A fuzzy concept is a concept of which the boundaries of application can vary according to context or conditions, instead of being fixed once and for all. This means the concept is vague in some way, lacking a fixed, precise meaning, without however being unclear or meaningless altogether, it has a definite meaning, which can be made more precise only through further elaboration and specification - including a closer definition of the context in which the concept is used. The study of the characteristics of fuzzy concepts and fuzzy language is called fuzzy semantics; the inverse of a "fuzzy concept" is a "crisp concept". A fuzzy concept is understood by scientists as a concept, "to an extent applicable" in a situation; that means the concept has gradations of unsharp boundaries of application. A fuzzy statement is a statement, true "to some extent", that extent can be represented by a scaled value; the best known example of a fuzzy concept around the world is an amber traffic light, indeed fuzzy concepts are used in traffic control systems.
The term is used these days in a more general, popular sense - in contrast to its technical meaning - to refer to a concept, "rather vague" for any kind of reason. In the past, the idea of reasoning with fuzzy concepts faced considerable resistance from academic elites, they did not want to endorse the use of imprecise concepts in argumentation. Yet although people might not be aware of it, the use of fuzzy concepts has risen gigantically in all walks of life from the 1970s onward; that is due to advances in electronic engineering, fuzzy mathematics and digital computer programming. The new technology allows complex inferences about "variations on a theme" to be anticipated and fixed in a program; the new neuro-fuzzy computational methods make it possible, to identify, to measure and respond to fine gradations of significance, with great precision. It means that useful concepts can be coded and applied to all kinds of tasks if, these concepts are never defined. Nowadays engineers and programmers represent fuzzy concepts mathematically, using fuzzy logic, fuzzy values, fuzzy variables and fuzzy sets.
Problems of vagueness and fuzziness have always existed in human experience. The boundary between different things can appear blurry. Sometimes people have to think, when they are not in the best frame of mind to do it, or, they have to talk about something out there, which just isn't defined. Across time, however and scientists began to reflect about those kinds of problems, in much more systematic ways; the ancient Sorites paradox first raised the logical problem of how we could define the threshold at which a change in quantitative gradation turns into a qualitative or categorical difference. With some physical processes this threshold is easy to identify. For example, water turns into steam at 100 °C or 212 °F. With many other processes and gradations, the point of change is much more difficult to locate, remains somewhat vague. Thus, the boundaries between qualitatively different things may be unsharp: we know that there are boundaries, but we cannot define them exactly. According to the modern idea of the continuum fallacy, the fact that a statement is to an extent vague, does not automatically mean that it is invalid.
The problem becomes one of how we could ascertain the kind of validity that the statement does have. The Nordic myth of Loki's wager suggested that concepts that lack precise meanings or precise boundaries of application cannot be usefully discussed at all. However, the 20th century idea of "fuzzy concepts" proposes that "somewhat vague terms" can be operated with, since we can explicate and define the variability of their application, by assigning numbers to gradations of applicability; this idea sounds simple enough. The intellectual origins of the species of fuzzy concepts as a logical category have been traced back to a diversity of famous and less well-known thinkers, including Eubulides, Cicero, Georg Wilhelm Friedrich Hegel, Karl Marx and Friedrich Engels, Friedrich Nietzsche, Hugh MacColl, Charles S. Peirce, Max Black, Jan Łukasiewicz, Emil Leon Post, Alfred Tarski, Georg Cantor, Nicolai A. Vasiliev, Kurt Gödel, Stanisław Jaśkowski and Donald Knuth. Across at least two and a half millennia, all of them had something to say about graded concepts with unsharp boundaries.
This suggests at least that the awareness of the existence of concepts with "fuzzy" characteristics, in one form or another, has a long history in human thought. Quite a few logicians and philosophers have tried to analyze the characteristics of fuzzy concepts as a recognized species, sometimes with the aid of some kind of many-valued logic or substructural logic. An early attempt in the post-WW2 era to create a theory of sets where set membership is a matter of degree was made by Abraham Kaplan and Hermann Schott in 1951, they intended to apply the idea to empirical research. Kaplan and Schott measured the degree of membership of empirical classes using real numbers between 0 and 1, they defined corresponding notions of intersection, union and subset. However, at the time, their idea "fell on stony ground". J. Barkley Rosser Sr. published a treatise on many-valued logics in 1952, anticipating "many-valued sets". Another treatise was published in 1963 by Aleksandr A. Zinov'ev and othersIn 1964, the American philosopher William Alston introduced the term "degree vagueness" to describe vagueness in an idea that resu
Philosophy is the study of general and fundamental questions about existence, values, reason and language. Such questions are posed as problems to be studied or resolved; the term was coined by Pythagoras. Philosophical methods include questioning, critical discussion, rational argument, systematic presentation. Classic philosophical questions include: Is it possible to know anything and to prove it? What is most real? Philosophers pose more practical and concrete questions such as: Is there a best way to live? Is it better to be just or unjust? Do humans have free will? "philosophy" encompassed any body of knowledge. From the time of Ancient Greek philosopher Aristotle to the 19th century, "natural philosophy" encompassed astronomy and physics. For example, Newton's 1687 Mathematical Principles of Natural Philosophy became classified as a book of physics. In the 19th century, the growth of modern research universities led academic philosophy and other disciplines to professionalize and specialize.
In the modern era, some investigations that were traditionally part of philosophy became separate academic disciplines, including psychology, sociology and economics. Other investigations related to art, politics, or other pursuits remained part of philosophy. For example, is beauty objective or subjective? Are there many scientific methods or just one? Is political utopia a hopeful dream or hopeless fantasy? Major sub-fields of academic philosophy include metaphysics, ethics, political philosophy and philosophy of science. Traditionally, the term "philosophy" referred to any body of knowledge. In this sense, philosophy is related to religion, natural science and politics. Newton's 1687 Mathematical Principles of Natural Philosophy is classified in the 2000s as a book of physics. In the first part of the first book of his Academics, Cicero introduced the division of philosophy into logic and ethics. Metaphysical philosophy was the study of existence, God, logic and other abstract objects; this division has changed.
Natural philosophy has split into the various natural sciences astronomy, chemistry and cosmology. Moral philosophy still includes value theory. Metaphysical philosophy has birthed formal sciences such as logic and philosophy of science, but still includes epistemology and others. Many philosophical debates that began in ancient times are still debated today. Colin McGinn and others claim. Chalmers and others, by contrast, see progress in philosophy similar to that in science, while Talbot Brewer argued that "progress" is the wrong standard by which to judge philosophical activity. In one general sense, philosophy is associated with wisdom, intellectual culture and a search for knowledge. In that sense, all cultures and literate societies ask philosophical questions such as "how are we to live" and "what is the nature of reality". A broad and impartial conception of philosophy finds a reasoned inquiry into such matters as reality and life in all world civilizations. Western philosophy is the philosophical tradition of the Western world and dates to Pre-Socratic thinkers who were active in Ancient Greece in the 6th century BCE such as Thales and Pythagoras who practiced a "love of wisdom" and were termed physiologoi.
Socrates was a influential philosopher, who insisted that he possessed no wisdom but was a pursuer of wisdom. Western philosophy can be divided into three eras: Ancient, Medieval philosophy, Modern philosophy; the Ancient era was dominated by Greek philosophical schools which arose out of the various pupils of Socrates, such as Plato, who founded the Platonic Academy and his student Aristotle, founding the Peripatetic school, who were both influential in Western tradition. Other traditions include Cynicism, Greek Skepticism and Epicureanism. Important topics covered by the Greeks included metaphysics, the nature of the well-lived life, the possibility of knowledge and the nature of reason. With the rise of the Roman empire, Greek philosophy was increasingly discussed in Latin by Romans such as Cicero and Seneca. Medieval philosophy is the period following the fall of the Western Roman Empire and was dominated by the ris
In biology, a ring species is a connected series of neighbouring populations, each of which can interbreed with sited related populations, but for which there exist at least two "end" populations in the series, which are too distantly related to interbreed, though there is a potential gene flow between each "linked" population. Such non-breeding, though genetically connected, "end" populations may co-exist in the same region thus closing a "ring"; the German term Rassenkreis, meaning a ring of populations, is used. Ring species have been cited as evidence of evolution, they illustrate what happens over time as populations genetically diverge because they represent, in living populations, what happens over time between long deceased ancestor populations and living populations, in which the intermediates have become extinct. The evolutionary biologist Richard Dawkins remarks that ring species "are only showing us in the spatial dimension something that must always happen in the time dimension".
Formally, the issue is that interfertility is not a transitive relation–if A can breed with B, B can breed with C, it does not follow that A can breed with C–and thus does not define an equivalence relation. A ring species is a species with a counterexample to the transitivity of interbreeding. However, it is unclear whether any of the examples of ring species cited by scientists permit gene flow from end to end, with many being debated and contested; the classic ring species is the Larus gull. In 1925 Jonathan Dwight found the genus to form a chain of varieties around the Arctic Circle. However, doubts have arisen as to. In 1938, Claud Buchanan Ticehurst argued that the greenish warbler had spread from Nepal around the Tibetan Plateau, while adapting to each new environment, meeting again in Siberia where the ends no longer interbreed; these and other discoveries led Mayr to first formulate a theory on ring species in his 1942 study Systematics and the Origin of Species. In the 1940s, Robert C.
Stebbins described the Ensatina salamanders around the Californian Central Valley as a ring species. In 2012, the first example of a ring species in plants was found in a spurge, forming a ring around the Caribbean Sea; the biologist Ernst Mayr championed the concept of ring species, claiming that it unequivocally demonstrated the process of speciation. A ring species is an alternative model to allopatric speciation, "illustrating how new species can arise through'circular overlap', without interruption of gene flow through intervening populations…" However, Jerry Coyne and H. Allen Orr point out that rings species more model parapatric speciation. Ring species attract the interests of evolutionary biologists and researchers of speciation leading to both thought provoking ideas and confusion concerning their definition. Contemporary scholars recognize that examples in nature have proved rare due to various factors such as limitations in taxonomic delineation or, "taxonomic zeal"—explained by the fact that taxonomists classify organisms into "species", while ring species cannot fit this definition.
Other reasons such as gene flow interruption from "vicariate divergence" and fragmented populations due to climate instability have been cited. Ring species present an interesting case of the species problem for those seeking to divide the living world into discrete species. All that distinguishes a ring species from two separate species is the existence of the connecting populations; the problem is whether to quantify the whole ring as a single species or to classify each population as a distinct species. Ring species illustrate that species boundaries arise and exist on a continuum. Many examples have been documented in nature. Debate exists concerning much of the research, with some authors citing evidence against their existence entirely; the following examples provide evidence that—despite the limited number of concrete, idealized examples in nature—continuums of species do exist and can be found in biological systems. This is characterized by sub-species level classifications such as clines, ecotypes and varieties.
Many examples have been disputed by researchers, "many of the cases have received little attention from researchers, making it difficult to assess whether they display the characteristics of ideal ring species."The following list gives examples of ring species found in nature. Some of the examples such as the Larus gull complex, the greenish warbler of Asia, the Ensatina salamanders of America, have been disputed. Acanthiza pusilla and A. ewingii Acacia karroo Alauda skylarks Alophoixus Aulostomus Camarhynchus psittacula and C. pauper Chaerephon pumilus species complex Ensatina salamanders Euphorbia tithymaloides is a group within the spurge family that has reproduced and evolved in a ring through Central America and the Caribbean, meeting in the Virgin Islands where they appear to be morphologically and ecologically distinct. Great tit, it is thought to have spread from Nepal around the inhospitable Tibetan Plateau, to rejoin in Siberia, where the
In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring by sexual reproduction. Other ways of defining species include their karyotype, DNA sequence, behaviour or ecological niche. In addition, paleontologists use the concept of the chronospecies since fossil reproduction cannot be examined. While these definitions may seem adequate, when looked at more they represent problematic species concepts. For example, the boundaries between related species become unclear with hybridisation, in a species complex of hundreds of similar microspecies, in a ring species. Among organisms that reproduce only asexually, the concept of a reproductive species breaks down, each clone is a microspecies. All species are given a two-part name, a "binomial"; the first part of a binomial is the genus.
The second part is called the specific epithet. For example, Boa constrictor is one of four species of the genus Boa. None of these is satisfactory definitions, but scientists and conservationists need a species definition which allows them to work, regardless of the theoretical difficulties. If species were fixed and distinct from one another, there would be no problem, but evolutionary processes cause species to change continually, to grade into one another. Species were seen from the time of Aristotle until the 18th century as fixed kinds that could be arranged in a hierarchy, the great chain of being. In the 19th century, biologists grasped. Charles Darwin's 1859 book The Origin of Species explained how species could arise by natural selection; that understanding was extended in the 20th century through genetics and population ecology. Genetic variability arises from mutations and recombination, while organisms themselves are mobile, leading to geographical isolation and genetic drift with varying selection pressures.
Genes can sometimes be exchanged between species by horizontal gene transfer. Viruses are a special case, driven by a balance of mutation and selection, can be treated as quasispecies. Biologists and taxonomists have made many attempts to define species, beginning from morphology and moving towards genetics. Early taxonomists such as Linnaeus had no option but to describe what they saw: this was formalised as the typological or morphological species concept. Ernst Mayr emphasised reproductive isolation, but this, like other species concepts, is hard or impossible to test. Biologists have tried to refine Mayr's definition with the recognition and cohesion concepts, among others. Many of the concepts are quite similar or overlap, so they are not easy to count: the biologist R. L. Mayden recorded about 24 concepts, the philosopher of science John Wilkins counted 26. Wilkins further grouped the species concepts into seven basic kinds of concepts: agamospecies for asexual organisms biospecies for reproductively isolated sexual organisms ecospecies based on ecological niches evolutionary species based on lineage genetic species based on gene pool morphospecies based on form or phenotype and taxonomic species, a species as determined by a taxonomist.
A typological species is a group of organisms in which individuals conform to certain fixed properties, so that pre-literate people recognise the same taxon as do modern taxonomists. The clusters of variations or phenotypes within specimens would differentiate the species; this method was used as a "classical" method of determining species, such as with Linnaeus early in evolutionary theory. However, different phenotypes are not different species. Species named in this manner are called morphospecies. In the 1970s, Robert R. Sokal, Theodore J. Crovello and Peter Sneath proposed a variation on this, a phenetic species, defined as a set of organisms with a similar phenotype to each other, but a different phenotype from other sets of organisms, it differs from the morphological species concept in including a numerical measure of distance or similarity to cluster entities based on multivariate comparisons of a reasonably large number of phenotypic traits. A mate-recognition species is a group of sexually reproducing organisms that recognize one another as potential mates.
Expanding on this to allow for post-mating isolation, a cohesion species is the most inclusive population of individuals having the potential for phenotypic cohesion through intrinsic cohesion mechanisms. A further development of the recognition concept is provided by the biosemiotic concept of species. In microbiology, genes can move even between distantly related bacteria extending to the whole bacterial domain; as a rule of thumb, microbiologists have assumed that kinds of Bacteria or Archaea with 16S ribosomal RNA gene sequences more similar than 97% to each other need to be checked by DNA-DNA hybridisation to decide if they belong to the same species or not. This concept was narrowed in 2006 to a similarity of 98.7%. DNA-DNA hybri
Metaphysics is the branch of philosophy that examines the fundamental nature of reality, including the relationship between mind and matter, between substance and attribute, between possibility and actuality. The word "metaphysics" comes from two Greek words that, together mean "after or behind or among the natural", it has been suggested that the term might have been coined by a first century CE editor who assembled various small selections of Aristotle’s works into the treatise we now know by the name Metaphysics. Metaphysics studies questions related to what it is for something to exist and what types of existence there are. Metaphysics seeks to answer, in an abstract and general manner, the questions: What is there? What is it like? Topics of metaphysical investigation include existence and their properties and time, cause and effect, possibility. Metaphysics study, conducted using deduction from that, known a priori. Like foundational mathematics, it tries to give a coherent account of the structure of the world, capable of explaining our everyday and scientific perception of the world, being free from contradictions.
In mathematics, there are many different ways. While metaphysics may, as a special case, study the entities postulated by fundamental science such as atoms and superstrings, its core topic is the set of categories such as object and causality which those scientific theories assume. For example: claiming that "electrons have charge" is a scientific theory. There are two broad stances about; the strong, classical view assumes that the objects studied by metaphysics exist independently of any observer, so that the subject is the most fundamental of all sciences. The weak, modern view assumes that the objects studied by metaphysics exist inside the mind of an observer, so the subject becomes a form of introspection and conceptual analysis; some philosophers, notably Kant, discuss both of these "worlds" and what can be inferred about each one. Some philosophers, such as the logical positivists, many scientists, reject the strong view of metaphysics as meaningless and unverifiable. Others reply that this criticism applies to any type of knowledge, including hard science, which claims to describe anything other than the contents of human perception, thus that the world of perception is the objective world in some sense.
Metaphysics itself assumes that some stance has been taken on these questions and that it may proceed independently of the choice—the question of which stance to take belongs instead to another branch of philosophy, epistemology. Ontology is the philosophical study of the nature of being, existence or reality, as well as the basic categories of being and their relations. Traditionally listed as the core of metaphysics, ontology deals with questions concerning what entities exist or may be said to exist and how such entities may be grouped, related within a hierarchy, subdivided according to similarities and differences. Identity is a fundamental metaphysical issue. Metaphysicians investigating identity are tasked with the question of what it means for something to be identical to itself, or — more controversially — to something else. Issues of identity arise in the context of time: what does it mean for something to be itself across two moments in time? How do we account for this? Another question of identity arises when we ask what our criteria ought to be for determining identity?
And how does the reality of identity interface with linguistic expressions? The metaphysical positions one takes on identity have far-reaching implications on issues such as the mind-body problem, personal identity and law; the ancient Greeks took extreme positions on the nature of change. Parmenides denied change altogether, while Heraclitus argued that change was ubiquitous: "ou cannot step into the same river twice." Identity, sometimes called Numerical Identity, is the relation that a "thing" bears to itself, which no "thing" bears to anything other than itself. A modern philosopher who made a lasting impact on the philosophy of identity was Leibniz, whose Law of the Indiscernibility of Identicals is still in wide use today, it states that if some object x is identical to some object y any property that x has, y will have as well. Put formally, it states ∀ x ∀ y However, it seems, that objects can change over time. If one were to look at a tree one day, the tree lost a leaf, it would seem that one could still be looking at that same tree.
Two rival theories to account for the relationship between change and identity are perdurantism, which treats the tree as a series of tree-stages, endurantism, which maintains that the organism—the same tree—is present at every stage in its history. Objects appear to us in space and time, while abstract entities such as classes, r
The sorites paradox is a paradox that arises from vague predicates. A typical formulation involves a heap of sand. Under the assumption that removing a single grain does not turn a heap into a non-heap, the paradox is to consider what happens when the process is repeated enough times: is a single remaining grain still a heap? If not, when did it change from a heap to a non-heap? The word "sorites" derives from the Greek word for heap; the paradox is so named because of its original characterization, attributed to Eubulides of Miletus. The paradox goes as follows: consider a heap of sand from which grains are individually removed. One might construct the argument, using premises, as follows: 1,000,000 grains of sand is a heap of sand A heap of sand minus one grain is still a heap. Repeated applications of Premise 2 forces one to accept the conclusion that a heap may be composed of just one grain of sand. Read observes that "the argument is itself a heap, or sorites, of steps of modus ponens": 1,000,000 grains is a heap.
If 1,000,000 grains is a heap 999,999 grains is a heap. So 999,999 grains is a heap. If 999,999 grains is a heap 999,998 grains is a heap. So 999,998 grains is a heap. If...... So 1 grain is a heap. Tension between small changes and big consequences gives rise to the Sorites Paradox... There are many variations... consideration of the difference between being... and seeming.... Another formulation is to start with a grain of sand, not a heap, assume that adding a single grain of sand to something, not a heap does not turn it into a heap. Inductively, this process can be repeated as much as one wants without constructing a heap. A more natural formulation of this variant is to assume a set of colored chips exists such that two adjacent chips vary in color too little for human eyesight to be able to distinguish between them. By induction on this premise, humans would not be able to distinguish between any colors; the removal of one drop from the ocean, will not make it'not an ocean', but since the volume of water in the ocean is finite after enough removals a litre of water left is still an ocean.
This paradox can be reconstructed for a variety of predicates, for example, with "tall", "rich", "old", "blue", "bald", so on. Bertrand Russell argued that all of natural language logical connectives, is vague. Other similar paradoxes are: Argument of the beard The bald man paradox On the face of it, there are some ways to avoid this conclusion. One may object to the first premise by denying, but 1,000,000 is just an arbitrarily large number, the argument will go through with any such number. So the response must deny outright. Peter Unger defends this solution. Alternatively, one may object to the second premise by stating that it is not true for all heaps of sand that removing one grain from it still makes a heap. A common first response to the paradox is to call any set of grains that has more than a certain number of grains in it a heap. If one were to set the "fixed boundary" at, say, 10,000 grains one would claim that for fewer than 10,000, it is not a heap. However, such solutions are unsatisfactory as there seems little significance to the difference between 9,999 grains and 10,000 grains.
The boundary, wherever it may be set, remains as arbitrary and so its precision is misleading. It is objectionable on both philosophical and linguistic grounds: the former on account of its arbitrariness, the latter on the ground that it is not how we use natural language. A second response attempts to find a fixed boundary. For example, a dictionary may define a "heap" as "a collection of things thrown together so as to form an elevation." This requires there to be enough grains. Thus, adding one grain atop a single layer produces a heap, removing the last grain above the bottom layer destroys the heap. Timothy Williamson and Roy Sorensen hold an approach that there are fixed boundaries but that they are unknowable. Supervaluationism is a semantics for dealing with irreferential singular vagueness, it allows one to retain the usual tautological laws when dealing with undefined truth values. As an example for a proposition about an irreferential singular term, consider the sentence "Pegasus likes licorice".
Since the name "Pegasus" fails to refer, no truth value can be assigned to the sentence. However, there are some statements about "Pegasus" which have definite truth values such as "Pegasus likes licorice or Pegasus doesn't like licorice"; this sentence is an instance of the tautology " p ∨ ¬ p ", i.e. the valid schema " p or not- p ". According to supervaluationism, it should be true regardless of whether or not its components have a truth value. "1,000 grains of sand is a heap of sand" may be considered a border case having no truth value, but "1,000 grains of sand is a heap of sand, or 1,000 grains of sand is not a heap of sand" should be true. Let v be a classical valuation defined on every atomic sentence of the language L, let A
The wolf known as the grey/gray wolf or timber wolf, is a canine native to the wilderness and remote areas of Eurasia and North America. It is the largest extant member of its family, with males averaging 43 -- females 36 -- 38.5 kg. It is distinguished from other Canis species by its larger size and less pointed features on the ears and muzzle, its winter fur is long and bushy and predominantly a mottled gray in color, although nearly pure white and brown to black occur. Mammal Species of the World, a standard reference work in zoology, recognises 38 subspecies of C. lupus. The gray wolf is the second most specialized member of the genus Canis, after the Ethiopian wolf, as demonstrated by its morphological adaptations to hunting large prey, its more gregarious nature, its advanced expressive behavior, it is nonetheless related enough to smaller Canis species, such as the coyote, golden jackal, to produce fertile hybrids. It is the only species of Canis to have a range encompassing both Eurasia and North America, originated in Eurasia during the Pleistocene, colonizing North America on at least three separate occasions during the Rancholabrean.
It is a social animal, travelling in nuclear families consisting of a mated pair, accompanied by the pair's adult offspring. The gray wolf is an apex predator throughout its range, with only humans and tigers posing a serious threat to it, it feeds on large ungulates, though it eats smaller animals, livestock and garbage. A seven-year-old wolf is considered to be old, the maximum lifespan is about 16 years; the global gray wolf population is estimated to be 300,000. The gray wolf is one of the world's best-known and most-researched animals, with more books written about it than any other wildlife species, it has a long history of association with humans, having been despised and hunted in most pastoral communities because of its attacks on livestock, while conversely being respected in some agrarian and hunter-gatherer societies. Although the fear of wolves is pervasive in many human societies, the majority of recorded attacks on people have been attributed to animals suffering from rabies. Non-rabid wolves have attacked and killed people children, but this is rare, as wolves are few, live away from people, have developed a fear of humans from hunters and shepherds.
The English'wolf' stems from the Old English wulf, itself thought to be derived from the Proto-Germanic *wulfaz. The Latin lupus is a Sabine loanword. Both derive from the Proto-Indo-European root * lukwos; the species Canis lupus was first recorded by Carl Linnaeus in his publication Systema Naturae in 1758, with the Latin classification translating into the English words "dog wolf". The 37 subspecies of Canis lupus are listed under the designated common name of "wolf" in Mammal Species of the World, published in 2005; the nominate subspecies is the Eurasian wolf known as the common wolf. The subspecies includes the domestic dog, eastern wolf and red wolf, but lists C. l. italicus as a synonym of C. l. lupus. However, the classification of several as either species or subspecies has been challenged; the evolution of the wolf occurred over a geologic time scale of at least 300,000 years. The gray wolf Canis lupus is a adaptable species, able to exist in a range of environments and which possesses a wide distribution across the Holarctic.
Studies of modern gray wolves have identified distinct sub-populations that live in close proximity to each other. This variation in sub-populations is linked to differences in habitat – precipitation, temperature and prey specialization – which affect cranio-dental plasticity; the archaeological and paleontological records show gray wolf continuous presence for at least the last 300,000 years. This continuous presence contrasts with genomic analyses, which suggest that all modern wolves and dogs descend from a common ancestral wolf population that existed as as 20,000 years ago; these analyses indicate a population bottleneck, followed by a rapid radiation from an ancestral population at a time during, or just after, the Last Glacial Maximum. However, the geographic origin of this radiation is not known. In 2018, whole genome sequencing was used to compare members of the genus Canis, along with the dhole and the African hunting dog. There is evidence of gene flow between African golden wolves, golden jackals, gray wolves.
One African golden wolf from the Egyptian Sinai Peninsula showed high admixture with the Middle Eastern gray wolves and dogs, highlighting the role of the land bridge between the African and Eurasian continents in canid evolution. There was evidence of gene flow between golden jackals and Middle Eastern wolves, less so with European and Asian wolves, least with North American wolves; the study proposes that the golden jackal ancestry found in North American wolves may have occurred before the divergence of the Eurasian and North American gray wolves. The study indicates that the common ancestor of the coyote and gray wolf has genetically admixed with a ghost population of an extinct unidentified canid; the canid is genetically close to the dhole and has evolved after the divergence of the African hunting dog from the other canid species. The basal position of the coyote compared to the wolf is proposed to be due to the coyote retaining more of the mitochondrial genome of this unknown canid.
In 2013, a genetic study found that the wolf population in Europe was divided along a north-south axis and formed five major clusters. Three clusters were identified occupying southern and