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64-687: The Tricholomataceae are a large family of fungi within the order Agaricales . Originally a classic " wastebasket taxon ", the family included any white-, yellow-, or pink-spored genera in the Agaricales not already classified as belonging to e.g. the Amanitaceae , Lepiotaceae , Hygrophoraceae , Pluteaceae , or Entolomataceae . The name derives from the Greek trichos (τριχος) meaning hair and loma (λωμα) meaning fringe or border, although not all members display this feature. The name "Tricholomataceae"

128-505: A 3D model of a human for example, the chest is a parent of the upper left arm, which is a parent of the lower left arm, which is a parent of the hand . This pattern is used in modeling and animation for almost everything built as a 3D digital model. Many grammatical theories, such as phrase-structure grammar , involve hierarchy. Direct–inverse languages such as Cree and Mapudungun distinguish subject and object on verbs not by different subject and object markers, but via

192-411: A branching hierarchy , one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher). For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy. Branching hierarchies are present within numerous systems, including organizations and classification schemes . The broad category of branching hierarchies can be further subdivided based on

256-514: A family tree ) and inheritance ( succession and heirship ). All the requisites of a well-rounded life and lifestyle can be organized using Maslow's hierarchy of human needs - according to Maslow's hierarchy of human needs. Learning steps often follow a hierarchical scheme—to master differential equations one must first learn calculus ; to learn calculus one must first learn elementary algebra ; and so on. Nature offers hierarchical structures, as numerous schemes such as Linnaean taxonomy ,

320-475: A reverse hierarchy , the conceptual pyramid of authority is turned upside-down, so that the apex is at the bottom and the base is at the top. This mode represents the idea that members of the higher rankings are responsible for the members of the lower rankings. Empirically, when we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure. On theoretical grounds we could expect complex systems to be hierarchies in

384-400: A business setting, a superior is a supervisor/boss and a peer is a colleague . Degree of branching refers to the number of direct subordinates or children an object has (in graph theory, equivalent to the number of other vertices connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in

448-446: A containment hierarchy is demonstrated in class inheritance in object-oriented programming . Two types of containment hierarchies are the subsumptive containment hierarchy and the compositional containment hierarchy. A subsumptive hierarchy " subsumes " its children, and a compositional hierarchy is " composed " of its children. A hierarchy can also be both subsumptive and compositional . A subsumptive containment hierarchy

512-402: A file on a computer desktop, one may first direct them towards the main folder, then the subfolders within the main folder. They will keep opening files within the folders until the designated file is located. For more complicated hierarchies, the stair structure represents hierarchical relationships through the use of visual stacking. Visually imagine the top of a downward staircase beginning at

576-428: A generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example: A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can only be

640-485: A hierarchy is diagrammed (see below ). In an organizational context, the following terms are often used related to hierarchies: In a mathematical context (in graph theory ), the general terminology used is different. Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with data structures , objects are known as nodes , superiors are called parents and subordinates are called children . In

704-511: A hierarchy of persons. In this system, the three (or four with Algonquian languages ) persons occur in a hierarchy of salience . To distinguish which is subject and which object, inverse markers are used if the object outranks the subject. On the other hand, languages include a variety of phenomena that are not hierarchical. For example, the relationship between a pronoun and a prior noun-phrase to which it refers commonly crosses grammatical boundaries in non-hierarchical ways. The structure of

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768-455: A hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates , although a system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a path . All parts of the hierarchy that are not linked vertically to one another nevertheless can be "horizontally" linked through

832-406: A higher-level entity can have on x' s properties and interactions. Furthermore, the entities found at each level are autonomous . Kulish (2002) suggests that almost every system of organization which humans apply to the world is arranged hierarchically. Some conventional definitions of the terms "nation" and "government" suggest that every nation has a government and that every government

896-471: A hundred taxonomic publications. Such descriptions typically result from either the discovery of organisms with unique combinations of characters that do not fit existing families, or from phylogenetic analyses that reveal the need for reclassification. The taxonomic term familia was first used by French botanist Pierre Magnol in his Prodromus historiae generalis plantarum, in quo familiae plantarum per tabulas disponuntur (1689) where he called

960-666: A lack of widespread consensus within the scientific community for extended periods. The continual publication of new data and diverse opinions plays a crucial role in facilitating adjustments and ultimately reaching a consensus over time. The naming of families is codified by various international bodies using the following suffixes: Name changes at the family level are regulated by the codes of nomenclature. For botanical families, some traditional names like Palmae ( Arecaceae ), Cruciferae ( Brassicaceae ), and Leguminosae ( Fabaceae ) are conserved alongside their standardized -aceae forms due to their historical significance and widespread use in

1024-524: A musical composition is often understood hierarchically (for example by Heinrich Schenker (1768–1835, see Schenkerian analysis ), and in the (1985) Generative Theory of Tonal Music , by composer Fred Lerdahl and linguist Ray Jackendoff ). The sum of all notes in a piece is understood to be an all-inclusive surface, which can be reduced to successively more sparse and more fundamental types of motion. The levels of structure that operate in Schenker's theory are

1088-449: A path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two co-workers or colleagues ; each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy. Heterarchy is one such form. Hierarchies have their own special vocabulary. These terms are easiest to understand when

1152-482: A phylogenomic study improved the resolution of Agaricales. A new suborder Tricholomatineae was proposed to cover Tricholomataceae, Lyophyllaceae , Entolomataceae , Macrocystidiaceae , and Clitocybe gibba . It roughly matches the "Tricholomatoid clade" of previous studies. Some species of fungus-growing ants in the genus Apterostigma cultivate species of Tricholomataceae. The extinct genus Archaeomarasmius , described from Turonian -age New Jersey amber,

1216-410: A problem. The use of parentheses is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example: (2 + 5) × (7 - 4). In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with

1280-439: A quadrilateral; it can never be a triangle , hexagon , etc. Nested hierarchies are the organizational schemes behind taxonomies and systematic classifications. For example, using the original Linnaean taxonomy (the version he laid out in the 10th edition of Systema Naturae ), a human can be formulated as: Taxonomies may change frequently (as seen in biological taxonomy ), but the underlying concept of nested hierarchies

1344-404: A required general property. These level hierarchies are characterized by bi-directional causation . Upward causation involves lower-level entities causing some property of a higher level entity; children entities may interact to yield parent entities, and parents are composed at least partly by their children. Downward causation refers to the effect that the incorporation of entity x into

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1408-509: A significant practical role in biological education and research. They provide an efficient framework for teaching taxonomy, as they group organisms with general similarities while remaining specific enough to be useful for identification purposes. For example, in botany, learning the characteristics of major plant families helps students identify related species across different geographic regions, since families often have worldwide distribution patterns. In many groups of organisms, families serve as

1472-466: A world in which complexity had to evolve from simplicity. System hierarchies analysis performed in the 1950s, laid the empirical foundations for a field that would become, from the 1980s, hierarchical ecology . The theoretical foundations are summarized by thermodynamics . When biological systems are modeled as physical systems , in the most general abstraction, they are thermodynamic open systems that exhibit self-organised behavior, and

1536-539: Is a branching hierarchy in which at least one object has two parent objects. For example, a graduate student can have two co-supervisors to whom the student reports directly and equally, and who have the same level of authority within the university hierarchy (i.e., they have the same position or tenure status). Possibly the first use of the English word hierarchy cited by the Oxford English Dictionary

1600-441: Is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and " IS-A hierarchy". The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that

1664-404: Is a direct extrapolation of the nested hierarchy concept. All of the ordered sets are still nested, but every set must be " strict "—no two sets can be identical. The shapes example above can be modified to demonstrate this: The notation x ⊊ y {\displaystyle x\subsetneq y\,} means x is a subset of y but is not equal to  y . A general example of

1728-480: Is a hierarchical ordering of nested sets . The concept of nesting is exemplified in Russian matryoshka dolls . Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll;

1792-503: Is a member of the level Mammalia "is a" member of the level Animalia ; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of " concepts ". For example, with the Linnaean hierarchy outlined above, an entity name like Animalia is a way to group all the species that fit the conceptualization of an animal. A compositional containment hierarchy

1856-405: Is always transitive . The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects. Mathematically, in its most general form, a hierarchy is a partially ordered set or poset . The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with

1920-420: Is always the same. In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of self-similarity and recursion . Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic. A containment hierarchy

1984-507: Is an ordering of the parts that make up a system—the system is "composed" of these parts. Most engineered structures, whether natural or artificial, can be broken down in this manner. The compositional hierarchy that every person encounters at every moment is the hierarchy of life . Every person can be reduced to organ systems , which are composed of organs , which are composed of tissues , which are composed of cells , which are composed of molecules , which are composed of atoms . In fact,

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2048-483: Is credited with first use of it as an abstract noun. Since hierarchical churches, such as the Roman Catholic (see Catholic Church hierarchy ) and Eastern Orthodox churches, had tables of organization that were "hierarchical" in the modern sense of the word (traditionally with God as the pinnacle or head of the hierarchy), the term came to refer to similar organizational methods in secular settings. A hierarchy

2112-631: Is hierarchical. Sociologists can analyse socioeconomic systems in terms of stratification into a social hierarchy (the social stratification of societies), and all systematic classification schemes ( taxonomies ) are hierarchical. Most organized religions , regardless of their internal governance structures, operate as a hierarchy under deities and priesthoods . Many Christian denominations have an autocephalous ecclesiastical hierarchy of leadership . Families can be viewed as hierarchical structures in terms of cousinship (e.g., first cousin once removed, second cousin, etc.), ancestry (as depicted in

2176-598: Is infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point. Organizations can be structured as a dominance hierarchy . In an organizational hierarchy, there is a single person or group with the most power or authority , and each subsequent level represents a lesser authority. Most organizations are structured in this manner, including governments , companies , armed forces , militia and organized religions . The units or persons within an organization may be depicted hierarchically in an organizational chart . In

2240-588: Is one of four known genera of Agaricales in the fossil record. Family (biology) Family ( Latin : familia , pl. : familiae ) is one of the eight major hierarchical taxonomic ranks in Linnaean taxonomy . It is classified between order and genus . A family may be divided into subfamilies , which are intermediate ranks between the ranks of family and genus. The official family names are Latin in origin; however, popular names are often used: for example, walnut trees and hickory trees belong to

2304-541: Is seen as having validity in describing Tricholoma and other genera that form part of a monophyletic family including Tricholoma . To that end, the International Botanical Congress has voted on two occasions (1988 and 2006) to conserve the name "Tricholomataceae" against competing names. This decision does not invalidate the use of segregate families from the Tricholomataceae, but simply validates

2368-420: Is typically depicted as a pyramid , where the height of a level represents that level's status and width of a level represents the quantity of items at that level relative to the whole. For example, the few Directors of a company could be at the apex , and the base could be thousands of people who have no subordinates. These pyramids are often diagrammed with a triangle diagram which serves to emphasize

2432-569: The Prodromus of Augustin Pyramus de Candolle and the Genera Plantarum of George Bentham and Joseph Dalton Hooker this word ordo was used for what now is given the rank of family. Families serve as valuable units for evolutionary, paleontological, and genetic studies due to their relatively greater stability compared to lower taxonomic levels like genera and species. Families play

2496-484: The "postal district" , consists of 18 objects (letters). The next level down is the "zone", where the objects are the digits 0–9. This is an example of an overlapping hierarchy , because each of these 10 objects has 18 parents. The hierarchy continues downward to generate, in theory, 7,200,000 unique codes of the format A0A 0A0 (the second and third letter positions allow 20 objects each). Most library classification systems are also hierarchical. The Dewey Decimal System

2560-472: The organization of life , and biomass pyramids attempt to document. While the above examples are often clearly depicted in a hierarchical form and are classic examples, hierarchies exist in numerous systems where this branching structure is not immediately apparent. For example, most postal-code systems are hierarchical. Using the Canadian postal code system as an example, the top level's binding concept,

2624-574: The set/subset relations between dissipative structures can be characterized in a hierarchy. Other hierarchical representations related to biology include ecological pyramids which illustrate energy flow or trophic levels in ecosystems , and taxonomic hierarchies, including the Linnean classification scheme and phylogenetic trees that reflect inferred patterns of evolutionary relationship among living and extinct species. CGI and computer-animation programs mostly use hierarchies for models. On

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2688-447: The -idae suffix for animal family names, derived from the Greek 'eidos' meaning 'resemblance' or 'like'. The adoption of this naming convention helped establish families as an important taxonomic rank. By the mid-1800s, many of Linnaeus's broad genera were being elevated to family status to accommodate the rapidly growing number of newly discovered species. In nineteenth-century works such as

2752-539: The Tricholomataceae include the Hydnangiaceae , Lyophyllaceae , Marasmiaceae , Mycenaceae , Omphalotaceae , Physalacriaceae , and Pleurotaceae . In 2014 a study recovered seven monophyletic genera within the Tricholomataceae: Leucopaxillus , Tricholoma , Pseudotricholoma , Porpoloma s.str, Dennisiomyces , Corneriella , and Albomagister . The aim of the study was to delimit

2816-510: The continued use of Tricholomataceae. Molecular phylogenetic analysis has greatly aided the demarcation of clear monophyletic groups among the Tricholomataceae. So far, some of these groups have been defined cladistically rather than being defined as formal Linnean taxa , though there have been several cases in which older proposed segregates from the Tricholomataceae have been validated by evidence coming from molecular phylogenetics . As of 2006, validly published families segregated from

2880-515: The degree. A flat hierarchy (also known for companies as flat organization ) is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span. Most often, systems intuitively regarded as hierarchical have at most a moderate span. Therefore, a flat hierarchy is often not viewed as a hierarchy at all. For example, diamonds and graphite are flat hierarchies of numerous carbon atoms that can be further decomposed into subatomic particles. An overlapping hierarchy

2944-539: The family Juglandaceae , but that family is commonly referred to as the "walnut family". The delineation of what constitutes a family—or whether a described family should be acknowledged—is established and decided upon by active taxonomists . There are not strict regulations for outlining or acknowledging a family, yet in the realm of plants, these classifications often rely on both the vegetative and reproductive characteristics of plant species. Taxonomists frequently hold varying perspectives on these descriptions, leading to

3008-556: The highly polyphyletic Tricholomataceae, and identify monophyletic groups within the tricholomatoid clade, which includes the families Tricholomataceae, Entolomataceae, and Lyophyllaceae. According to this study there have been several different ways of distributing Porpoloma , which is highly polyphyletic . This study suggests that the genus is distributed in four groups within the Trichlomatoid clade; Porpoloma s.str, Corneriella , Pseudotricholoma . and Pogonoloma . In 2015,

3072-527: The last two levels apply to all matter , at least at the macroscopic scale . Moreover, each of these levels inherit all the properties of their children . In this particular example, there are also emergent properties —functions that are not seen at the lower level (e.g., cognition is not a property of neurons but is of the brain )—and a scalar quality (molecules are bigger than atoms, cells are bigger than molecules, etc.). Both of these concepts commonly exist in compositional hierarchies, but they are not

3136-429: The left and descending on the right. Child elements are towards the bottom of the stairs and parent elements are at the top. This structure represents hierarchical relationships through the use of visual stacking. In plain English, a hierarchy can be thought of as a set in which: The first requirement is also interpreted to mean that a hierarchy can have no circular relationships ; the association between two objects

3200-406: The literature. Family names are typically formed from the stem of a type genus within the family. In zoology, when a valid family name is based on a genus that is later found to be a junior synonym , the family name may be maintained for stability if it was established before 1960. In botany, some family names that were found to be junior synonyms have been conserved due to their widespread use in

3264-907: The primary level for taxonomic identification keys, making them particularly valuable for field guides and systematic work as they often represent readily recognizable groups of related organisms with shared characteristics. In ecological and biodiversity research, families frequently serve as the foundational level for identification in survey work and environmental studies. This is particularly useful because families often share life history traits or occupy similar ecological niches . Some families show strong correlations between their taxonomic grouping and ecological functions, though this relationship varies among different groups of organisms. The stability of family names has practical importance for applied biological work, though this stability faces ongoing challenges from new scientific findings. Modern molecular studies and phylogenetic analyses continue to refine

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3328-407: The problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations. A nested hierarchy or inclusion hierarchy

3392-477: The rules of visual hierarchy . Visual hierarchy is also important for proper organization of files on computers. An example of visually representing hierarchy is through nested clusters. Nested clusters represent hierarchical relationships using layers of information. The child element is within the parent element, such as in a Venn diagram . This structure is most effective in representing simple hierarchical relationships. For example, when directing someone to open

3456-469: The same property value are grouped together, and each of those resulting levels is referred to as a class . "Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to

3520-486: The scientific literature. The family-group in zoological nomenclature includes several ranks: superfamily (-oidea), family (-idae), subfamily (-inae), and tribe (-ini). Under the principle of coordination, a name established at any of these ranks can be moved to another rank while retaining its original authorship and date, requiring only a change in suffix to reflect its new rank. New family descriptions are relatively rare in taxonomy, occurring in fewer than one in

3584-567: The seventy-six groups of plants he recognised in his tables families ( familiae ). The concept of rank at that time was not yet settled, and in the preface to the Prodromus Magnol spoke of uniting his families into larger genera , which is far from how the term is used today. In his work Philosophia Botanica published in 1751, Carl Linnaeus employed the term familia to categorize significant plant groups such as trees , herbs , ferns , palms , and so on. Notably, he restricted

3648-470: The size differences between the levels (but not all triangle/pyramid diagrams are hierarchical; for example, the 1992 USDA food guide pyramid ). An example of a triangle diagram appears to the right. Another common representation of a hierarchical scheme is as a tree diagram . Phylogenetic trees , charts showing the structure of § Organizations , and playoff brackets in sports are often illustrated this way. More recently, as computers have allowed

3712-399: The storage and navigation of ever larger data sets, various methods have been developed to represent hierarchies in a manner that makes more efficient use of the available space on a computer's screen. Examples include fractal maps, TreeMaps and Radial Trees . In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on

3776-517: The system as a whole. Categorization in this way yields two broad classes: linear and branching . In a linear hierarchy , the maximum degree is 1. In other words, all of the objects can be visualized in a line-up, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. This is referring to the objects and not the levels ; every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects. In

3840-594: The understanding of family relationships, sometimes leading to reclassification. The impact of these changes varies among different groups of organisms – while some families remain well-defined and easily recognizable, others require revision as new evidence emerges about evolutionary relationships. This balance between maintaining nomenclatural stability and incorporating new scientific discoveries remains an active area of taxonomic practice. Hierarchy A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in

3904-556: The use of this term solely within the book's morphological section, where he delved into discussions regarding the vegetative and generative aspects of plants. Subsequently, in French botanical publications, from Michel Adanson 's Familles naturelles des plantes (1763) and until the end of the 19th century, the word famille was used as a French equivalent of the Latin ordo (or ordo naturalis ). The family concept in botany

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3968-412: Was further developed by the French botanists Antoine Laurent de Jussieu and Michel Adanson . Jussieu's 1789 Genera Plantarum divided plants into 100 'natural orders,' many of which correspond to modern plant families. However, the term 'family' did not become standardized in botanical usage until after the mid-nineteenth century. In zoology , the family as a rank intermediate between order and genus

4032-600: Was in 1881, when it was used in reference to the three orders of three angels as depicted by Pseudo-Dionysius the Areopagite (5th–6th centuries). Pseudo-Dionysius used the related Greek word (ἱεραρχία, hierarchia ) both in reference to the celestial hierarchy and the ecclesiastical hierarchy . The Greek term hierarchia means 'rule of a high priest', from hierarches (ἱεράρχης, 'president of sacred rites, high-priest') and that from hiereus (ἱερεύς, 'priest') and arche (ἀρχή, 'first place or power, rule'). Dionysius

4096-435: Was introduced by Pierre André Latreille in his Précis des caractères génériques des insectes, disposés dans un ordre naturel (1796). He used families (some of them were not named) in some but not in all his orders of "insects" (which then included all arthropods ). The standardization of zoological family names began in the early nineteenth century. A significant development came in 1813 when William Kirby introduced

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