps needed to contradict a clade.


Shortcomings

These measures each have their weaknesses. For example, smaller or larger clades tend to attract larger support values than mid-sized clades, simply as a result of the number of taxa in them. Bootstrap support can provide high estimates of node support as a result of noise in the data rather than the true existence of a clade.


Limitations and workarounds

Ultimately, there is no way to measure whether a particular phylogenetic hypothesis is accurate or not, unless the true relationships among the taxa being examined are already known (which may happen with bacteria or viruses under laboratory conditions). The best result an empirical phylogeneticist can hope to attain is a tree with branches that are well supported by the available evidence. Several potential pitfalls have been identified:


Homoplasy

Certain characters are more likely to evolve convergently than others; logically, such characters should be given less weight in the reconstruction of a tree. Weights in the form of a model of evolution can be inferred from sets of molecular data, so that
maximum likelihood In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statis ...
or
Bayesian Thomas Bayes (/beɪz/; c. 1701 – 1761) was an English statistician, philosopher, and Presbyterian minister. Bayesian () refers either to a range of concepts and approaches that relate to statistical methods based on Bayes' theorem, or a follower ...
methods can be used to analyze them. For molecular sequences, this problem is exacerbated when the taxa under study have diverged substantially. As time since the divergence of two taxa increase, so does the probability of multiple substitutions on the same site, or back mutations, all of which result in homoplasies. For morphological data, unfortunately, the only objective way to determine convergence is by the construction of a tree – a somewhat circular method. Even so, weighting homoplasious characters does indeed lead to better-supported trees. Further refinement can be brought by weighting changes in one direction higher than changes in another; for instance, the presence of thoracic wings almost guarantees placement among the pterygote insects because, although wings are often lost secondarily, there is no evidence that they have been gained more than once.


Horizontal gene transfer

In general, organisms can inherit genes in two ways: vertical gene transfer and
horizontal gene transfer Horizontal gene transfer (HGT) or lateral gene transfer (LGT) is the movement of genetic material between unicellular and/or multicellular organisms other than by the ("vertical") transmission of DNA from parent to offspring (reproduction). HG ...
. Vertical gene transfer is the passage of genes from parent to offspring, and horizontal (also called lateral) gene transfer occurs when genes jump between unrelated organisms, a common phenomenon especially in
prokaryote A prokaryote () is a single-celled organism that lacks a nucleus and other membrane-bound organelles. The word ''prokaryote'' comes from the Greek πρό (, 'before') and κάρυον (, 'nut' or 'kernel').Campbell, N. "Biology:Concepts & Connec ...
s; a good example of this is the acquired
antibiotic resistance Antimicrobial resistance (AMR) occurs when microbes evolve mechanisms that protect them from the effects of antimicrobials. All classes of microbes can evolve resistance. Fungi evolve antifungal resistance. Viruses evolve antiviral resistance. ...
as a result of gene exchange between various bacteria leading to multi-drug-resistant bacterial species. There have also been well-documented cases of horizontal gene transfer between eukaryotes. Horizontal gene transfer has complicated the determination of phylogenies of organisms, and inconsistencies in phylogeny have been reported among specific groups of organisms depending on the genes used to construct evolutionary trees. The only way to determine which genes have been acquired vertically and which horizontally is to parsimoniously assume that the largest set of genes that have been inherited together have been inherited vertically; this requires analyzing a large number of genes.


Hybrids, speciation, introgressions and incomplete lineage sorting

The basic assumption underlying the mathematical model of cladistics is a situation where species split neatly in bifurcating fashion. While such an assumption may hold on a larger scale (bar horizontal gene transfer, see above),
speciation Speciation is the evolutionary process by which populations evolve to become distinct species. The biologist Orator F. Cook coined the term in 1906 for cladogenesis, the splitting of lineages, as opposed to anagenesis, phyletic evolution within ...
is often much less orderly. Research since the cladistic method was introduced has shown that
hybrid speciation Hybrid speciation is a form of speciation where hybridization between two different species leads to a new species, reproductively isolated from the parent species. Previously, reproductive isolation between two species and their parents was tho ...
, once thought rare, is in fact quite common, particularly in plants. Also paraphyletic speciation is common, making the assumption of a bifurcating pattern unsuitable, leading to
phylogenetic network A phylogenetic network is any graph used to visualize evolutionary relationships (either abstractly or explicitly) between nucleotide sequences, genes, chromosomes, genomes, or species. They are employed when reticulation events such as hybridi ...
s rather than trees.
Introgression Introgression, also known as introgressive hybridization, in genetics is the transfer of genetic material from one species into the gene pool of another by the repeated backcrossing of an interspecific hybrid with one of its parent species. Intro ...
can also move genes between otherwise distinct species and sometimes even genera, complicating phylogenetic analysis based on genes. This phenomenon can contribute to "incomplete lineage sorting" and is thought to be a common phenomenon across a number of groups. In species level analysis this can be dealt with by larger sampling or better whole genome analysis. Often the problem is avoided by restricting the analysis to fewer, not closely related specimens.


Taxon sampling

Owing to the development of advanced sequencing techniques in
molecular biology Molecular biology is the branch of biology that seeks to understand the molecular basis of biological activity in and between cells, including biomolecular synthesis, modification, mechanisms, and interactions. The study of chemical and physi ...
, it has become feasible to gather large amounts of data (DNA or amino acid sequences) to infer phylogenetic hypotheses. For example, it is not rare to find studies with character matrices based on whole
mitochondrial A mitochondrion (; ) is an organelle found in the Cell (biology), cells of most Eukaryotes, such as animals, plants and Fungus, fungi. Mitochondria have a double lipid bilayer, membrane structure and use aerobic respiration to generate adenosi ...
genomes (~16,000 nucleotides, in many animals). However, simulations have shown that it is more important to increase the number of taxa in the matrix than to increase the number of characters, because the more taxa there are, the more accurate and more robust is the resulting phylogenetic tree. This may be partly due to the breaking up of long branches.


Phylogenetic signal

Another important factor that affects the accuracy of tree reconstruction is whether the data analyzed actually contain a useful phylogenetic signal, a term that is used generally to denote whether a character evolves slowly enough to have the same state in closely related taxa as opposed to varying randomly. Tests for phylogenetic signal exist.


Continuous characters

Morphological characters that sample a continuum may contain phylogenetic signal, but are hard to code as discrete characters. Several methods have been used, one of which is gap coding, and there are variations on gap coding. In the original form of gap coding:
group means for a character are first ordered by size. The pooled within-group standard deviation is calculated ... and differences between adjacent means ... are compared relative to this standard deviation. Any pair of adjacent means is considered different and given different integer scores ... if the means are separated by a "gap" greater than the within-group standard deviation ... times some arbitrary constant.
If more taxa are added to the analysis, the gaps between taxa may become so small that all information is lost. Generalized gap coding works around that problem by comparing individual pairs of taxa rather than considering one set that contains all of the taxa.


Missing data

In general, the more data that are available when constructing a tree, the more accurate and reliable the resulting tree will be. Missing data are no more detrimental than simply having fewer data, although the impact is greatest when most of the missing data are in a small number of taxa. Concentrating the missing data across a small number of characters produces a more robust tree.


The role of fossils

Because many characters involve embryological, or soft-tissue or molecular characters that (at best) hardly ever fossilize, and the interpretation of fossils is more ambiguous than that of living taxa, extinct taxa almost invariably have higher proportions of missing data than living ones. However, despite these limitations, the inclusion of fossils is invaluable, as they can provide information in sparse areas of trees, breaking up long branches and constraining intermediate character states; thus, fossil taxa contribute as much to tree resolution as modern taxa. Fossils can also constrain the age of lineages and thus demonstrate how consistent a tree is with the stratigraphic record; stratocladistics incorporates age information into data matrices for phylogenetic analyses.


See also

*
List of phylogenetics software This list of phylogenetics software is a compilation of computational phylogenetics software used to produce phylogenetic trees. Such tools are commonly used in comparative genomics, cladistics, and bioinformatics. Methods for estimating phylogenie ...
*
Bayesian network A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Bay ...
*
Bioinformatics Bioinformatics () is an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combine ...
*
Cladistics Cladistics (; ) is an approach to biological classification in which organisms are categorized in groups ("clades") based on hypotheses of most recent common ancestry. The evidence for hypothesized relationships is typically shared derived cha ...
*
Computational biology Computational biology refers to the use of data analysis, mathematical modeling and computational simulations to understand biological systems and relationships. An intersection of computer science, biology, and big data, the field also has fou ...
* Disk-covering method *
Evolutionary dynamics Evolutionary dynamics is the study of the mathematical principles according to which biological organisms as well as cultural ideas evolve and evolved. This is mostly achieved through the mathematical discipline of population genetics, along with ...
*
Microbial phylogenetics Microbial phylogenetics is the study of the manner in which various groups of microorganisms are genetically related. This helps to trace their evolution. To study these relationships biologists rely on comparative genomics, as physiology and compa ...
*
PHYLIP PHYLogeny Inference Package (PHYLIP) is a free computational phylogenetics package of programs for inferring evolutionary trees (Phylogenetics, phylogenies). It consists of 65 Porting, portable programs, i.e., the source code is written in the prog ...
*
Phylogenetic comparative methods Phylogenetic comparative methods (PCMs) use information on the historical relationships of lineages ( phylogenies) to test evolutionary hypotheses. The comparative method has a long history in evolutionary biology; indeed, Charles Darwin used diff ...
*
Phylogenetic tree A phylogenetic tree (also phylogeny or evolutionary tree Felsenstein J. (2004). ''Inferring Phylogenies'' Sinauer Associates: Sunderland, MA.) is a branching diagram or a tree showing the evolutionary relationships among various biological spec ...
*
Phylogenetics In biology, phylogenetics (; from Greek φυλή/ φῦλον [] "tribe, clan, race", and wikt:γενετικός, γενετικός [] "origin, source, birth") is the study of the evolutionary history and relationships among or within groups o ...
*
Population genetics Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and pop ...
*
Quantitative comparative linguistics Quantitative comparative linguistics is the use of quantitative analysis as applied to comparative linguistics. Examples include the statistical fields of lexicostatistics and glottochronology, and the borrowing of phylogenetics from biology. His ...
*
Statistical classification In statistics, classification is the problem of identifying which of a set of categories (sub-populations) an observation (or observations) belongs to. Examples are assigning a given email to the "spam" or "non-spam" class, and assigning a diagno ...
*
Systematics Biological systematics is the study of the diversification of living forms, both past and present, and the relationships among living things through time. Relationships are visualized as evolutionary trees (synonyms: cladograms, phylogenetic tr ...
*
Taxonomy (biology) In biology, taxonomy () is the scientific study of naming, defining ( circumscribing) and classifying groups of biological organisms based on shared characteristics. Organisms are grouped into taxa (singular: taxon) and these groups are given ...


References


Further reading

* * * *


External links

* {{Use dmy dates, date=April 2017
Phylogenetics In biology, phylogenetics (; from Greek φυλή/ φῦλον [] "tribe, clan, race", and wikt:γενετικός, γενετικός [] "origin, source, birth") is the study of the evolutionary history and relationships among or within groups o ...