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The ongoing lower level of species extinction intensity occurring between episodes of mass extinctions. Extinction is a normal part of the history of life. Out of every 100 species that have ever lived on Earth, 99 are no longer in existence.…

A kind of mathematics whose variables can only be True or False. A variable is called Boolean if it can only hold two possible values: True or False. The value True can be represented by the number one and False by zero. For example, if A is a…

A mathematical system that details the properties and relationships of spatial objects such as points, lines, shapes, and planes. Euclidean geometry is also known as flat geometry or planar geometry, because planes in Euclidean geometry have the…

Typically, an aquatic vertebrate with scales, gills, and paired fins. Fishes (Fig. 1) are found throughout the world's waterways, from saltwater oceans to freshwater streams and ponds. About 35,000 species of fishes have been described to date. Many…

The inverse function of an exponential function in mathematics. Stated less technically, a logarithm is the opposite of an exponent. Logarithms are used to solve equations in which the variable is an exponent. Historically, tables of logarithms…

A branch of mathematics involving numerical measures of how likely it is that a particular event will occur. A probability is a number between 0 and 1. An event that will never occur has a probability of zero, and an event that is certain to occur…

In medicine and health sciences, a value expected for an individual whose state of health is known and well described, and the interval of values broadly expected for a population, respectively. Results of clinical laboratory tests and other…

The field of knowledge concerned with collecting, analyzing, and presenting data. Statistical methods are regularly used by researchers in the physical, biological, and social sciences, as well as engineers, business managers, government officials…

A subdiscipline of paleobiology that investigates the processes of preservation and their influence on information in the fossil record. Taphonomy is the study of fossilization and considers the processes at work in the incorporation of living…

The study of systems consisting of arbitrary sets of elements of unspecified type, together with certain operations satisfying prescribed lists of axioms. Abstract algebra has been developed since the mid-1920s and has become a basic idiom of…

Most commonly, a generic name for all fossil resins, although it has been restricted by some to refer only to succinite, the mineralogical species of fossil resin that includes most of the Baltic Coast deposits. The time necessary to transform resin…

A statistical technique that partitions the total variation in experimental data into components assignable to specific sources. Analysis of variance is applicable to data for which (1) effects of sources are additive, (2) uncontrolled or…

A genus of fossil birds in the extinct order Archaeopterygiformes, characterized by flight feathers like those of modern birds. Archaeopteryx is generally accepted as the oldest known fossil bird. It represents a unique snapshot of evolution; most…

A discipline that combines biology, mathematics, and computer science to acquire, store, analyze, and disseminate complex biological data. The term bioinformatics was coined by Paulien Hogeweg and Ben Hesper in the early 1970s to describe the "the…

In its simplest form, a vector is a directed line segment. Physical quantities, such as velocity, acceleration, force, and displacement, are vector quantities, or simply vectors, because they can be represented by directed line segments. The algebra…

A class in the phylum Mollusca that is exclusively marine and includes squids, octopuses, and cuttlefishes. The molluscan class Cephalopoda is one of the major taxonomic groupings of marine animals and contains both extant members—squids (Fig. 1),…

An order of the class Reptilia, including the turtles, terrapins, and tortoises; also termed Testudines. The order Chelonia (often referred to as Testudines) comprises one of the oldest groups of reptiles on Earth. Members of the Chelonia…

A natural and extremely useful extension of the familiar real numbers. They can be introduced formally as follows. Consider the two-dimensional real vector space consisting of all ordered pairs (a1, a2) of real numbers. Geometrically this space can…

Any living or fossil member of the plant division Pinophyta, consisting chiefly of woody trees or shrubs that produce cones and evergreen needles. Conifers are predominantly cone-bearing, evergreen trees and shrubs belonging to the order Pinales, as…

A curve traced in the plane by a point on a circle that rolls, without slipping, on a line. If the line is the x axis of a rectangular coordinate system, at whose origin O the moving point P touches the axis, parametric equations of the cycloid are…

A branch of mathematics that deals with intrinsic properties of curves and surfaces in three-dimensional Euclidean space. The intrinsic properties are those which are independent of the geometrical object's orientation or location in space. The…

In arithmetic and algebra, the process of finding one of two factors of a number (or polynomial) when their product and one of the factors are given. The symbol ÷ now used mostly in elementary English and American arithmetics to denote division…

The number e usually defined as the limit approached by the expression as n approaches infinity. If the given expression is expanded by the binomial theorem, and if one uses the theorem that the limit of the quotient of two polynomials of equal…

The death and disappearance of a species. The extinction of a species usually represents an end point in a long series of population extinctions. During the extinction process, unique evolutionary history is lost at every stage, but the death of the…

A method of quantitative multivariate analysis with the goal of representing the interrelationships among a set of continuously measured variables (usually represented by their intercorrelations) by a number of underlying, linearly independent…

In algebra, the term "field" is used to designate an algebraic system or structure containing at least two elements and having two binary rules of composition: addition and multiplication (that is, if a and b are any two elements of the field, then…

A record of earlier life buried in rock. Originally meaning any distinctive object that has been dug up (from Latin fodio, dig), the term “fossil” soon came to refer particularly to things resembling animals and plants. These objects were known…

A branch of mathematics concerned with the properties of space, including points, lines, curves, planes and surfaces in space, and figures bounded by them. Multiple kinds of geometry exist, dealing with everyday concepts such as lengths, angles, and…

An uncrewed, controlled-flight vehicle that is guided to a target by guidance and control equipment. This equipment may be carried in the missile vehicle itself, or guidance may be directed from the launch site. The term is generally reserved for…

Optical instruments that establish an optical line or axis for the purpose of aiming a weapon. The axis includes the observer's eye, a suitable mark in the instrument, and the target. For a pistol, the traditional iron sights employ a rear notch and…

Intentional generation of interfering signals in the electromagnetic spectrum by powerful transmitters as a countermeasure intended to block a communication, radar, or infrared system or to impair its effectiveness appreciably. Radio broadcasts or…

The common name for a member of the agnathan fishes. The fish superclass Agnatha (subphylum Vertebrata, phylum Chordata) comprises the jawless vertebrates (agnathans). Members include cyclostomes (modern lampreys and hagfishes), various extinct…

A topological group with only countably many connected components whose identity component is open and is an analytic group. An analytic group or connected Lie group is a topological group with the additional structure of a smooth manifold such that…

That branch of mathematics which deals with solutions of systems of linear equations and the related geometric notions of vector spaces and linear transformations. It is fundamental in the theory of the calculus of functions of several variables and…

A lineage of true elephants in the extinct genus Mammuthus that occupied Eurasia and North America in the late Cenozoic Era. Mammoths (genus Mammuthus) are extinct elephants assigned to the mammalian order Proboscidea (Fig. 1). They inhabited…

The widespread, catastrophic loss of many species in a relatively short period of geological time. Earth has supported life for approximately 3.5 billion years, and it is normal for species to become extinct and for new species to arise through…

The application of mathematics to biological systems. Just as physics underlies many engineering technologies, biology serves as a foundation for such disciplines as medicine, agriculture, animal husbandry, and environmental sciences, in which…

The study of the patterns and relationships that arise between abstract concepts. Though studied purely for its own sake, mathematics is the language with which all rigorous science is discussed. As the German-born U.S. theoretical physicist Albert…

A major phylum of the animal kingdom comprising a diverse group of unsegmented, soft-bodied invertebrates. The phylum Mollusca is one of the most significant groupings of invertebrate animals. Members of the Mollusca, termed mollusks or molluscs,…

A mammalian order containing the egg-laying platypus and echidnas. Members of the order Monotremata (monotremes) are egg-laying mammals belonging to the subclass Prototheria (in some alternative classifications, the monotremes have been assigned to…

Weapons that arm warships. Of the wide variety of such weapons, three important categories are exclusively naval: antiship missiles, torpedoes, and mines. Other weapons all correspond to land-based types, but submarine-launched ballistic missiles…

A small extinct order of articulated brachiopods that ranges in age from Early to Middle Cambrian and includes the earliest known calcitic brachiopods. Classification The order Obolellida is included within the class Obolellata, subphylum…

An order of coleoid cephalopods, characterized by eight appendages (which encircle the mouth), a saclike body, and an internal shell that is much modified or reduced from that of its ancestors. Members of the order Octopoda (subclass Coleoidea,…

A morphologically distinct type of trace fossil left by boring organisms in hard biogenic substrates. Oichnus Bromley 1981 is a formal taxonomic name with the rank of ichnogenus (a trace fossil genus). Oichnus is a Latin-derived term that…

A suborder of trilobites (a class of extinct arthropods) and a diverse clade consisting of roughly 100 distinct species. The trilobites constituting the suborder Olenellina belong to the order Redlichiida in the class Trilobita. These extinct…

A class of the subphylum Asterozoa (phylum Echinodermata), comprising the brittle stars and basket stars, in which the arms are usually clearly demarcated from a central disk and perform whiplike locomotor movements, and the tube feet are…

A taxonomic fish group comprising the bony fishes. The Osteichthyes grouping (often considered a superclass) consists of the classes Actinopterygii (ray-finned fishes) and Sarcopterygii (lungfishes and lobefins, or coelacanths, but excluding…

Fossil lobe-finned (sarcopterygian) fishes of Devonian to Permian age (395–270 million years ago), the ancestral group for the land vertebrates, or “tetrapods.” Phylogeny The term “osteolepiforms” is applied to a range of fossil fishes, found…

An order of extinct jawless vertebrate fishes, also called Cephalaspida, known from the Middle Silurian to Upper Devonian of Europe, Asia, and North America. They were mostly small, about 2 in. (5 cm) to 2 ft (60 cm) in length. The head and part of…

A major taxon of the Crustacea containing small bivalved animals 0.004–1.4 in. (0.1–33 mm) long, with most between 0.04 and 0.08 in. (1 and 2 mm). Members of the Ostracoda inhabit aquatic environments in nearly all parts of the world.…

A popular name applied to several groups of extinct jawless vertebrates (fishes). Most ostracoderms were covered with an external skeleton or armor of bone, from which is derived their name, meaning “shell-skinned” (see illustration). They are known…

A peculiar arthropod, evidently related to the Pycnogonida and represented by a number of well-preserved fossils from the Devonian Hunsrück shales. Palaeoisopus was formerly considered by a number of paleontologists to have an anterior jointed…

A large, extinct assemblage of primitive ray-finned (actinopterygian) fishes known from the Silurian to Cretaceous, which were most numerous in Carboniferous and Permian times. They are known as fossils from all continents except Antarctica.…

A tiny fossil fish found only in rocks of Middle Devonian age within a small geographic region of Caithness, Scotland, and principally at one site, Achanarras Quarry, where it is surprisingly abundant. One of the most enigmatic of all fossil fishes,…

The study of chemical processes used by organisms that lived in the geological past. Most information on the nature of life in the geological past comes from the study of fossils; a record of biochemical processes that occurred can be found in the…

The study of pollen grains and spores, both extant and extinct, as well as other organic microfossils. Although the origin of the discipline dates back to the seventeenth century, when modern pollen was first examined microscopically, the term…

A fossil lobe-finned (sarcopterygian) fish from rock strata of the Baltic region dating to the Middle–Late Devonian Period (about 372–368 million years ago), which provides key evidence about the evolutionary transition from fish to land vertebrates…

An extinct order of relatively large placental mammals represented by Paleocene-Eocene fossils from western Europe, North America, and eastern Asia. Pantodonts were an early evolutionary experiment in large-bodied herbivory by primitive placental…

A medium-sized class of extinct blastozoan echinoderms containing about 17–19 genera, ranging from the late Early Ordovician to the Early Silurian throughout North America and in northern Europe. Their maximum standing diversity (13 genera) occurred…

A ratio comparison of two quantities expressed by using 100 equal parts, or hundredths; symbolized %. There are three major uses of percent: part of a whole, rate, and comparison of any two quantities. Part of a whole The basic idea of percent is as…

An order of herbivorous, odd-toed, hoofed mammals, including the living horses, zebras, donkeys, rhinoceroses, tapirs, and their extinct relatives. Members of the order Perissodactyla, or perissodactyls, are odd-toed ungulates (mammals with hooves).…

A concentration of appreciable numbers of petrified tree trunks exposed at the earth surface, standing upright in the position of growth, lying prostrate, or both. Petrifaction is a form of mineral emplacement or embedding, by which the organic…

An order of mammals comprising the living pangolins and their poorly known fossil predecessors. All living members of the mammalian order Pholidota, that is, the pangolins (also termed scaly anteaters), belong to the family Manidae and are assigned…

An alleged fossil human based on craniodental fragments that were eventually discovered to constitute a skillful hoax. The Piltdown man hoax was the scientifically most successful fraud in the history of anthropology. Between 1908 and 1914, Charles…

One of the major divisions of the seed plants. The most familiar and common representatives of the division Pinophyta are the evergreen, cone-bearing trees of the order Pinales (within the class Pinopsida). Members are known colloquially as…

The single class of the division Pinophyta (Gymnospermae). The class Pinopsida contains both living and fossil taxa. The living representatives of the Pinopsida are woody plants; most are trees with a central axis and excurrent branches. Leaves are…

A class of fishes (Pisces) known from the Devonian Period, and a few that survived into the base of the Carboniferous. They were true fishes or gnathostomes, and can be distinguished from other fishes by the following characters: the gill chamber…

A small group of marine reptiles forming part of the Sauropterygia, known only from deposits of Triassic age in Europe, the Near East (Israel), North Africa (Tunisia), and China. The earliest occurrence of placodonts is in the uppermost Lower…

The worldwide array of plant life, including plants that have roots in the soil, plants that live on or within other plants and animals, plants that float on or swim in water, and plants that are carried in the air. Fungi used to be included in the…

A Paleozoic (Ordovician and Devonian) order of sea stars of the class Asteroidea; only two genera have been recognized. Platyasteridans have relatively elongate flat arms; broad, transversely aligned ventral arm plates; and paxilliform aboral plates…

An order of the Podocopa (Ostracoda) containing a single family, Cytherellidae, and two extinct superorders. Platycopids are small marine or brackish-water ostracods with an asymmetrical shell that is oblong, nearly rectangular, and laterally…

One of two Recent subclasses of Ostracoda. The two (Podocopa and Myodocopa) may share many characteristics but differ significantly in others. Shared characteristics include a carapace (shell) with a straight-to-concave ventral margin and somewhat…

The only order of the superorder Polymixiomorpha, comprising the beardfishes. The order Polymixiiformes (infraclass Teleostei, class Actinopterygii) consists of one family (Polymixiidae) with one genus (Polymixia) and ten extant species. Several…

A class within the phylum Mollusca whose members are popularly called chitons, coat-of-mail shells, or sea cradles. The class Polyplacophora (alternatively Loricata) lies within the phylum Mollusca and comprises the chitons. Members of classes…

A division of the plant kingdom, commonly called the ferns, which is widely distributed throughout the world but is most abundant and varied in moist, tropical regions. The Polypodiophyta are sometimes treated as a class Polypodiopsida of a broadly…

A distinctive and apparently ancient order of actinopterygian fishes comprising the subclass Cladistia, commonly known as bichirs and reedfishes. The following combination of characteristics distinguishes members of the order Polypteriformes from…

An order of placental mammals containing the largest and most powerful living terrestrial mammals—the elephants. Proboscideans once had a wide distribution, reaching every continent except Australia and Antarctica. Although early forms lacked both…

One of the four subclasses of the class Mammalia. Prototheria contains a single order, the Monotremata. No ancestral genera of fossil monotremes are known, and the structure of the living monotremes is so specialized that the affinities of the…

A group long recognized as an order of fossil plants (subdivision Psilopsida) collected in rocks of Late Silurian and Devonian age. It has been subdivided, on the basis of many data, into three categories whose descriptions include the chief kinds…

An order of small, delicate insects, referred to as psocids, bark lice, or book lice. The order Psocoptera (an equivalent name is Corrodentia) belongs to a group (clade), the Acercaria, that also includes the Hemiptera (true bugs, aphids, and…

A subclass of the molluscan class Gastropoda, containing about 23,500 species of snails that are grouped into three orders (or superorders): Systellommatophora, Basommatophora, and Stylommatophora. Pulmonates include most of the common snails found…

An order of very specialized deep-bodied fishes near the holostean level of organization that are known only from the fossil record. They were a widespread group that first appeared in the Upper Triassic of Europe with the genus Eomesodon,…

A class of vertebrates composed of turtles, lizards, snakes, crocodilians, amphisbaenians, and tuataras, as well as a variety of extinct forms. The members of the vertebrate class Reptilia are tetrapods, meaning that they possess four limbs or are…

The assertion that under certain light restrictions the surface integral of (∇ × ℑ) · ν over a surface patch S is equal to the line integral of ℑ · τ taken around C, the boundary curve of S, provided the sense of transcription of C is right-handed…

One of the four fundamental operations of arithmetic and algebra. The first printed use of the symbol − to denote subtraction is in Johann Widman's Behennde und hüpsche Rechnung, Leipzig, 1489. Subtraction is often regarded as an operation inverse…

A two-dimensional geometric figure (a collection of points) in three-dimensional space. The simplest example is a plane—a flat surface. Some other common surfaces are spheres, cylinders, and cones, the names of which are also used to describe the…

A term describing a relationship of two figures (usually of the same dimension) in the neighborhood of a common point. The figures are tangent at a point P if they touch at P but do not intersect in a sufficiently small neighborhood of P. To be more…

The most recent and successful group (infraclass) of actinopterygians (ray-finned fishes), first appearing in the Upper Triassic. The members of the Teleostei (teleosts) constitute one of the major fish groups belonging to the class Actinopterygii…

One of the largest recognized groups of early amphibians with about 180 described genera. The Temnospondyli first appear in the fossil record in the lower Carboniferous and reach substantial diversity in the later Carboniferous and Permian. The…

The systematic study of tensors which led to an extension and generalization of vectors, begun in 1900 by two Italian mathematicians, G. Ricci and T. Levi-Civita, following G. F. B. Riemann's proposal concerning a generalization of Euclidean…

A proposition arrived at by the methods of logical deduction from a set of basic postulates or axioms accepted as primitive and therefore not subject to deductive proof. So long as a theorem is part of a purely formal system, it is not meaningful to…

The branch of mathematics concerned with finding facts concerning the roots of algebraic equations and finding methods for obtaining them. The most important type of algebraic equation is the polynomial equation in one unknown which is an expression…

One of the four subclasses of the class Mammalia, including all living mammals except the monotremes. The Theria were by far the most successful of the several mammalian stocks that arose from the mammallike reptiles in the Triassic. The subclass is…

An important paleontological concept that denotes temporal mixing (or age mixing) of fossils. Unlike live-collected organisms, fossils found together within a single stratum need not be contemporaneous with one another, but may represent mixed…

The study and application of topological transformation groups. Topological dynamics originated in the late-nineteenth-century investigations of the qualitative behavior of the solutions to the differential equations of classical mechanics by Henri…

The branch of mathematics that studies the qualitative properties of spaces, as opposed to the more delicate and refined geometric or analytic properties. While there are earlier results that belong to the field, the beginning of the subject as a…

A surface obtained by rotating a circle about a line that lies in the plane of the circle but that has no points in common with the circle (see illustration). The equations x = u cos v, y = u sin v, z = [r2 − (u − b)2]1/2, b > r > 0, represent the…

A plane curve for which the length of any tangent between the curve and a fixed line is constant c. If the x axis is the fixed line, its differential equation is Eq. (1). 1 With ψ, the inclination of the tangent, as pa­ram­eter, this yields Eqs.…

The study of triangles and the trigonometric functions. One common use for trigonometry is to measure heights and distances that are awkward or impossible to measure by ordinary means. Surveyors use it to find heights of mountains and distances…

A class of extinct Paleozoic arthropods, occurring in marine rocks of Early Cambrian through Late Permian age. The members of the extinct arthropod class Trilobita are commonly known as trilobites (Fig. 1). With about 5000 described genera and…