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An ongoing current event in which a large number of living species are threatened with extinction or are going extinct because of environmentally destructive human activities. The Earth is presently in the midst of a mass extinction event. In the…

Any of several leguminous plants, or their seeds, long utilized as food by humans or livestock. There are more than 40,000 varieties of beans, with only a small number of these being mass-produced for human or animal consumption. In particular,…

The response of corals to environmental stress in which they eject the single-cell algae that live within the transparent coral tissue, making the white coral skeleton visible. Corals (Fig. 1) are animals that live in a partnership (symbiosis) with…

Marine animal life inhabiting the portion of the oceans below the upper limit of the continental slopes. The marine animals that make up the deep-sea fauna live below the photic zone of the oceans. In general, the deep sea may be regarded as that…

A species translocated from one region or continent to another outside its normal range, particularly when the translocation is the result of human activity (intentional or otherwise). Many thousands of species, including animals, plants, fungi,…

The branch of mathematics dealing with the solution of equations. These equations involve unknowns, or variables, along with fixed numbers from a specified system (Fig. 1). The origins of algebra were based on the need to develop equations that…

The study of zero sets of polynomial equations. Examples of zero sets of polynomial equations studied in algebraic geometry are the parabola y − x2 = 0, thought of as sitting in the (x, y)-plane, and the locus of all points (t, t2, t3, t4), which is…

A natural process in which harmful or beneficial effects are caused by secondary metabolites that spread from a donor organism to a recipient and are produced by plants, algae, bacteria, and fungi. Allelopathy is a key ecological process and has…

A discipline within the field of animal behavior that focuses on the reception and use of signals. Animal communication could well include all of animal behavior because a liberal definition of the term signal could encompass all stimuli perceived…

The scientific study of past material culture. The initial objective of archeology (often spelled archaeology) is to construct cultural chronologies that order past material culture into meaningful temporal segments. The intermediate objective is to…

The study of behavior change in response to drugs, chemicals, or other environmental conditions or agents. Behavioral toxicology investigates the effect of toxic exposure on organismal behavior. The toxic exposure can involve various chemicals,…

The destruction of organic compounds by microorganisms. Biodegradation is a process (carried out by microorganisms) that decomposes organic material into its constituent elements or new compounds. Microorganisms, particularly bacteria (and fungi to…

A microbial (often bacterial) community that is enveloped by an adhesive substance (the glycocalyx) at the interface of a liquid and a surface. Biofilms (see illustration) are defined as highly structured communities of microorganisms that are…

The study of the cycling of chemicals between organisms and the surface environment of the Earth. The chemicals either can be taken up by organisms and used for growth and synthesis of living matter or can be processed to obtain energy. The chemical…

The use of parasitoids, predators, and pathogens to reduce injurious pest insect populations and consequently the damage that they cause. Biological insect control (or insect biocontrol) is the regulation of insect populations by biological means.…

The branch of mathematics dealing with two fundamental operations, differentiation and integration, which are carried out on functions. The subject of calculus (Fig. 1), as traditionally developed in college textbooks, is partly an elementary…

A heart-shaped curve generated by a point of a circle that rolls (without slipping) on a fixed circle of the same diameter. In point-wise construction of the curve, let O be a fixed point of a circle C of diameter a, and Q a variable point of C. Lay…

A theory of mathematical structure in which smooth continuous inputs lead to discontinuous responses. Water suddenly boils, ice melts, a building crashes to the ground, or the earth unexpectedly buckles and quakes. The French mathematician René Thom…

The branch of mathematics which studies arrangements of elements (usually a finite number) into sets under certain prescribed constraints. Problems combinatorialists attempt to solve include the enumeration problem (how many such arrangements are…

The theory of complex systems. Complexity theory arises from the need to understand the richness in structure and behavior often seen in large systems. The property that distinguishes complex systems from systems that are large but simple is the…

The solid of revolution obtained by revolving a right triangle about one of its shorter sides is called a cone, or more precisely a right circular cone (see illustration). More generally, the term cone is used in solid geometry to describe a solid…

A special operation in mathematics in which a set of points in one coordinate system is mapped or transformed into a corresponding set in another coordinate system, preserving the angle of intersection between pairs of curves.A mapping or…

Management of the human use of natural resources to provide the maximum benefit to current generations while maintaining capacity to meet the needs of future generations. Conservation includes both the protection and rational use of natural…

Schemes for locating points in a given space by means of numerical quantities specified with respect to some frame of reference. These quantities are the coordinates of a point. To each set of coordinates there corresponds just one point in any…

Pathological conditions affecting the health of coral and causing its physiological dysfunction. Broadly defined, coral disease (Fig. 1) is any impairment to coral health resulting in physiological disturbance and breakdown. It usually involves…

A measure of the three-dimensional structure of live coral communities on reefs. Coral reef structural complexity is an intrinsic element of coral reef ecosystems and quantitates the surface area of coral in relation to its linear area. The…

A large, tawny brown wild cat, Puma concolor (family Felidae), once widespread over most of the Americas; also known as catamount, mountain lion, painter, and puma. The cougar (Puma concolor; see illustration) is a carnivorous member of the family…

An applied branch of decision theory. Decision analysis offers individuals and organizations a methodology for making decisions; it also offers techniques for modeling decision problems mathematically and finding optimal decisions numerically.…

A broad range of concepts which have been developed to both describe and prescribe the process of decision making, where a choice is made from a finite set of possible alternatives. Normative decision theory describes how decisions should be made in…

A mathematical operation performed on a function to determine the effect of a change in the value of the independent variable. Functions of one variable are considered in this article. For differentiation of functions of several variablesPartial…

For a polynomial f(x) = an xn + an−1 xn−1 + + a1 x + a0, the discriminant is given by the expression where x1, x2, …, xn are the roots of the equation f(x) = 0. There are n(n − 1)/2 terms (xi − xj)2 in the product corresponding to all possible…

The adaptation of an animal or plant through breeding in captivity to a life intimately associated with and advantageous to humans. Domesticated plants and animals differ genetically and morphologically from their wild counterparts, often in ways…

Plants occupying sand dunes and the slacks, or swales, and flats between them. The density and diversity of dune vegetation are greater on coastal dunes than on desert dunes. Dune Plant geography Sand Zonation A zonation pattern is evident in the…

A mathematical abstraction corresponding to an expression of the type βγ + δ∊ + · · · , in which the elements (dyad symbols) consist of two vector symbols in juxtaposition without the intervention of either the dot (·) or cross (×). Essentially a…

The earliest representatives of people anatomically similar to living humans that evolved from more archaic humans approximately 150,000–300,000 years ago. The general process by which early modern humans (Homo sapiens) emerged from late archaic…

The biological sonar that bats, toothed whales, and certain other animals use to navigate without the visual system. Echolocation, or biosonar, is the physiological process that certain animals use to locate objects by reflected sound, primarily in…

The interaction of at least two organisms or species such that, for each, the birth or growth rates are depressed and the death rate increased by the presence of the other organisms or species. Ecological competition is the conflict that arises…

The study of the flow of energy within an ecological system from the time the energy enters the living system until it is ultimately degraded to heat and irretrievably lost from the system. It is also referred to as production ecology, because…

The methods required for the measurement of features of plant and animal populations or for quantifying energy flow or other aspects of ecological communities. Ecologists are concerned with such a wide range of variables that they may use many other…

The use of computer simulations or mathematical equations to address questions that cannot be answered solely by experiments or observations. Ecological models have two major aims: to provide general insight into how ecological systems or ecological…

A directional change in an ecological community. Populations of animals and plants are in a dynamic state. Through the continual turnover of individuals, a population may expand or decline depending on the success of its members in survival and…

The study of insects that have a direct influence on humanity. Though this includes beneficial as well as harmful species, most attention is devoted to the latter and how they become pests and are controlled. The emphasis on managing harmful insects…

An obligate association formed between the roots of many plant species, especially trees, and a diverse range of soil fungi. The fungi and the finest, terminal root tips interact to form joint organs called ectomycorrhizas (Fig. 1). In…

One of the solutions of an eigenvalue equation. A parameter-dependent equation that possesses nonvanishing solutions only for particular values (eigenvalues) of the parameter is an eigenvalue equation, the associated solutions being the…

One of the values of the parameter in an eigenvalue equation for which the equation has a solution. A linear eigenvalue equation is a parameter-dependent equation of the form (1) 1that possesses nonvanishing solutions, |v(n), only for particular…

A member of the class of curves that are intersections of a plane with a cone of revolution. The ellipse is obtained when the plane cuts all the elements of one nappe, and does not go through the apex. In the illustration, denote the distance…

The elliptic functions were developed originally by K. F. Gauss, N. H. Abel, K. G. J. Jacobi, and others in order to solve the problem of finding the arc length of an ellipse, but they proved to have remarkable applications in physics, probability…

A peculiar order of silk-spinning, orthopteroid insects, commonly called the embiids or web spinners, which are related to termites. The order Embioptera (also known as Embiidina or Embiodea) comprises about 300–400 described species, which are…

The sum of all external factors, both biotic (living) and abiotic (nonliving), to which an organism is exposed. All of the outside factors to which an organism is exposed comprise its environment (Fig. 1). The environment has a tremendous influence…

A curve traced by a point on a circle that rolls on the convex side of a fixed circle. The term is also occasionally applied to the curve generated by a point on the prolongation of the radius of a circle as the circle rolls on a straight line. If…