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 descendants, nor does it show how much they have changed, so many differing evolutionary trees can be consistent with the same cladogram. A cladogram uses lines that branch off in different directions ending at a clade , a group of organisms with a last common ancestor . There are many shapes of cladograms but they all have lines that branch off from other lines. The lines can be traced back to where they branch off. These branching off points represent a hypothetical ancestor (not an actual entity) which can be inferred to exhibit the traits shared among the terminal taxa above it. This hypothetical ancestor might then provide clues about the order of evolution of various features, adaptation, and other evolutionary narratives about ancestors. Although traditionally such cladograms were generated largely on the basis of morphological characters, DNA and RNA sequencing data and computational phylogenetics are now very commonly used in the generation of cladograms, either on their own or in combination with morphology.
71-445: The characteristics used to create a cladogram can be roughly categorized as either morphological (synapsid skull, warm blooded, notochord , unicellular, etc.) or molecular (DNA, RNA, or other genetic information). Prior to the advent of DNA sequencing, cladistic analysis primarily used morphological data. Behavioral data (for animals) may also be used. As DNA sequencing has become cheaper and easier, molecular systematics has become
142-445: A t e s {\displaystyle n.states} , c i occupies a range from 1 to ( n . s t a t e s − 1 ) / ( n . t a x a − ⌈ n . t a x a / n . s t a t e s ⌉ ) {\displaystyle (n.states-1)/(n.taxa-\lceil n.taxa/n.states\rceil )} . The retention index (RI)
213-445: A metric to measure how consistent a candidate cladogram is with the data. Most cladogram algorithms use the mathematical techniques of optimization and minimization. In general, cladogram generation algorithms must be implemented as computer programs, although some algorithms can be performed manually when the data sets are modest (for example, just a few species and a couple of characteristics). Some algorithms are useful only when
284-450: A 'first-order condition' or a set of first-order conditions. Optima of equality-constrained problems can be found by the Lagrange multiplier method. The optima of problems with equality and/or inequality constraints can be found using the ' Karush–Kuhn–Tucker conditions '. While the first derivative test identifies points that might be extrema, this test does not distinguish a point that is
355-422: A candidate solution satisfies the first-order conditions, then the satisfaction of the second-order conditions as well is sufficient to establish at least local optimality. The envelope theorem describes how the value of an optimal solution changes when an underlying parameter changes. The process of computing this change is called comparative statics . The maximum theorem of Claude Berge (1963) describes
426-536: A character in a phylogenetic analysis as they do not contribute anything to our understanding of relationships. However, homoplasy is often not evident from inspection of the character itself (as in DNA sequence, for example), and is then detected by its incongruence (unparsimonious distribution) on a most-parsimonious cladogram. Note that characters that are homoplastic may still contain phylogenetic signal . A well-known example of homoplasy due to convergent evolution would be
497-523: A common lineal origin, it is now viewed as analogous, convergent , or from a different lineal origin. Pikaia appears to have a proto-notochord, and notochords are present in several basal chordates such as Haikouella , Haikouichthys , and Myllokunmingia , all from the Cambrian . The Ordovician oceans included many diverse species of Agnatha and early Gnathostomata which possessed notochords, either with attached bony elements or without, most notably
568-410: A critical role in signaling the development of motor neurons. The secretion of SHH by the notochord establishes the ventral pole of the dorsal-ventral axis in the developing embryo. The notochord is the defining feature ( synapomorphy ) of chordates , and was present throughout life in many of the earliest chordates. Although the stomochord of hemichordates was once thought to be homologous or from
639-417: A dataset, the degree to which each character carries phylogenetic information, and the fashion in which additive characters are coded, rendering it unfit for purpose. c i occupies a range from 1 to 1/[ n.taxa /2] in binary characters with an even state distribution; its minimum value is larger when states are not evenly spread. In general, for a binary or non-binary character with n . s t
710-462: A fully random dataset, and negative values indicate more homoplasy still (and tend only to occur in contrived examples). The HER is presented as the best measure of homoplasy currently available. Notochord In zoology and developmental anatomy , the notochord is an elastic, rod-like anatomical structure found in animals of the phylum Chordata . A notochord is one of five synapomorphies , or shared derived characteristics, used to identify
781-464: A homologous structure, the axochord, that was present in annelid-like ancestors of the chordates). Deciding between these two scenarios (or possibly another yet to be proposed) should be facilitated by much more thorough studies of gene regulatory networks in a wide spectrum of animals. In most vertebrates, the notochord develops into secondary structures. In other chordates , the notochord is retained as an essential anatomical structure. The evolution of
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#1732869839972852-559: A large area of applied mathematics . Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete : An optimization problem can be represented in the following way: Such a formulation is called an optimization problem or a mathematical programming problem (a term not directly related to computer programming , but still in use for example in linear programming – see History below). Many real-world and theoretical problems may be modeled in this general framework. Since
923-457: A larger clade. The incongruence length difference test (ILD) is a measurement of how the combination of different datasets (e.g. morphological and molecular, plastid and nuclear genes) contributes to a longer tree. It is measured by first calculating the total tree length of each partition and summing them. Then replicates are made by making randomly assembled partitions consisting of the original partitions. The lengths are summed. A p value of 0.01
994-613: A minimum from one that is a maximum or one that is neither. When the objective function is twice differentiable, these cases can be distinguished by checking the second derivative or the matrix of second derivatives (called the Hessian matrix ) in unconstrained problems, or the matrix of second derivatives of the objective function and the constraints called the bordered Hessian in constrained problems. The conditions that distinguish maxima, or minima, from other stationary points are called 'second-order conditions' (see ' Second derivative test '). If
1065-451: A more and more popular way to infer phylogenetic hypotheses. Using a parsimony criterion is only one of several methods to infer a phylogeny from molecular data. Approaches such as maximum likelihood , which incorporate explicit models of sequence evolution, are non-Hennigian ways to evaluate sequence data. Another powerful method of reconstructing phylogenies is the use of genomic retrotransposon markers , which are thought to be less prone to
1136-420: A second notochord near the dorsal neural tube, 180 degrees opposite of the normal notochord location, one can induce the formation of motor neurons in the dorsal tube. Motor neuron formation generally occurs in the ventral neural tube, while the dorsal tube generally forms sensory cells . The notochord secretes a protein called sonic hedgehog (SHH), a key morphogen regulating organogenesis and having
1207-452: A species as a chordate. The notochord is derived from the embryonic mesoderm and consists of an inner core of vacuolated cells filled with glycoproteins , covered by two helical collagen - elastin sheaths. It lies along the rostral - caudal axis of the body (i.e. longitudinally or " head to tail "), dorsal to the gut tube and ventral to the dorsal nerve cord . Some chordates, such as tunicates , develop notochord during
1278-493: A structural design, one would desire a design that is both light and rigid. When two objectives conflict, a trade-off must be created. There may be one lightest design, one stiffest design, and an infinite number of designs that are some compromise of weight and rigidity. The set of trade-off designs that improve upon one criterion at the expense of another is known as the Pareto set . The curve created plotting weight against stiffness of
1349-409: Is a character state that is shared by two or more taxa due to some cause other than common ancestry. The two main types of homoplasy are convergence (evolution of the "same" character in at least two distinct lineages) and reversion (the return to an ancestral character state). Characters that are obviously homoplastic, such as white fur in different lineages of Arctic mammals, should not be included as
1420-432: Is a transient structure ventral to the notochord, and is primarily responsible for correct development of the dorsal aorta. Notochord flexion , when the notochord bends to form a part of the developing caudal fin, is a hallmark of an early growth stage of some fish. By the age of 4, all notochord residue is replaced by a population of chondrocyte -like cells of unclear origin. Persistence of notochordal cells within
1491-458: Is always necessary to continuously evaluate the quality of a data model by using a cost function where a minimum implies a set of possibly optimal parameters with an optimal (lowest) error. Typically, A is some subset of the Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , often specified by a set of constraints , equalities or inequalities that
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#17328698399721562-455: Is delegated to the decision maker. In other words, defining the problem as multi-objective optimization signals that some information is missing: desirable objectives are given but combinations of them are not rated relative to each other. In some cases, the missing information can be derived by interactive sessions with the decision maker. Multi-objective optimization problems have been generalized further into vector optimization problems where
1633-419: Is found ventral to the neural tube . Notogenesis is the development of the notochord by epiblasts that form the floor of the amnion cavity. The progenitor notochord is derived from cells migrating from the primitive node and pit. The notochord forms during gastrulation and soon after induces the formation of the neural plate ( neurulation ), synchronizing the development of the neural tube . On
1704-449: Is found in the nucleus pulposus of the intervertebral discs. Isolated notochordal remnants may escape their lineage-specific destination in the nucleus pulposus and instead attach to the outer surfaces of the vertebral bodies , from which notochordal cells largely regress. During development of amphibians and fish, the notochord induces development of the hypochord through secretion of vascular endothelial growth factor . The hypochord
1775-404: Is no such maximum as the objective function is unbounded, so the answer is " infinity " or " undefined ". Consider the following notation: or equivalently This represents the value (or values) of the argument x in the interval (−∞,−1] that minimizes (or minimize) the objective function x + 1 (the actual minimum value of that function is not what the problem asks for). In this case,
1846-509: Is not guaranteed that different solutions will be obtained even with different starting points in multiple runs of the algorithm. Common approaches to global optimization problems, where multiple local extrema may be present include evolutionary algorithms , Bayesian optimization and simulated annealing . The satisfiability problem , also called the feasibility problem , is just the problem of finding any feasible solution at all without regard to objective value. This can be regarded as
1917-461: Is null or negative. The extreme value theorem of Karl Weierstrass states that a continuous real-valued function on a compact set attains its maximum and minimum value. More generally, a lower semi-continuous function on a compact set attains its minimum; an upper semi-continuous function on a compact set attains its maximum point or view. One of Fermat's theorems states that optima of unconstrained problems are found at stationary points , where
1988-630: Is obtained by multiplying the CI by the RI; in effect this stretches the range of the CI such that its minimum theoretically attainable value is rescaled to 0, with its maximum remaining at 1. The homoplasy index (HI) is simply 1 − CI. This measures the amount of homoplasy observed on a tree relative to the maximum amount of homoplasy that could theoretically be present – 1 − (observed homoplasy excess) / (maximum homoplasy excess). A value of 1 indicates no homoplasy; 0 represents as much homoplasy as there would be in
2059-409: Is obtained for 100 replicates if 99 replicates have longer combined tree lengths. Some measures attempt to measure the amount of homoplasy in a dataset with reference to a tree, though it is not necessarily clear precisely what property these measures aim to quantify The consistency index (CI) measures the consistency of a tree to a set of data – a measure of the minimum amount of homoplasy implied by
2130-526: Is usually done by comparison to the character states of one or more outgroups . States shared between the outgroup and some members of the in-group are symplesiomorphies; states that are present only in a subset of the in-group are synapomorphies. Note that character states unique to a single terminal (autapomorphies) do not provide evidence of grouping. The choice of an outgroup is a crucial step in cladistic analysis because different outgroups can produce trees with profoundly different topologies. A homoplasy
2201-423: The conodonts , placoderms , and ostracoderms . Even after the evolution of the vertebral column in chondrichthyes and osteichthyes , these taxa remained common and are well represented in the fossils record. Several species (see list below) have reverted to the primitive state, retaining the notochord into adulthood, though the reasons for this are not well understood. Scenarios for the evolutionary origin of
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2272-545: The gut tube and ventral to the neural tube . The notochord is composed primarily of a glycoproteins core that is encased in a sheath of collagen fibers. This is wound into two opposing helices . The glycoproteins are stored in vacuolated, turgid cells, which are covered with caveolae on their cell surface. The angle between these fibers determines whether increased pressure in the core will result in shortening and thickening versus lengthening and thinning. Alternating contraction of muscle fibers attached to each side of
2343-403: The larval stage but lose it through subsequent stages into adulthood. The notochord is important for signaling the dorso-ventral patterning of cells coming from the mesodermal progenitors. This helps form the precursors needed for certain organs and the embryo to develop. In summary, the notochord plays essential roles in embryonic development. The notochord provides a directional reference to
2414-412: The mesoderm , which grows medially and surrounds it. From the mesoderm surrounding the neural tube and notochord, the skull , vertebral column, and the membranes of the brain and medulla spinalis are developed. Because it originates from the primitive node and is ultimately positioned with the mesodermal space, it is considered to be derived from mesoderm. A postembryonic vestige of the notochord
2485-410: The ventral aspect of the neural groove, an axial thickening of the endoderm takes place. (In bipedal chordates, e.g. humans, this surface is properly referred to as the anterior surface). This thickening appears as a furrow (the chordal furrow) the margins of which anastomose (come into contact), and so convert it into a solid rod of polygonal-shaped cells (the notochord) which is then separated from
2556-591: The (partial) ordering is no longer given by the Pareto ordering. Optimization problems are often multi-modal; that is, they possess multiple good solutions. They could all be globally good (same cost function value) or there could be a mix of globally good and locally good solutions. Obtaining all (or at least some of) the multiple solutions is the goal of a multi-modal optimizer. Classical optimization techniques due to their iterative approach do not perform satisfactorily when they are used to obtain multiple solutions, since it
2627-434: The adult animal, and the notochord is not vacuolated. In all vertebrates other than the hagfish , the notochord is present only during early embryonic development and is later replaced by the bony and/or cartilaginous vertebral column , with its original structure being integrated into the intervertebral discs as the nucleus pulposus . The notochord is a long, rod-like midline structure that develops dorsal to
2698-411: The answer is x = −1 , since x = 0 is infeasible, that is, it does not belong to the feasible set . Similarly, or equivalently represents the { x , y } pair (or pairs) that maximizes (or maximize) the value of the objective function x cos y , with the added constraint that x lie in the interval [−5,5] (again, the actual maximum value of the expression does not matter). In this case,
2769-408: The best designs is known as the Pareto frontier . A design is judged to be "Pareto optimal" (equivalently, "Pareto efficient" or in the Pareto set) if it is not dominated by any other design: If it is worse than another design in some respects and no better in any respect, then it is dominated and is not Pareto optimal. The choice among "Pareto optimal" solutions to determine the "favorite solution"
2840-431: The character, "presence of wings". Although the wings of birds, bats , and insects serve the same function, each evolved independently, as can be seen by their anatomy . If a bird, bat, and a winged insect were scored for the character, "presence of wings", a homoplasy would be introduced into the dataset, and this could potentially confound the analysis, possibly resulting in a false hypothesis of relationships. Of course,
2911-434: The characteristic data are molecular (DNA, RNA); other algorithms are useful only when the characteristic data are morphological. Other algorithms can be used when the characteristic data includes both molecular and morphological data. Algorithms for cladograms or other types of phylogenetic trees include least squares , neighbor-joining , parsimony , maximum likelihood , and Bayesian inference . Biologists sometimes use
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2982-512: The continuity of an optimal solution as a function of underlying parameters. For unconstrained problems with twice-differentiable functions, some critical points can be found by finding the points where the gradient of the objective function is zero (that is, the stationary points). More generally, a zero subgradient certifies that a local minimum has been found for minimization problems with convex functions and other locally Lipschitz functions , which meet in loss function minimization of
3053-408: The development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes
3124-399: The endoderm. In vertebrates, it extends throughout the entire length of the future vertebral column, and reaches as far as the anterior end of the midbrain , where it ends in a hook-like extremity in the region of the future dorsum sellae of the sphenoid bone . Initially, it exists between the neural tube and the endoderm of the yolk-sac; soon, the notochord becomes separated from them by
3195-403: The first derivative or the gradient of the objective function is zero (see first derivative test ). More generally, they may be found at critical points , where the first derivative or gradient of the objective function is zero or is undefined, or on the boundary of the choice set. An equation (or set of equations) stating that the first derivative(s) equal(s) zero at an interior optimum is called
3266-425: The following is valid: it suffices to solve only minimization problems. However, the opposite perspective of considering only maximization problems would be valid, too. Problems formulated using this technique in the fields of physics may refer to the technique as energy minimization , speaking of the value of the function f as representing the energy of the system being modeled . In machine learning , it
3337-411: The following notation: This denotes the minimum value of the objective function x + 1 , when choosing x from the set of real numbers R {\displaystyle \mathbb {R} } . The minimum value in this case is 1, occurring at x = 0 . Similarly, the notation asks for the maximum value of the objective function 2 x , where x may be any real number. In this case, there
3408-425: The former as actual solutions to the original problem. Global optimization is the branch of applied mathematics and numerical analysis that is concerned with the development of deterministic algorithms that are capable of guaranteeing convergence in finite time to the actual optimal solution of a nonconvex problem. Optimization problems are often expressed with special notation. Here are some examples: Consider
3479-510: The members of A have to satisfy. The domain A of f is called the search space or the choice set , while the elements of A are called candidate solutions or feasible solutions . The function f is variously called an objective function , criterion function , loss function , cost function (minimization), utility function or fitness function (maximization), or, in certain fields, an energy function or energy functional . A feasible solution that minimizes (or maximizes)
3550-451: The neural network. The positive-negative momentum estimation lets to avoid the local minimum and converges at the objective function global minimum. Further, critical points can be classified using the definiteness of the Hessian matrix : If the Hessian is positive definite at a critical point, then the point is a local minimum; if the Hessian matrix is negative definite, then the point is
3621-406: The notochord result in a side-to-side motion resembling stern sculling , which allows tail swimming and undulation . The stiffened notochord prevents movement through telescoping motion such as that of an earthworm . The notochord plays a key role in signaling and coordinating development. Embryos of modern vertebrates form transient notochord structures during gastrulation . The notochord
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#17328698399723692-423: The notochord were comprehensively reviewed by Annona, Holland, and D'Aniello (2015). They point out that, although many of these ideas have not been well supported by advances in molecular phylogenetics and developmental genetics, two of them have actually been revived under the stimulus of modern molecular approaches (the first proposes that the notochord evolved de novo in chordates, and the second derives it from
3763-400: The notochord within the phylum Chordata is considered in detail by Holland and Somorjai (2020). Vertebrates now have spines so they do not need a notochord. The following organisms retain a post-embryonic notochord: The notochord of the lancelet (amphioxus) protrudes beyond the anterior end of the neural tube. This projection serves a second purpose in allowing the animal to burrow within
3834-406: The objective function is called an optimal solution . In mathematics, conventional optimization problems are usually stated in terms of minimization. A local minimum x * is defined as an element for which there exists some δ > 0 such that the expression f ( x *) ≤ f ( x ) holds; that is to say, on some region around x * all of the function values are greater than or equal to
3905-705: The only reason a homoplasy is recognizable in the first place is because there are other characters that imply a pattern of relationships that reveal its homoplastic distribution. A cladogram is the diagrammatic result of an analysis, which groups taxa on the basis of synapomorphies alone. There are many other phylogenetic algorithms that treat data somewhat differently, and result in phylogenetic trees that look like cladograms but are not cladograms. For example, phenetic algorithms, such as UPGMA and Neighbor-Joining, group by overall similarity, and treat both synapomorphies and symplesiomorphies as evidence of grouping, The resulting diagrams are phenograms, not cladograms, Similarly,
3976-498: The problem of reversion that plagues sequence data. They are also generally assumed to have a low incidence of homoplasies because it was once thought that their integration into the genome was entirely random; this seems at least sometimes not to be the case, however. Researchers must decide which character states are "ancestral" ( plesiomorphies ) and which are derived ( synapomorphies ), because only synapomorphic character states provide evidence of grouping. This determination
4047-434: The program settles on a local minimum rather than the desired global minimum. To help solve this problem, many cladogram algorithms use a simulated annealing approach to increase the likelihood that the selected cladogram is the optimal one. The basal position is the direction of the base (or root) of a rooted phylogenetic tree or cladogram. A basal clade is the earliest clade (of a given taxonomic rank[a]) to branch within
4118-403: The results of model-based methods (Maximum Likelihood or Bayesian approaches) that take into account both branching order and "branch length," count both synapomorphies and autapomorphies as evidence for or against grouping, The diagrams resulting from those sorts of analysis are not cladograms, either. There are several algorithms available to identify the "best" cladogram. Most algorithms use
4189-629: The sediment of shallow waters. There, amphioxus is a filter feeder and spends most of its life partially submerged within the sediment. Optimization (mathematics) Mathematical optimization (alternatively spelled optimisation ) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization . Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics , and
4260-419: The set of feasible elements), it is also the global minimum, but a nonconvex problem may have more than one local minimum not all of which need be global minima. A large number of algorithms proposed for solving the nonconvex problems – including the majority of commercially available solvers – are not capable of making a distinction between locally optimal solutions and globally optimal solutions, and will treat
4331-509: The solutions are the pairs of the form {5, 2 k π } and {−5, (2 k + 1) π } , where k ranges over all integers . Operators arg min and arg max are sometimes also written as argmin and argmax , and stand for argument of the minimum and argument of the maximum . Fermat and Lagrange found calculus-based formulae for identifying optima, while Newton and Gauss proposed iterative methods for moving towards an optimum. The term " linear programming " for certain optimization cases
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#17328698399724402-405: The special case of mathematical optimization where the objective value is the same for every solution, and thus any solution is optimal. Many optimization algorithms need to start from a feasible point. One way to obtain such a point is to relax the feasibility conditions using a slack variable ; with enough slack, any starting point is feasible. Then, minimize that slack variable until the slack
4473-432: The surrounding tissue as a midline structure during the embryonic development , acts as a precursor for vertebrae and a primitive axial endoskeleton , and can allow for facilitated tail motion when swimming. In cephalochordates ( lancelets ), the notochord persists throughout life as the main structural support of the body. In tunicates , the notochord is present only in the larval stage, becoming completely absent in
4544-459: The term parsimony for a specific kind of cladogram generation algorithm and sometimes as an umbrella term for all phylogenetic algorithms. Algorithms that perform optimization tasks (such as building cladograms) can be sensitive to the order in which the input data (the list of species and their characteristics) is presented. Inputting the data in various orders can cause the same algorithm to produce different "best" cladograms. In these situations,
4615-422: The theoretical aspects of linear programming (like the theory of duality ) around the same time. Other notable researchers in mathematical optimization include the following: In a number of subfields, the techniques are designed primarily for optimization in dynamic contexts (that is, decision making over time): Adding more than one objective to an optimization problem adds complexity. For example, to optimize
4686-403: The tree. It is calculated by counting the minimum number of changes in a dataset and dividing it by the actual number of changes needed for the cladogram. A consistency index can also be calculated for an individual character i , denoted c i . Besides reflecting the amount of homoplasy, the metric also reflects the number of taxa in the dataset, (to a lesser extent) the number of characters in
4757-423: The user should input the data in various orders and compare the results. Using different algorithms on a single data set can sometimes yield different "best" cladograms, because each algorithm may have a unique definition of what is "best". Because of the astronomical number of possible cladograms, algorithms cannot guarantee that the solution is the overall best solution. A nonoptimal cladogram will be selected if
4828-400: The value at that element. Local maxima are defined similarly. While a local minimum is at least as good as any nearby elements, a global minimum is at least as good as every feasible element. Generally, unless the objective function is convex in a minimization problem, there may be several local minima. In a convex problem , if there is a local minimum that is interior (not on the edge of
4899-456: The vertebra may cause a pathologic condition: persistent notochordal canal . If the notochord and the nasopharynx do not separate properly during embryonic development, a depression (Tornwaldt bursa) or Tornwaldt cyst may form. The cells are the likely precursors to a rare cancer called chordoma . Research into the notochord has played a key role in understanding the development of the central nervous system . By transplanting and expressing
4970-585: Was due to George B. Dantzig , although much of the theory had been introduced by Leonid Kantorovich in 1939. ( Programming in this context does not refer to computer programming , but comes from the use of program by the United States military to refer to proposed training and logistics schedules, which were the problems Dantzig studied at that time.) Dantzig published the Simplex algorithm in 1947, and also John von Neumann and other researchers worked on
5041-450: Was proposed as an improvement of the CI "for certain applications" This metric also purports to measure of the amount of homoplasy, but also measures how well synapomorphies explain the tree. It is calculated taking the (maximum number of changes on a tree minus the number of changes on the tree), and dividing by the (maximum number of changes on the tree minus the minimum number of changes in the dataset). The rescaled consistency index (RC)
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