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An ecosystem model is an abstract, usually
mathematical Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, representation of an ecological system (ranging in scale from an individual
population Population is a set of humans or other organisms in a given region or area. Governments conduct a census to quantify the resident population size within a given jurisdiction. The term is also applied to non-human animals, microorganisms, and pl ...
, to an ecological community, or even an entire
biome A biome () is a distinct geographical region with specific climate, vegetation, and animal life. It consists of a biological community that has formed in response to its physical environment and regional climate. In 1935, Tansley added the ...
), which is studied to better understand the real system. Using data gathered from the field, ecological relationships—such as the relation of sunlight and water availability to
photosynthetic Photosynthesis ( ) is a Biological system, system of biological processes by which Photoautotrophism, photosynthetic organisms, such as most plants, algae, and cyanobacteria, convert light energy, typically from sunlight, into the chemical ener ...
rate, or that between predator and prey populations—are derived, and these are combined to form
ecosystem An ecosystem (or ecological system) is a system formed by Organism, organisms in interaction with their Biophysical environment, environment. The Biotic material, biotic and abiotic components are linked together through nutrient cycles and en ...
models. These model systems are then studied in order to make predictions about the dynamics of the real system. Often, the study of inaccuracies in the model (when compared to empirical observations) will lead to the generation of hypotheses about possible ecological relations that are not yet known or well understood. Models enable researchers to simulate large-scale experiments that would be too costly or unethical to perform on a real ecosystem. They also enable the simulation of ecological processes over very long periods of time (i.e. simulating a process that takes centuries in reality, can be done in a matter of minutes in a computer model). Ecosystem models have applications in a wide variety of disciplines, such as
natural resource Natural resources are resources that are drawn from nature and used with few modifications. This includes the sources of valued characteristics such as commercial and industrial use, aesthetic value, scientific interest, and cultural value. ...
management,
ecotoxicology Ecotoxicology is the study of the effects of toxic chemicals on biological organisms, especially at the population biology, population, biological community, community, ecosystem, and biosphere levels. Ecotoxicology is a multidisciplinary field, ...
and
environmental health Environmental health is the branch of public health concerned with all aspects of the natural environment, natural and built environment affecting human health. To effectively control factors that may affect health, the requirements for a hea ...
,
agriculture Agriculture encompasses crop and livestock production, aquaculture, and forestry for food and non-food products. Agriculture was a key factor in the rise of sedentary human civilization, whereby farming of domesticated species created ...
, and
wildlife conservation Wildlife conservation refers to the practice of protecting wild species and their habitats in order to maintain healthy wildlife species or populations and to restore, protect or enhance natural ecosystems. Major threats to wildlife include habita ...
. Ecological modelling has even been applied to archaeology with varying degrees of success, for example, combining with archaeological models to explain the diversity and mobility of stone tools.


Types of models

There are two major types of ecological models, which are generally applied to different types of problems: (1) ''analytic'' models and (2) ''simulation'' / ''computational'' models. Analytic models are typically relatively simple (often linear) systems, that can be accurately described by a set of mathematical equations whose behavior is well-known. Simulation models on the other hand, use numerical techniques to solve problems for which analytic solutions are impractical or impossible. Simulation models tend to be more widely used, and are generally considered more ecologically realistic, while analytic models are valued for their mathematical elegance and explanatory power. Ecopath is a powerful software system which uses simulation and computational methods to model
marine ecosystems Marine ecosystems are the largest of Earth's aquatic ecosystems and exist in waters that have a high salt content. These systems contrast with freshwater ecosystems, which have a lower salt content. Marine waters cover more than 70% of the sur ...
. It is widely used by marine and fisheries scientists as a tool for modelling and visualising the complex relationships that exist in real world marine ecosystems.


Model design

The process of model design begins with a specification of the problem to be solved, and the objectives for the model. Ecological systems are composed of an enormous number of biotic and abiotic factors that interact with each other in ways that are often unpredictable, or so complex as to be impossible to incorporate into a computable model. Because of this
complexity Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity, randomness, collective dynamics, hierarchy, and emergence. The term is generally used to c ...
,
ecosystem An ecosystem (or ecological system) is a system formed by Organism, organisms in interaction with their Biophysical environment, environment. The Biotic material, biotic and abiotic components are linked together through nutrient cycles and en ...
models typically simplify the systems they are studying to a limited number of components that are well understood, and deemed relevant to the problem that the model is intended to solve. The process of simplification typically reduces an ecosystem to a small number of
state variable A state variable is one of the set of Variable (mathematics), variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behavi ...
s and
mathematical functions In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words ''map'', ''mapping'', ''transformation'', ''correspondence'', and ''operator'' are sometimes used synonymously. The set is called ...
that describe the nature of the relationships between them. The number of ecosystem components that are incorporated into the model is limited by aggregating similar processes and entities into functional groups that are treated as a unit. After establishing the components to be modeled and the relationships between them, another important factor in ecosystem model structure is the representation of
space Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless ...
used. Historically, models have often ignored the confounding issue of space. However, for many ecological problems spatial dynamics are an important part of the problem, with different spatial environments leading to very different outcomes. ''Spatially explicit models'' (also called "spatially distributed" or "landscape" models) attempt to incorporate a heterogeneous spatial environment into the model. A spatial model is one that has one or more state variables that are a function of space, or can be related to other spatial variables.


Validation

After construction, models are ''validated'' to ensure that the results are acceptably accurate or realistic. One method is to test the model with multiple sets of data that are independent of the actual system being studied. This is important since certain inputs can cause a faulty model to output correct results. Another method of validation is to compare the model's output with data collected from field observations. Researchers frequently specify beforehand how much of a disparity they are willing to accept between parameters output by a model and those computed from field data.


Examples


The Lotka–Volterra equations

One of the earliest, and most well-known, ecological models is the predator-prey model of Alfred J. Lotka (1925) and
Vito Volterra Vito Volterra (, ; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to Mathematical and theoretical biology, mathematical biology and Integral equation, integral equations, being one of the ...
(1926). This model takes the form of a pair of
ordinary differential equation In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable (mathematics), variable. As with any other DE, its unknown(s) consists of one (or more) Function (mathematic ...
s, one representing a prey
species A species () is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. It is the basic unit of Taxonomy (biology), ...
, the other its predator. : \frac = \alpha . X - \beta . X . Y : \frac = \gamma . \beta . X . Y - \delta . Y where, Volterra originally devised the model to explain fluctuations in
fish A fish (: fish or fishes) is an aquatic animal, aquatic, Anamniotes, anamniotic, gill-bearing vertebrate animal with swimming fish fin, fins and craniate, a hard skull, but lacking limb (anatomy), limbs with digit (anatomy), digits. Fish can ...
and
shark Sharks are a group of elasmobranch cartilaginous fish characterized by a ribless endoskeleton, dermal denticles, five to seven gill slits on each side, and pectoral fins that are not fused to the head. Modern sharks are classified within the ...
populations observed in the
Adriatic Sea The Adriatic Sea () is a body of water separating the Italian Peninsula from the Balkans, Balkan Peninsula. The Adriatic is the northernmost arm of the Mediterranean Sea, extending from the Strait of Otranto (where it connects to the Ionian Se ...
after the
First World War World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...
(when
fishing Fishing is the activity of trying to catch fish. Fish are often caught as wildlife from the natural environment (Freshwater ecosystem, freshwater or Marine ecosystem, marine), but may also be caught from Fish stocking, stocked Body of water, ...
was curtailed). However, the equations have subsequently been applied more generally. Although simple, they illustrate some of the salient features of ecological models: modelled biological
population Population is a set of humans or other organisms in a given region or area. Governments conduct a census to quantify the resident population size within a given jurisdiction. The term is also applied to non-human animals, microorganisms, and pl ...
s experience growth, interact with other populations (as either predators, prey or
competitors Competition is a rivalry where two or more parties strive for a common goal which cannot be shared: where one's gain is the other's loss (an example of which is a zero-sum game). Competition can arise between entities such as organisms, indi ...
) and suffer mortality. A credible, simple alternative to the Lotka-Volterra predator-prey model and its common prey dependent generalizations is the ratio dependent or Arditi-Ginzburg model. The two are the extremes of the spectrum of predator interference models. According to the authors of the alternative view, the data show that true interactions in nature are so far from the Lotka-Volterra extreme on the interference spectrum that the model can simply be discounted as wrong. They are much closer to the ratio dependent extreme, so if a simple model is needed one can use the Arditi-Ginzburg model as the first approximation.


Others

The theoretical ecologist Robert Ulanowicz has used
information theory Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...
tools to describe the structure of ecosystems, emphasizing
mutual information In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual Statistical dependence, dependence between the two variables. More specifically, it quantifies the "Information conten ...
(correlations) in studied systems. Drawing on this methodology and prior observations of complex ecosystems, Ulanowicz depicts approaches to determining the stress levels on ecosystems and predicting system reactions to defined types of alteration in their settings (such as increased or reduced energy flow, and
eutrophication Eutrophication is a general term describing a process in which nutrients accumulate in a body of water, resulting in an increased growth of organisms that may deplete the oxygen in the water; ie. the process of too many plants growing on the s ...
.
Conway's Game of Life The Game of Life, also known as Conway's Game of Life or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial ...
and its variations model ecosystems where proximity of the members of a population are factors in population growth.


See also

* Compartmental models in epidemiology * Dynamic global vegetation model *
Ecological forecasting Ecological forecasting uses knowledge of physics, ecology and physiology, to predict how ecological populations, communities, or ecosystems will change in the future in response to environmental factors such as climate change. The goal of the approa ...
* Gordon Arthur Riley * Land Surface Model (LSM version 1.0) * Liebig's law of the minimum *
Mathematical biology Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development ...
*
Population dynamics Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. Population dynamics is a branch of mathematical biology, and uses mathematical techniques such as differenti ...
*
Population ecology Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment (biophysical), environment, such as birth rate, birth and death rates, and by immigration an ...
*
Rapoport's rule Rapoport's rule is an ecogeographical rule that states that latitudinal ranges of plants and animals are generally smaller at lower latitudes than at higher latitudes. Background Stevens (1989) named the rule after Eduardo H. Rapoport, who ha ...
*
Scientific modelling Scientific modelling is an activity that produces models representing empirical objects, phenomena, and physical processes, to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate. It ...
*
System dynamics System dynamics (SD) is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays. Overview System dynamics is a methodology and mathematical ...


References


Further reading

* * * *


External links


Ecological modelling resources
(ecobas.org)
Exposure Assessment Models
United States Environmental Protection Agency
Ecotoxicology & Models
(ecotoxmodels.org) {{modelling ecosystems Biological systems Environmental terminology Fisheries science Habitat Mathematical and theoretical biology Population models Systems ecology