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Aircraft on display No operational B-2s have been retired by the Air Force to be put on display. B-2s have made occasional appearances on ground display at various air shows. B-2 test article (s/n AT-1000), the second of two built without engines or instruments and used for static testing, was placed on display in 20...
Northrop B-2 Spirit
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Beavers (genus Castor) are large, semiaquatic rodents of the Northern Hemisphere. There are two existing species: the North American beaver (Castor canadensis) and the Eurasian beaver (C. fiber). Beavers are the second-largest living rodents, after capybaras, weighing up to . They have stout bodies with large heads, lo...
Beaver
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Etymology The English word beaver comes from the Old English word or and is connected to the German word and the Dutch word . The ultimate origin of the word is an Indo-European root for . Cognates of beaver is the source for several European placenames, including those of Beverley, Bièvres, Biberbach, Biebrich, Bi...
Beaver
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The more basal castorids had several unique features: more complex occlusion between cheek teeth, parallel rows of upper teeth, premolars that were only slightly smaller than molars, the presence of a third set of premolars (P3), a hole in the stapes of the inner ear, a smooth palatine bone (with the palatine opening c...
Beaver
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The genus Castor likely originated in Eurasia. The earliest fossil remains appear to be C. neglectus, found in Germany and dated 12–10 mya. Mitochondrial DNA studies place the common ancestor of the two living species at around 8 mya. The ancestors of the North American beaver would have crossed the Bering Land Bridge ...
Beaver
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Beavers have large skulls with powerful chewing muscles. They have four chisel-shaped incisors that continue to grow throughout their lives. The incisors are covered in a thick enamel that is colored orange or reddish-brown by iron compounds. The lower incisors have roots that are almost as long as the entire lower jaw...
Beaver
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The beaver's sex organs are inside the body, and the male's penis has a cartilaginous baculum. They have only one opening, a cloaca, which is used for reproduction, scent-marking, defecation, and urination. The cloaca evolved secondarily, as most mammals have lost this feature, and may reduce the area vulnerable to inf...
Beaver
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Beavers can hold their breath for as long as 15 minutes but typically remain underwater for no more than five or six minutes. Dives typically last less than 30 seconds and are usually no more than deep. When diving, their heart rate decreases to 60 beats per minute, half its normal pace, and blood flow is directed mor...
Beaver
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Beavers live in freshwater ecosystems such as rivers, streams, lakes and ponds. Water is the most important component of beaver habitat; they swim and dive in it, and it provides them refuge from land predators. It also restricts access to their homes and allows them to move building objects more easily. Beavers prefer...
Beaver
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Beavers usually live up to 10 years. Felids, canids, and bears may prey upon them. Beavers are protected from predators when in their lodges, and prefer to stay near water. Parasites of the beaver include the bacteria Francisella tularensis, which causes tularemia; the protozoan Giardia duodenalis, which causes giardia...
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Beavers make two types of lodges: bank lodges and open-water lodges. Bank lodges are burrows dug along the shore and covered in sticks. The more complex freestanding, open-water lodges are built over a platform of piled-up sticks. The lodge is mostly sealed with mud, except for a hole at the top which acts as an air ve...
Beaver
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The beaver works as an ecosystem engineer and keystone species, as its activities can have a great impact on the landscape and biodiversity of an area. Aside from humans, few other extant animals appear to do more to shape their environment. When building dams, beavers alter the paths of streams and rivers, allowing fo...
Beaver
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Beaver activity impacts communities of aquatic invertebrates. Damming typically leads to an increase of slow or motionless water species, like dragonflies, oligochaetes, snails, and mussels. This is to the detriment of rapid water species like black flies, stoneflies, and net-spinning caddisflies. Beaver floodings crea...
Beaver
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Beavers are mainly nocturnal and crepuscular, and spend the daytime in their shelters. In northern latitudes, beaver activity is decoupled from the 24-hour cycle during the winter, and may last as long as 29 hours. They do not hibernate during winter, and spend much of their time in their lodges. Family life The core ...
Beaver
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Beavers typically disperse from their parental colonies during the spring or when the winter snow melts. They often travel less than , but long-distance dispersals are not uncommon when previous colonizers have already exploited local resources. Beavers are able to travel greater distances when free-flowing water is av...
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Beavers sometimes come into conflict with humans over land use; individual beavers may be labeled as "nuisance beavers". Beavers can damage crops, timber stocks, roads, ditches, gardens, and pastures via gnawing, eating, digging, and flooding. They occasionally attack humans and domestic pets, particularly when infecte...
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Beavers have been hunted, trapped, and exploited for their fur, meat, and castoreum. Since the animals typically stayed in one place, trappers could easily find them and could kill entire families in a lodge. Many pre-modern people mistakenly thought that castoreum was produced by the testicles or that the castor sacs ...
Beaver
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Beaver pelts were used to make hats; felters would remove the guard hairs. The number of pelts needed depended on the type of hat, with Cavalier and Puritan hats requiring more fur than top hats. In the late 16th century, Europeans began to deal in North American furs due to the lack of taxes or tariffs on the continen...
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Bears are carnivoran mammals of the family Ursidae (). They are classified as caniforms, or doglike carnivorans. Although only eight species of bears are extant, they are widespread, appearing in a wide variety of habitats throughout most of the Northern Hemisphere and partially in the Southern Hemisphere. Bears are f...
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Etymology The English word "bear" comes from Old English and belongs to a family of names for the bear in Germanic languages, such as Swedish , also used as a first name. This form is conventionally said to be related to a Proto-Indo-European word for "brown", so that "bear" would mean "the brown one". However, Ringe ...
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The family Ursidae is one of nine families in the suborder Caniformia, or "doglike" carnivorans, within the order Carnivora. Bears' closest living relatives are the pinnipeds, canids, and musteloids. (Some scholars formerly argued that bears are directly derived from canids and should not be classified as a separate fa...
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The earliest members of Ursidae belong to the extinct subfamily Amphicynodontinae, including Parictis (late Eocene to early middle Miocene, 38–18 Mya) and the slightly younger Allocyon (early Oligocene, 34–30 Mya), both from North America. These animals looked very different from today's bears, being small and raccoon-...
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The raccoon-sized, dog-like Cephalogale is the oldest-known member of the subfamily Hemicyoninae, which first appeared during the middle Oligocene in Eurasia about 30 Mya. The subfamily includes the younger genera Phoberocyon (20–15 Mya), and Plithocyon (15–7 Mya). A Cephalogale-like species gave rise to the genus Ursa...
Bear
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The subfamily Ursinae experienced a dramatic proliferation of taxa about 5.3–4.5 Mya, coincident with major environmental changes; the first members of the genus Ursus appeared around this time. The sloth bear is a modern survivor of one of the earliest lineages to diverge during this radiation event (5.3 Mya); it took...
Bear
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The second alternative phylogenetic hypothesis was implemented by McKenna et al. (1997) to classify all the bear species into the superfamily Ursoidea, with Hemicyoninae and Agriotheriinae being classified in the family "Hemicyonidae". Amphicynodontinae under this classification were classified as stem-pinnipeds in the...
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Unlike most other land carnivorans, bears are plantigrade. They distribute their weight toward the hind feet, which makes them look lumbering when they walk. They are capable of bursts of speed but soon tire, and as a result mostly rely on ambush rather than the chase. Bears can stand on their hind feet and sit up stra...
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Bears have small rounded ears so as to minimize heat loss, but neither their hearing or sight are particularly acute. Unlike many other carnivorans they have color vision, perhaps to help them distinguish ripe nuts and fruits. They are unique among carnivorans in not having touch-sensitive whiskers on the muzzle; howev...
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Extant bears are found in sixty countries primarily in the Northern Hemisphere and are concentrated in Asia, North America, and Europe. An exception is the spectacled bear; native to South America, it inhabits the Andean region. The sun bear's range extends below the equator in Southeast Asia. The Atlas bear, a subspec...
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Most bears are opportunistic omnivores and consume more plant than animal matter, and appear to have evolved from an ancestor which was a low-protein macronutrient omnivore. They eat anything from leaves, roots, and berries to insects, carrion, fresh meat, and fish, and have digestive systems and teeth adapted to such ...
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The sloth bear is not as specialized as polar bears and the panda, has lost several front teeth usually seen in bears, and developed a long, suctioning tongue to feed on the ants, termites, and other burrowing insects. At certain times of the year, these insects can make up 90% of their diets. Some individuals become a...
Bear
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Bears produce a number of vocal and non-vocal sounds. Tongue-clicking, grunting or chuffing many be made in cordial situations, such as between mothers and cubs or courting couples, while moaning, huffing, snorting or blowing air is made when an individual is stressed. Barking is produced during times of alarm, excitem...
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Gestation typically lasts six to nine months, including delayed implantation, and litter size numbers up to four cubs. Giant pandas may give birth to twins but they can only suckle one young and the other is left to die. In northern living species, birth takes place during winter dormancy. Cubs are born blind and helpl...
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Bears do not have many predators. The most important are humans, and as they started cultivating crops, they increasingly came in conflict with the bears that raided them. Since the invention of firearms, people have been able to kill bears with greater ease. Felids like the tiger may also prey on bears, particularly c...
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Laws have been passed in many areas of the world to protect bears from habitat destruction. Public perception of bears is often positive, as people identify with bears due to their omnivorous diets, their ability to stand on two legs, and their symbolic importance. Support for bear protection is widespread, at least in...
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Bears have been popular subjects in art, literature, folklore and mythology. The image of the mother bear was prevalent throughout societies in North America and Eurasia, based on the female's devotion and protection of her cubs. In many Native American cultures, the bear is a symbol of rebirth because of its hibernati...
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Bears are popular in children's stories, including Winnie the Pooh, Paddington Bear, Gentle Ben and "The Brown Bear of Norway". An early version of "Goldilocks and the Three Bears", was published as "The Three Bears" in 1837 by Robert Southey, many times retold, and illustrated in 1918 by Arthur Rackham. The Hanna-Barb...
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The bald eagle (Haliaeetus leucocephalus) is a bird of prey found in North America. A sea eagle, it has two known subspecies and forms a species pair with the white-tailed eagle (Haliaeetus albicilla), which occupies the same niche as the bald eagle in the Palearctic. Its range includes most of Canada and Alaska, all o...
Bald eagle
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There are two recognized subspecies of bald eagle: H. l. leucocephalus (Linnaeus, 1766) is the nominate subspecies. It is found in the southern United States and Baja California Peninsula. H. l. washingtoniensis (Audubon, 1827), synonym H. l. alascanus (Townsend, 1897), the northern subspecies, is larger than souther...
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The plumage of the immature is a dark brown overlaid with messy white streaking until the fifth (rarely fourth, very rarely third) year, when it reaches sexual maturity. Immature bald eagles are distinguishable from the golden eagle (Aquila chrysaetos), the only other very large, non-vulturine raptorial bird in North A...
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The size of the bird varies by location and generally corresponds with Bergmann's rule: the species increases in size further away from the equator and the tropics. For example, eagles from South Carolina average in mass and in wingspan, smaller than their northern counterparts. One field guide in Florida listed simi...
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The bald eagle's natural range covers most of North America, including most of Canada, all of the continental United States, and northern Mexico. It is the only sea eagle endemic to North America. Occupying varied habitats from the bayous of Louisiana to the Sonoran Desert and the eastern deciduous forests of Quebec an...
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The bald eagle typically requires old-growth and mature stands of coniferous or hardwood trees for perching, roosting, and nesting. Tree species reportedly is less important to the eagle pair than the tree's height, composition and location. Perhaps of paramount importance for this species is an abundance of comparativ...
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The bald eagle is usually quite sensitive to human activity while nesting, and is found most commonly in areas with minimal human disturbance. It chooses sites more than from low-density human disturbance and more than from medium- to high-density human disturbance. However, bald eagles will occasionally nest in larg...
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Behavior The bald eagle is a powerful flier, and soars on thermal convection currents. It reaches speeds of when gliding and flapping, and about while carrying fish. Its dive speed is between , though it seldom dives vertically. Regarding their flying abilities, despite being morphologically less well adapted to fast...
Bald eagle
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To hunt fish, the eagle swoops down over the water and snatches the fish out of the water with its talons. They eat by holding the fish in one claw and tearing the flesh with the other. Eagles have structures on their toes called spicules that allow them to grasp fish. Osprey also has this adaptation. Bird prey may occ...
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They obtain much of their food as carrion or via a practice known as kleptoparasitism, by which they steal prey away from other predators. Due to their dietary habits, bald eagles are frequently viewed in a negative light by humans. Thanks to their superior foraging ability and experience, adults are generally more lik...
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In the Pacific Northwest, spawning trout and salmon provide most of the bald eagles' diet from late summer throughout fall. Though bald eagles occasionally catch live salmon, they usually scavenge spawned salmon carcass. Southeast Alaskan eagles largely prey on pink salmon (Oncorhynchus gorbuscha), coho salmon (O. kisu...
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Bald eagles are also known to eat the following fish species: rainbow trout (Oncorhynchus mykiss), white catfish (Ameiurus catus), rock greenling (Hexagrammos lagocephalus), Pacific cod (Gadus macrocephalus), Atka mackerel (Pleurogrammus monopterygius), largemouth bass (Micropterus salmoides), northern pike (Esox luciu...
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Fish taken by bald eagles varies in size, but bald eagles take larger fish than other piscivorous birds in North America, typically range from and prefer fish. When experimenters offered fish of different sizes in the breeding season around Lake Britton in California, fish measuring were taken 71.8% of the time by p...
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Behind fish, the next most significant prey base for bald eagles are other waterbirds. The contribution of such birds to the eagle's diet is variable, depending on the quantity and availability of fish near the water's surface. Waterbirds can seasonally comprise from 7% to 80% of the prey selection for eagles in certai...
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Due to easy accessibility and lack of formidable nest defense against eagles by such species, bald eagles are capable of preying on such seabirds at all ages, from eggs to mature adults, and they can effectively cull large portions of a colony. Along some portions of the North Pacific coastline, bald eagles which had h...
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While they usually target small to medium-sized seabirds, larger seabirds such as great black-backed gulls (Larus marinus) and northern gannets (Morus bassanus) and brown pelicans (Pelecanus occidentalis) of all ages can successfully be taken by bald eagles. Similarly, large waterbirds are occasionally killed. Geese su...
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Mammalian preys are generally less frequently taken than fish or avian prey. However, in some regions, such as landlocked areas of North America, wintering bald eagles may become habitual predators of medium-sized mammals that occur in colonies or local concentrations, such as prairie dogs (Cynomys sp.) and jackrabbits...
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Where available, seal colonies can provide a lot of food. On Protection Island, Washington, they commonly feed on harbor seal (Phoca vitulina) afterbirths, still-borns and sickly seal pups. Similarly, bald eagles in Alaska readily prey on sea otter (Enhydra lutris) pups. Small to medium-sized terrestrial mammalian carn...
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Together with the golden eagle, bald eagles are occasionally accused of preying on livestock, especially sheep (Ovis aries). There are a handful of proven cases of lamb predation, some specimens weighing up to , by bald eagles. Still, they are much less likely to attack a healthy lamb than a golden eagle. Both species ...
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When competing for food, eagles will usually dominate other fish-eaters and scavengers, aggressively displacing mammals such as coyotes (Canis latrans) and foxes, and birds such as corvids, gulls, vultures and other raptors. Occasionally, coyotes, bobcats (Lynx rufus) and domestic dogs (Canis familiaris) can displace e...
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The bald eagle is thought to be much more numerous in North America than the golden eagle, with the bald species estimated to number at least 150,000 individuals, about twice as many golden eagles there are estimated to live in North America. Due to this, bald eagles often outnumber golden eagles at attractive food sou...
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Compared to most other raptors, which mostly nest in April or May, bald eagles are early breeders: nest building or reinforcing is often by mid-February, egg laying is often late February (sometimes during deep snow in the North), and incubation is usually mid-March and early May. Eggs hatch from mid-April to early May...
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In Sonora, Mexico, eagles have been observed nesting on top of hecho catcuses (Pachycereus pectin-aboriginum). Nests located on cliffs and rock pinnacles have been reported historically in California, Kansas, Nevada, New Mexico and Utah, but currently are only verified to occur only in Alaska and Arizona. The eggs aver...
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A young eaglet can gain up to a day, the fastest growth rate of any North American bird. The young eaglets pick up and manipulate sticks, play tug of war with each other, practice holding things in their talons, and stretch and flap their wings. By eight weeks, the eaglets are strong enough to flap their wings, lift t...
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The average lifespan of bald eagles in the wild is around 20 years, with the oldest confirmed one having been 38 years of age. In captivity, they often live somewhat longer. In one instance, a captive individual in New York lived for nearly 50 years. As with size, the average lifespan of an eagle population appears to ...
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Most non-human-related mortality involves nestlings or eggs. Around 50% of eagles survive their first year. However, in the Chesapeake Bay area, 100% of 39 radio-tagged nestlings survived to their first year. Nestling or egg fatalities may be due to nest collapses, starvation, sibling aggression or inclement weather. A...
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Once a common sight in much of the continent, the bald eagle was severely affected in the mid-20th century by a variety of factors, among them the thinning of egg shells attributed to use of the pesticide DDT. Bald eagles, like many birds of prey, were especially affected by DDT due to biomagnification. DDT itself was ...
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The species was first protected in the U.S. and Canada by the 1918 Migratory Bird Treaty, later extended to all of North America. The Bald and Golden Eagle Protection Act, approved by the U.S. Congress in 1940, protected the bald eagle and the golden eagle, prohibiting commercial trapping and killing of the birds. The ...
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The bald eagle was officially removed from the U.S. federal government's list of endangered species on July 12, 1995, by the U.S. Fish & Wildlife Service, when it was reclassified from "endangered" to "threatened". On July 6, 1999, a proposal was initiated "To Remove the Bald Eagle in the Lower 48 States From the List ...
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Accipitrimorphae
Animals
Role in Native American culture The bald eagle is a sacred bird in some North American cultures, and its feathers, like those of the golden eagle, are central to many religious and spiritual customs among Native Americans. Eagles are considered spiritual messengers between gods and humans by some cultures. Many pow wow...
Bald eagle
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Biology and health sciences
Accipitrimorphae
Animals
The bald eagle is the national symbol of the United States. It was adopted as a national emblem in 1782, but not designated the "national bird" until an act of Congress in December 2024. The founders of the United States were fond of comparing their new republic with the Roman Republic, in which eagle imagery (usually...
Bald eagle
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Biology and health sciences
Accipitrimorphae
Animals
The brown bear (Ursus arctos) is a large bear native to Eurasia and North America. Of the land carnivorans, it is rivaled in size only by its closest relative, the polar bear, which is much less variable in size and slightly bigger on average. The brown bear is a sexually dimorphic species, as adult males are larger an...
Brown bear
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While the brown bear's range has shrunk, and it has faced local extinctions across its wide range, it remains listed as a least concern species by the International Union for Conservation of Nature (IUCN) with a total estimated population in 2017 of 110,000. Populations that were hunted to extinction in the 19th and 20...
Brown bear
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DNA analysis shows that, apart from recent, human-caused population fragmentation, brown bears in North America are generally part of a single interconnected population system, with the exception of the population (or subspecies) in the Kodiak Archipelago, which has probably been isolated since the end of the last Ice ...
Brown bear
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Biology and health sciences
Carnivora
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Brown bears first emigrated to North America from Eurasia via Beringia during the Illinoian Glaciation. Genetic evidence suggests that several brown bear populations migrated into North America, aligning with the glacial cycles of the Pleistocene. The founding population of most North American brown bears arrived first...
Brown bear
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Brown bears generally weigh , with males outweighing females. They have a head-and-body length of and a shoulder height of . The tail is relatively short, as in all bears, ranging from in length. The smallest brown bears, females during spring among barren-ground populations, can weigh so little as to roughly match t...
Brown bear
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Adults have massive, heavily built, concave skulls, which are large in proportion to the body. The projections of the skull are well developed. Skull lengths of Russian brown bears tend to be for males, and for females. Brown bears have the broadest skull of any extant ursine bear. The width of the zygomatic arches i...
Brown bear
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Brown bears inhabit the broadest range of habitats of any living bear species. They seem to have no altitudinal preferences and have been recorded from sea level to an elevation of in the Himalayas. In most of their range, brown bears seem to prefer semi-open country, with a scattering of vegetation, that can allow th...
Brown bear
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In Europe, in 2010, there were 14,000 brown bears in ten fragmented populations, from Spain (estimated at only 20–25 animals in the Pyrenees in 2010, in a range shared between Spain, France, and Andorra, and some 210 animals in Asturias, Cantabria, Galicia, and León, in the Picos de Europa and adjacent areas in 2013) i...
Brown bear
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The smallest populations are most vulnerable to habitat loss and fragmentation, whereas the largest are primarily threatened by overhunting. The use of land for agriculture may negatively effect brown bears. Additionally, roads and railway tracks could pose a serious threat, as oncoming vehicles may collide with crossi...
Brown bear
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Brown bears have one of the largest brains of any extant carnivoran relative to their body size and have been shown to engage in tool use, which requires advanced cognitive abilities. This species is mostly solitary, although bears may gather in large numbers at major food sources (e.g., open garbage dumps or rivers co...
Brown bear
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Brown bears also produce various vocalizations. Huffing occurs when the animal is tense, while woofing is made when alarmed. Both sounds are produced by exhalations, though huffing is harsher and is made continuously (approximately twice per second). Growls and roars are made when aggressive. Growling is "harsh" and "g...
Brown bear
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The mating season occurs from mid-May to early July, shifting to later in the year the farther north the bears are found. Brown bears are polygynandrous, remaining with the same mate for a couple of days to a couple of weeks and mating multiply during the mating season. Outside of this narrow time frame, adult male and...
Brown bear
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Males take no part in raising cubs – parenting is left entirely to the females. Through the process of delayed implantation, a female's fertilized egg divides and floats freely in the uterus for six months. During winter dormancy, the fetus attaches to the uterine wall. The cubs are born eight weeks later, while the mo...
Brown bear
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The cubs are dependent on the mother and a close bond is formed. During the dependency stage, the cubs learn (rather than inherit as instincts from birth) survival techniques, such as which foods have the highest nutritional value and where to obtain them; how to hunt, fish, and defend themselves; and where to den. Inc...
Brown bear
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The brown bear is one of the most omnivorous animals and has been recorded as consuming the greatest variety of foods of any bear. Despite their reputation, most brown bears are not highly carnivorous, as they derive up to 90% of their dietary food energy from vegetable matter. They often feed on a variety of plant lif...
Brown bear
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In the Kamchatka peninsula and several parts of coastal Alaska, brown bears feed mostly on spawning salmon, whose nutrition and abundance explain the enormous size of the bears in those areas. The fishing techniques of bears are well-documented. They often congregate around falls when the salmon are forced to breach th...
Brown bear
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When emerging from hibernation, brown bears, whose broad paws allow them to walk over most ice and snow, may pursue large prey such as moose, whose hooves cannot support them on encrusted snow. Similarly, predatory attacks on large prey sometimes occur at riverbeds, when it is more difficult for the prey specimen to ru...
Brown bear
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Adult bears are generally immune to predatory attacks except from large Siberian (Amur) tigers and other bears. Following a decrease of ungulate populations from 1944 to 1959, 32 cases of Siberian tigers attacking both Ussuri brown bears (Ursus arctos lasiotus) and Ussuri black bears (U. thibetanus ussuricus) were reco...
Brown bear
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Brown bears usually dominate other bear species in areas where they coexist. Due to their smaller size, American black bears are at a competitive disadvantage to grizzly bears in open, unforested areas. Although displacement of black bears by grizzly bears has been documented, actual killing of black bears by grizzlies...
Brown bear
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Brown bears are susceptible to parasites such as flukes, ticks, tapeworms, roundworms, and biting lice. It is thought that brown bears may catch canine distemper virus (CDV) from other caniforms such as stray dogs and wolves. A captive individual allegedly succumbed to Aujeszky's disease. Hibernation physiology A stu...
Brown bear
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Humans have been recorded hunting brown bears for over 10,300–9,300 years. Bears were hunted throughout their range in Europe, Asia and North America by both the native Americans and Europeans. The former usually killed bears for survival needs, while the latter for sports or population control. In Europe, between the ...
Brown bear
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Bears have been recorded in captivity as early as 1,500 BC. As of 2017, there are more than 700 brown bears in zoos and wildlife parks worldwide. Captive bears are largely lethargic and spend a considerable amount of time doing nothing. When active, captive bears may engage in repetitive back and forth motion, known wi...
Brown bear
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Bears have been popular subjects in art, literature, folklore, and mythology. The image of the mother bear was prevalent throughout societies in North America and Eurasia, based on the female's devotion and protection of her cubs. The earliest cave paintings of bears occurred in the Paleolithic, with over 100 recorded ...
Brown bear
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There is evidence of prehistoric bear worship, though this is disputed by archaeologists. It is possible that bear worship existed in early Chinese and Ainu cultures. The Romans built small carved figures of bears that were used during the burials of infants. In Ancient Greek mythology, bears were considered similar to...
Brown bear
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Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). This motion pattern typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new ...
Brownian motion
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Physical sciences
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The Roman philosopher-poet Lucretius' scientific poem "On the Nature of Things" () has a remarkable description of the motion of dust particles in verses 113–140 from Book II. He uses this as a proof of the existence of atoms: Although the mingling, tumbling motion of dust particles is caused largely by air currents, ...
Brownian motion
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Einstein's theory There are two parts to Einstein's theory: the first part consists in the formulation of a diffusion equation for Brownian particles, in which the diffusion coefficient is related to the mean squared displacement of a Brownian particle, while the second part consists in relating the diffusion coeffici...
Brownian motion
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This expression (which is a normal distribution with the mean and variance usually called Brownian motion ) allowed Einstein to calculate the moments directly. The first moment is seen to vanish, meaning that the Brownian particle is equally likely to move to the left as it is to move to the right. The second moment ...
Brownian motion
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Physics
Dynamic equilibrium is established because the more that particles are pulled down by gravity, the greater the tendency for the particles to migrate to regions of lower concentration. The flux is given by Fick's law, where . Introducing the formula for , we find that In a state of dynamical equilibrium, this speed mu...
Brownian motion
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An identical expression to Einstein's formula for the diffusion coefficient was also found by Walther Nernst in 1888 in which he expressed the diffusion coefficient as the ratio of the osmotic pressure to the ratio of the frictional force and the velocity to which it gives rise. The former was equated to the law of van...
Brownian motion
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where is the viscosity coefficient, and is the radius of the particle. Associating the kinetic energy with the thermal energy , the expression for the mean squared displacement is times that found by Einstein. The fraction 27/64 was commented on by Arnold Sommerfeld in his necrology on Smoluchowski: "The numerical ...
Brownian motion
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These orders of magnitude are not exact because they don't take into consideration the velocity of the Brownian particle, , which depends on the collisions that tend to accelerate and decelerate it. The larger is, the greater will be the collisions that will retard it so that the velocity of a Brownian particle can ne...
Brownian motion
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Astrophysics: star motion within galaxies In stellar dynamics, a massive body (star, black hole, etc.) can experience Brownian motion as it responds to gravitational forces from surrounding stars. The rms velocity of the massive object, of mass , is related to the rms velocity of the background stars by where is t...
Brownian motion
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https://en.wikipedia.org/wiki/Brownian%20motion
Physical sciences
Thermodynamics
Physics