Ecosystem model - Citizendia

Ecosystem models, or ecological models, are mathematical representations of ecosystems. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and An ecosystem is a natural unit consisting of all plants animals and micro-organisms( Biotic factors in an area functioning together with all of the non-living physical ( 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). Food chains, also called food networks and/or trophic networks, describe the feeding relationships between species within an Ecosystem. In Ecology, trophic dynamics is the system of trophic levels ( Greek trophē, food which describe the position that an organism occupies Biomass refers to living and recently dead Biological material that can be used as fuel or for industrial production Inventory is a list for goods and Materials, or those goods and materials themselves held available in stock by a Business. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance A chemical element is a type of Atom that is distinguished by its Atomic number; that is by the number of Protons in its nucleus. Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6 A nutrient is food or chemicals that an organism needs to live and grow or a substance used in an organism's metabolism which must be taken in from its environment Chemical species are Atoms Molecules molecular fragments Ions etc Nitrogen (ˈnaɪtɹəʤɪn is a Chemical element that has the symbol N and Atomic number 7 and Atomic weight 14 Phosphorus, (ˈfɒsfərəs is the Chemical element that has the symbol P and Atomic number 15

1 Overview
- 1.1 Complexity
- 1.2 Structure
2 Examples
3 References
4 See also
5 External links

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 The dynamical system concept is a mathematical Formalization for any fixed "rule" which describes the Time dependence of a point's position A prediction is a statement or claim that a particular Event will occur in the Future in more certain terms than a forecast.

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. In general usage complexity often tends to be used to characterize something with many parts in intricate arrangement Pragmatism generally considered to have originated in the late nineteenth century with Charles Peirce, who first stated the Pragmatic maxim. These may be particular species of interest, or may be broad functional types such as autotrophs, heterotrophs or saprotrophs. In Ecology, functional groups are collections of Organisms based on morphological, Physiological, behavioral Biochemical, or An autotroph (from the Greek autos = self and trophe = nutrition is an Organism that produces complex Organic compounds from simple A heterotrophs, or chemoorganotrophy ( Greek heterone = (another and trophe = nutrition is an Organism that requires 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. The field of biogeochemistry involves scientific study of the chemical, physical, geological, and biological processes and reactions

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

Structure

The process of simplification described above typically reduces an ecosystem to a small number of state variables. In Ecology, functional response is a term used to describe the relationship between the density A computer simulation, a computer model or a computational model is a Computer program, or network of computers that attempts to simulate an See also Scale model A physical model is a smaller or larger physical copy of an object Terrain, or relief, is the third or vertical dimension of land surface. An ocean (from Greek, ''Okeanos'' (Oceanus) is a major body of saline water, and a principal component of the Hydrosphere. Idealization ( British English: idealisation) is the process by which scientific models assume facts about the phenomenon being modeled that are certainly A cellular automaton (plural cellular automata) is a discrete model studied in computability theory, Mathematics, Theoretical biology A continuous automaton can be described as a Cellular automaton extended so the valid states a cell can take are not just discrete (for example the states consist of integers Uncertainty is a term used in subtly different ways in a number of fields including Philosophy, Statistics, Economics, Finance, Insurance 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. 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 Continuum mechanics is a branch of Mechanics that deals with the analysis of the Kinematics and mechanical behavior of materials modeled as a continuum e g. mass of carbon per unit area/volume).

The components are then linked together by mathematical functions that describe the nature of the relationships between them. The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function 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. A habitat (which is Latin for "it inhabits" is an Ecological or environmental area that is inhabited by a particular Species. Heterogeneous is an adjective used to describe an object or system consisting of multiple items having a large number of structural variations 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 In Psychology and the Cognitive sciences perception is the process of attaining awareness or understanding of sensory Information. Foraging theory is a branch of Behavioral ecology that studies the foraging behavior of animals in response to the environment in which the animal lives

Typically relationships are derived statistically or heuristically. Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. heuristic (hyu̇-ˈris-tik is a method to help solve a problem commonly an informal method For example, some standard functional forms describing these relationships are linear, quadratic, hyperbolic or sigmoid functions. In Mathematics, the term linear function can refer to either of two different but related concepts A quadratic function, in Mathematics, is a Polynomial function of the form f(x=ax^2+bx+c \\! where a \ne 0 \\! In Mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular functions A sigmoid function is a Mathematical function that produces a sigmoid curve &mdash a curve having an "S" shape 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]. Crawford Stanley (Buzz Holling ( 6 December 1930, Theresa New York) is a Canadian ecologist, and Emeritus Eminent Scholar and Professor in Ecological Mammals ( class Mammalia) are a class of Vertebrate Animals characterized by the presence of Sweat glands, including sweat glands 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). Biochemistry is the study of the chemical processes in living Organisms It deals with the Structure and function of cellular components such as In Chemistry, saturation has five different meanings In Physical chemistry, saturation is the point at which a Solution of a substance In Biochemistry, a binding site is a region on a Protein, DNA, or RNA to which specific other Molecules and Ions &mdash Diffusion is the net movement of particles (typically molecules from an area of high concentration to an area of low concentration by uncoordinated random movement In Physics and Fluid mechanics, a boundary layer is that layer of Fluid in the immediate vicinity of a bounding surface

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. Space is the extent within which Matter is physically extended and objects and Events have positions relative to one another Historically, models have often ignored the confounding issue of space, utilising zero-dimensional approaches, such as ordinary differential equations. In Mathematics, a Topological space is zero-dimensional or 0-dimensional, if its Topological dimension is zero or equivalently if it has a 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 With increases in computational power, models which incorporate space are increasingly used (e. Moore's law describes an important trend in the History of computer hardware. g. partial differential equations, cellular automata). In Mathematics, partial differential equations ( PDE) are a type of Differential equation, i This inclusion of space permits dynamics not present in non-spatial frameworks, and illuminates processes that lead to pattern formation in ecological systems. The dynamical system concept is a mathematical Formalization for any fixed "rule" which describes the Time dependence of a point's position The science of pattern formation deals with the visible ( statistically) orderly outcomes of Self-organisation and the common principles behind similar

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]. Alfred James Lotka ( March 2, 1880 - December 5, 1949) was a US Mathematician, Physical chemist, and Statistician Vito Volterra ( May 3, 1860 - October 11, 1940) was an Italian Mathematician and Physicist, best known for his This model takes the form of a pair of ordinary differential equations, one representing a prey species, the other its predator. 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 In Biology, a species is one of the basic units of Biological classification and a Taxonomic rank.

$\frac{dX}{dt} = \alpha . X - \beta . X . Y$

$\frac{dY}{dt} = \gamma . \beta . X . Y - \delta . Y$

where,

$X$ is the number/concentration of the prey species;
$Y$ is the number/concentration of the predator species;
$α$ is the prey species' growth rate;

$β$ is the predation rate of $Y$ upon $X$ ;
$γ$ is the assimilation efficiency of $Y$ ;
$δ$ is the mortality rate of the predator species

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). Assimilation is the process of taking digested food which is circulating the body and then using it to help rebuild cells Fish are aquatic Vertebrate animals that are typically ectothermic (previously Cold-blooded) covered with scales, and equipped with two Sharks ( Superorder Selachimorpha) are a type of Fish with a full cartilaginous Skeleton and a highly streamlined body World War I (abbreviated WWI; also known as the First World War, the Great War, and the War to End All For the fishing industry and the practice of fishing see Fishing. 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. In Biology a population is the collection of inter-breeding organisms of a particular Species; in Sociology The Malthusian growth model, sometimes called the simple exponential growth model is essentially Exponential growth based on a constant rate of Compound interest The competitive Lotka–Volterra equations are a simple model of the Population dynamics of species competing for some common resource. Mortality rate is a measure of the number of Deaths (in general or due to a specific cause in some population scaled to the size of that population per unit time

References

^ Holling, C. S. (1959). The components of predation as revealed by a study of small mammal predation of the European Pine Sawfly. Canadian Entomologist 91, 293-320
^ Earlier work on smallpox by Daniel Bernoulli and human overpopulation by Thomas Malthus predates that of Lotka and Volterra, but is not strictly ecological in nature
^ Lotka, A. Smallpox is an Infectious disease unique to humans caused by either of two virus variants named Variola major and Variola minor. Daniel Bernoulli ( Groningen, 29 January 1700 &ndash 27 July 1782 was a Dutch - Swiss Mathematician, who is particularly remembered for his applications Overpopulation refers to a condition where an Organism 's numbers exceed the Carrying capacity of its Habitat. Thomas Robert Malthus FRS (13 February 1766 – 23 December 1834 was an English political economist and demographer who expressed views J. (1925). The Elements of Physical Biology, Williams & Williams Co. , Baltimore, USA
^ Volterra, V. (1926). Fluctuations in the abundance of a species considered mathematically. Nature 118, 558-560
^ Begon, M. , Harper, J. L. and Townsend, C. R. (1988). Ecology: Individuals, Populations and Communities, Blackwell Scientific Publications Inc. Ecology From Individuals to Ecosystems is a 2006 Higher education Textbook on general Ecology written by Michael Begon, Colin , Oxford, UK

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)
LAMBDA is a MatLab toolkit for estimating multivariate autoregressive models for a multi-species community from time-series data. In order to model the progress of an epidemic in a large Population comprising many different individuals in various fields such a population diversity must be reduced Gordon Arthur Riley ( 11 June 1911 &ndash 7 October 1985) was an American biological oceanographer most associated with KEYCOP is the acronym for the EU-project Key coastal processes in the mesotrophic Skagerrak and the oligotrophic Aegean and was funded by the European Commission 's The Land Surface Model (LSM is a unidimensional computational model developed by Gordon Bonan that describes ecological processes joined in many Ecosystem models Liebig's Law of the Minimum, often simply called Liebig's Law or the Law of the Minimum, is a principle developed in Agricultural science by Carl Sprengel For use of basic artimethics in Biology see relevant topic such as Serial dilution. Population dynamics is the study of marginal and long-term changes in the numbers individual weights and age composition of individuals in one or several Populations and Population ecology is a major sub-field of Ecology that deals with the dynamics of Species Populations and how these populations interact with the environment Rapoport’s rule is an ecological hypothesis that states that latitudinal ranges of Plants and Animals are generally smaller at low than at high Scientific modelling is the process of generating abstract, conceptual, Graphical and or mathematical models. System dynamics is an approach to understanding the behaviour of Complex systems over time An ecoregion ( ecological region) sometimes called a bioregion, is an ecologically and geographically defined area smaller than a "realm" or " Vegetation is a general term for the plant life of a region it refers to the Ground cover provided by plants For the UKMET model see Tropical cyclone forecast model. The Met Office (originally an abbreviation for Meteorological Office, Plankton consist of any drifting Organisms ( Animals Plants Archaea, or Bacteria) that inhabit the Pelagic zone of For the UKMET model see Tropical cyclone forecast model. The Met Office (originally an abbreviation for Meteorological Office,

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