Ecosystem models, or ecological models, are mathematical representations of ecosystems. Typically they simplify complex foodwebs down to their major components or trophic levels, and quantify these as either numbers of organisms, biomass or the inventory/concentration of some pertinent chemical element (for instance, carbon or a nutrient species such as nitrogen or phosphorus). Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... An ecosystem, a contraction of ecological and system, refers to the collection of biotic and abiotic components and processes that comprise and govern the behavior of some defined subset of the biosphere. ... Figure 1. ... In ecology, the trophic level (Greek trophē, food) is the position that an organism occupies in a food chain - what it eats, and what eats it. ... This article or section does not cite its references or sources. ... |0. ... In business management, inventory consists of a list of goods and materials held available in stock. ... In chemistry, concentration is the measure of how much of a given substance there is mixed with another substance. ... The periodic table of the chemical elements (this version outdated on October 13, 2006) A chemical element, or element for short, is a pure substance that cannot be decomposed into any simpler substance. ... General Name, Symbol, Number carbon, C, 6 Chemical series nonmetals Group, Period, Block 14, 2, p Appearance black (graphite) colorless (diamond) Atomic mass 12. ... This article does not cite its references or sources. ... Chemical species is a common, general name for atoms, molecules, molecular fragments and ions as entities being subjected to a chemical process or to a measurement. ... General Name, Symbol, Number nitrogen, N, 7 Chemical series nonmetals Group, Period, Block 15, 2, p Appearance colorless gas Atomic mass 14. ... General Name, Symbol, Number phosphorus, P, 15 Chemical series nonmetals Group, Period, Block 15, 3, p Appearance waxy white/ red/ black/ colorless Atomic mass 30. ...

Overview

Complexity

Ecosystem models are a development of theoretical ecology that aim to characterise the major dynamics of ecosystems, both to synthesise the understanding of such systems and to allow predictions of their behaviour (in general terms, or in response to particular changes). Theoretical ecology refers to several intellectual traditions. ... A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. ... A prediction or forecast is a statement or claim that a particular event will occur in the future. ...

Because of the complexity of ecosystems (in terms of numbers of species/ecological interactions), ecosystem models typically simplify the systems they are studying to a limited number of pragmatic components. These may be particular species of interest, or may be broad functional types such as autotrophs, heterotrophs or saprotrophs. In biogeochemistry, ecosystem models usually include representations of non-living "resources" such as nutrients, which are consumed by (and may be depleted by) living components of the model. For the Computer Science term, see Computational complexity theory. ... For themes emphasized by Charles Peirce, see Pragmaticism. ... Green (from chlorophyll) fronds of a maidenhair fern: a photoautotroph Flowchart to determine if a species is autotroph, heterotroph, or a subtype An autotroph (from the Greek autos = self and trophe = nutrition) is an organism that produces organic compounds from carbon dioxide as a carbon source, using either light or... Flowchart to determine if a species is autotroph, heterotroph, or a subtype A heterotroph (Greek heterone = (an)other and trophe = nutrition) is an organism that requires organic substrates to get its carbon for growth and development. ... A Saprotroph (or saprobe) is an organism that obtains its nutrients from non-living organic matter, usually dead and decaying plant or animal matter, by absorbing soluble organic compounds. ... The field of biogeochemistry involves scientific study of the chemical, physical, geological, and biological processes and reactions that govern the composition of the natural environment (including the biosphere, the hydrosphere, the pedosphere, the atmosphere, and the lithosphere), and the cycles of matter and energy that transport the Earths chemical...

This simplification is driven by a number of factors:

• Ignorance: while understood in broad outline, the details of a particular foodweb may not be known; this applies both to identifying relevant species, and to the functional responses linking them (which are often extremely difficult to quantify)
• Computation: practical constraints on simulating large numbers of ecological elements; this is particularly true when ecosystem models are embedded within other models (such as physical models of terrain or ocean bodies, or idealised models such as cellular automata or coupled map lattices)
• Understanding: depending upon the nature of the study, complexity can confound the analysis of an ecosystem model; the more interacting components a model has, the less straightforward it is to extract and separate causes and consequences; this is compounded when uncertainty about components obscures the accuracy of a simulation

A computer simulation or a computer model is a computer program that attempts to simulate an abstract model of a particular system. ... A physical model is used in various contexts to mean a physical representation of some thing. ... For other uses, see Ocean (disambiguation). ... Idealization is the process by which scientific models assume facts about the phenomenon being modeled that are certainly false. ... A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ... A continuous automaton can be described as a cellular automaton whereby the valid states a cell can take are not discrete, but continuous, for example, [0,1]. Such automata can be used to model certain physical reactions more closely, such as diffusion. ... Uncertainty is a term used in subtly different ways in a number of fields, including philosophy, statistics, economics, finance, insurance, psychology, engineering and science. ...

Structure

The process of simplification described above typically reduces an ecosystem to a small number of state variables. Depending upon the system under study, these may represent ecological components in terms of numbers of discrete individuals or quantify the component more continuously as a measure of the total biomass of all organisms of that type, often using a common model currency (e.g. mass of carbon per unit area/volume). Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. ... Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ...

The components are then linked together by mathematical functions that describe the nature of the relationships between them. For instance, in models which include predator-prey relationships, the two components are usually linked by some function that relates total prey captured to the populations of both predators and prey. Deriving these relationships is often extremely difficult given habitat heterogeneity, the details of component behavioral ecology (including issues such as perception, foraging behaviour), and the difficulties involved in unobtrusively studying these relationships under field conditions. Partial plot of a function f. ... Habitat (from the Latin for it inhabits) is the place where a particular species lives and grows. ... Look up Heterogeneous in Wiktionary, the free dictionary. ... Behavioral ecology is the study of the ecological and evolutionary basis for animal behavior, and the roles of behavior in enabling an animal to adapt to its environment (both intrinsic and extrinsic). ... In psychology and the cognitive sciences, perception is the process of acquiring, interpreting, selecting, and organizing sensory information. ... Foraging just means looking for food (or, metaphorically, anything else). ...

Typically relationships are derived statistically or heuristically. For example, some standard functional forms describing these relationships are linear, quadratic, hyperbolic or sigmoid functions. The latter two are known in ecology as type II and type III responses, named by C. S. Holling in early, groundbreaking work on predation in mammals^[1]. Both describe relationships in which a linkage between components saturates at some maximum rate (e.g. above a certain concentration of prey organisms, predators cannot catch any more per unit time). Some ecological interactions are derived explicitly from the biochemical processes that underlie them; for instance, nutrient processing by an organism may saturate because of either a limited number of binding sites on the organism's exterior surface or the rate of diffusion of nutrient across the boundary layer surrounding the organism (see also Michaelis-Menten kinetics). Template:Otherusescccc A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ... Look up Heuristic in Wiktionary, the free dictionary. ... A linear function is a mathematical function term of the form: f(x) = m x + c where c is a constant. ... f(x) = x2 - x - 2 A quadratic function, in mathematics, is a polynomial function of the form , where are real numbers and . ... In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. ... The logistic curve A sigmoid function is a mathematical function that produces a sigmoid curve — a curve having an S shape. ... C. S. (Buzz) Holling is a retired Canadian ecologist. ... Subclasses Allotheria* Order Multituberculata (extinct) Order Volaticotheria (extinct) Order Palaeoryctoides (extinct) Order Triconodonta (extinct) Prototheria Order Monotremata Theria Infraclass Marsupialia Infraclass Eutheria The mammals are the class of vertebrate animals characterized by the production of milk in females for the nourishment of young, from mammary glands present on most species... Biochemistry is the study of the chemical processes and transformations in living organisms. ... In chemistry, saturation has four different meanings: In physical chemistry, saturation is the point at which a solution of a substance can dissolve no more of that substance and additional amounts of that substance will appear as a precipitate. ... A binding site is a region on a protein to which specific ligands bind. ... This article or section does not cite its references or sources. ... In physics and fluid mechanics, the boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. ... Michaelis-Menten kinetics describes the kinetics of many enzymes. ...

After establishing the components to be modelled and the relationships between them, another important factor in ecosystem model structure is the representation of space used. Historically, models have often ignored the confounding issue of space, utilising zero-dimensional approaches, such as ordinary differential equations. With increases in computational power, models which incorporate space are increasingly used (e.g. partial differential equations, cellular automata). This inclusion of space permits dynamics not present in non-spatial frameworks, and illuminates processes that lead to pattern formation in ecological systems. Space has been an interest for philosophers and scientists for much of human history. ... A topological space is zero-dimensional if its topological dimension is zero, or equivalently, if it has a base consisting of clopen sets. ... In mathematics, an ordinary differential equation (or ODE) is a relation that contains functions of only one independent variable, and one or more of its derivatives with respect to that variable. ... Growth of transistor counts for Intel processors (dots) and Moores Law (upper line=18 months; lower line=24 months) Moores Law is the empirical observation made in 1965 that the number of transistors on an integrated circuit for minimum component cost doubles every 24 months. ... In mathematics, a partial differential equation (PDE) is a relation involving an unknown function of several independent variables and its partial derivatives with respect to those variables. ... A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. ... The science of pattern formation deals with the visible, (statistically) orderly outcomes of self-organisation and the common principles behind similar patterns. ...

Examples

One of the earliest^[2], and most well-known, ecological models is the predator-prey model of Alfred J. Lotka (1925)^[3] and Vito Volterra (1926)^[4]. This model takes the form of a pair of ordinary differential equations, one representing a prey species, the other its predator. A hawk consuming its prey, a small rodent. ... Alfred James Lotka (March 2, 1880 - December 5, 1949) was a US mathematician and statistician, most famous for his work in population dynamics. ... Vito Volterra (May 3, 1860 - October 11, 1940) was an Italian mathematician and physicist, best known for his contributions to mathematical biology. ... In mathematics, an ordinary differential equation (or ODE) is a relation that contains functions of only one independent variable, and one or more of its derivatives with respect to that variable. ... In biology, a species is one of the basic units of biodiversity. ...

where,

Volterra originally devised the model to explain fluctuations in fish and shark populations observed in the Adriatic Sea after the First World War (when fishing was curtailed). However, the equations have subsequently been applied more generally^[5]. Although simple, they illustrate some of the salient features of ecological models: modelled biological populations experience growth, interact with other populations (as either predators, prey or competitors) and suffer mortality. This article or section is in need of attention from an expert on the subject. ... A giant grouper at the Georgia Aquarium Fish are aquatic vertebrates that are typically cold-blooded; covered with scales, and equipped with two sets of paired fins and several unpaired fins. ... Orders Carcharhiniformes Heterodontiformes Hexanchiformes Lamniformes Orectolobiformes Pristiophoriformes Squaliformes Squatiniformes Symmoriida(extinct) Sharks (superorder Selachimorpha) are fish with a full cartilaginous skeleton[1] and a streamlined body. ... A satellite image of the Adriatic Sea. ... Ypres, 1917, in the vicinity of the Battle of Passchendaele. ... A lobster boat unloading its catch in Ilfracombe harbour, North Devon, England. ... The Malthusian growth model, sometimes called the simple exponential growth model, is essentially exponential growth based on a constant rate of compound interest. ...

References

Smallpox (also known by the Latin names Variola or Variola vera) is a highly contagious disease unique to humans. ... Daniel Bernoulli Daniel Bernoulli (Groningen, January 29, 1700 – Basel, March 17, 1782) was a Dutch-born mathematician who spent much of his life in Basel, Switzerland. ... Map of countries by population (See List of countries by population. ... Thomas Robert Malthus, FRS (February 13, 1766 – December 23, 1834), usually known as Thomas Malthus, although he preferred to be known as Robert Malthus, was an English demographer and political economist. ...

External links

• TRIFFID, an ecosystem model of terrestrial vegetation (used by the UK Met Office)
• HadOCC, an ecosystem model of the oceanic plankton (used by the UK Met Office)

To meet Wikipedias quality standards, this article or section may require cleanup. ... The new building on the edge of Exeter The Met Office (originally an abbreviation for Meteorological Office, but now the official name in itself), which has its headquarters at Exeter in Devon, is the United Kingdoms national weather service. ... Oceanic may mean: of or relating to the ocean of or relating to Oceania a person or the peoples of Oceania, such as Micronesians and Polynesians. ... Photomontage of plankton organisms Plankton are defined as any drifting organism that inhabits the water column of oceans, seas, and bodies of fresh water. ... The new building on the edge of Exeter The Met Office (originally an abbreviation for Meteorological Office, but now the official name in itself), which has its headquarters at Exeter in Devon, is the United Kingdoms national weather service. ...

See also

• Compartmental models in epidemiology
• Mathematical biology
• Population dynamics
• Population ecology
• Scientific modelling
• System dynamics