View source for Ecosystem model

{{Redirect|Ecological modelling|the peer-reviewed journal|Ecological Modelling}}
{{short description| A typically mathematical representation of an ecological system }}

[[File:Fasham Ducklow McKelvie 1990.svg|250px|right|thumb|A structural diagram of the open ocean [[plankton]] ecosystem model of [[Michael Fasham|Fasham]], Ducklow & McKelvie (1990).<ref name="fdm1990">{{cite journal |doi=10.1357/002224090784984678 |title=A nitrogen-based model of plankton dynamics in the oceanic mixed layer |journal=Journal of Marine Research |volume=48 |issue=3 |pages=591–639 |year=1990 |last1=Fasham |first1=M. J. R. |last2=Ducklow |first2=H. W. |last3=McKelvie |first3=S. M. }}</ref>]]
An '''ecosystem model''' is an [[abstract model|abstract]], usually [[mathematical model|mathematical]], representation of an [[ecological system]] (ranging in scale from an individual [[population]], to an [[ecological community]], or even an entire [[biome]]), which is studied to better understand the real system.<ref>{{cite book|author=Hall, Charles A.S.|author2=Day, John W.|name-list-style=amp|title=Ecosystem Modeling in Theory and Practice: An Introduction with Case Histories|publisher=University Press of Colorado|year=1990|isbn=978-0-87081-216-3|pages=7–8}}</ref>

Using data gathered from the field, ecological relationships—such as the relation of sunlight and water availability to [[photosynthetic]] rate, or that between [[predator and prey]] populations—are derived, and these are combined to form [[ecosystem]] 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).<ref>Hall & Day, 1990: pp. 13-14</ref>

Ecosystem models have applications in a wide variety of disciplines, such as [[natural resource]] management,<ref>{{Cite book |doi=10.1007/0-387-21563-8_1 |chapter=Opportunities for Using Ecological Models for Resource Management |title=Ecological Modeling for Resource Management |pages=3–19 |year=2003 |last1=Dale |first1=Virginia H. |isbn=978-0-387-95493-6 }}</ref> [[ecotoxicology]] and [[environmental health]],<ref>{{cite book|author=Pastorok, Robert A.|chapter=Introduction|title=Ecological modeling in risk assessment: chemical effects on populations, ecosystems, and landscapes|publisher=CRC Press|year=2002|isbn=978-1-56670-574-5|page=[https://archive.org/details/ecologicalmodeli0000unse/page/7 7]|chapter-url=https://books.google.com/books?id=LNdRGbpDWgUC&pg=PA7|url=https://archive.org/details/ecologicalmodeli0000unse/page/7}}</ref><ref>{{cite book|author=Forbes, Valery E.|chapter=The Role of Ecological Modeling in Risk Assessments Seen From an Academic's Point of View|editor=Thorbek, Pernille|title=Ecological Models for Regulatory Risk Assessments of Pesticides: Developing a Strategy for the Future|publisher=CRC Press|year=2009|isbn=978-1-4398-0511-4|page=89|chapter-url=https://books.google.com/books?id=CYzT5ZIy2NEC&pg=PA89}}</ref> [[agriculture]],<ref>{{cite book|author=Palladino, Paolo|chapter=Ecological Modeling and Integrated Pest Management|title=Entomology, ecology and agriculture: the making of scientific careers in North America, 1885-1985|publisher=Psychology Press|year=1996|isbn=978-3-7186-5907-4|page=153|chapter-url=https://books.google.com/books?id=0JgLY_0QlWEC&pg=PA153}}</ref> and [[wildlife conservation]].<ref>{{cite book|author=Millspaugh, Joshua J.|chapter=General Principles for Developing Landscape Models for Wildlife Conservation|title=Models for planning wildlife conservation in large landscapes|publisher=Academic Press|year=2008|isbn=978-0-12-373631-4|page=1|chapter-url=https://books.google.com/books?id=GLtcJs2f810C&pg=PA1|display-authors=etal}}</ref> 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.<ref>{{cite journal |doi=10.1016/j.jaa.2013.08.004 |title=Multiple Optima in Hoabinhian flaked stone artefact palaeoeconomics and palaeoecology at two archaeological sites in Northwest Thailand |journal=Journal of Anthropological Archaeology |volume=32 |issue=4 |pages=553–564 |year=2013 |last1=Marwick |first1=Ben |doi-access=free }}</ref>

==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.<ref>{{cite book|author=Jørgensen, Sven Erik|title=Handbook of environmental and ecological modeling|publisher=CRC Press|year=1996|isbn=978-1-56670-202-7|pages=403–404|url=https://books.google.com/books?id=hGJ1Jm6txQEC&pg=PA403}}</ref><ref>{{cite book|author=Grant, William Edward|author2=Swannack, Todd M.|name-list-style=amp|title=Ecological modeling: a common-sense approach to theory and practice|publisher=John Wiley & Sons|year=2008|isbn=978-1-4051-6168-8|page=74|url=https://books.google.com/books?id=K3qUumawqEoC&pg=PA74}}</ref><ref>Hall & Day, 1990 p. 9</ref> [[Ecopath]] is a powerful software system which uses simulation and computational methods to model [[marine ecosystems]]. 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.<ref>{{cite journal |doi=10.1006/jmsc.2000.0726 |title=Ecopath, Ecosim, and Ecospace as tools for evaluating ecosystem impact of fisheries |journal=ICES Journal of Marine Science |volume=57 |issue=3 |pages=697–706 |year=2000 |last1=Pauly |first1=D. |doi-access=free }}</ref><ref>{{cite journal |doi=10.1016/j.ecolmodel.2003.09.003 |title=Ecopath with Ecosim: Methods, capabilities and limitations |journal=Ecological Modelling |volume=172 |issue=2–4 |pages=109–139 |year=2004 |last1=Christensen |first1=Villy |last2=Walters |first2=Carl J. }}</ref><ref>Christensen V (2009) [ftp://ftp.fisheries.ubc.ca/FCRR/17-3.pdf#page=166  "The future of Ecopath"]{{Dead link|date=August 2019 |bot=InternetArchiveBot |fix-attempted=yes }} In: Palomares, MLD, Morissette L, Cisneros-Montemayor A, Varkey D, Coll M, Piroddi C (Eds), ''Ecopath 25 Years Conference Proceedings: Extended Abstracts'', Fisheries Centre Research Reports '''17'''(3): 159–160. University of British Columbia.</ref><ref>{{cite journal |doi=10.1111/fme.12134 |title=Modelling the food web for assessment of the impact of stock supplementation in a reservoir ecosystem in India |journal=Fisheries Management and Ecology |volume=22 |issue=5 |pages=359–370 |year=2015 |last1=Khan |first1=M. F. |last2=Preetha |first2=P. |last3=Sharma |first3=A. P. }}</ref><ref>{{cite journal |doi=10.1007/s10641-014-0255-6 |title=Characterizing trophic interactions of a catfish dominated tropical reservoir ecosystem to assess the effects of management practices |journal=Environmental Biology of Fishes |volume=98 |pages=237–247 |year=2014 |last1=Panikkar |first1=Preetha |last2=Khan |first2=M. Feroz |last3=Desai |first3=V. R. |last4=Shrivastava |first4=N. P. |last5=Sharma |first5=A. P. |s2cid=16992082 }}</ref><ref>{{cite journal |doi=10.1016/j.ecolmodel.2007.10.029 |title=Comparative mass-balanced trophic models to assess the impact of environmental management measures in a tropical reservoir ecosystem |journal=Ecological Modelling |volume=212 |issue=3–4 |pages=280–291 |year=2008 |last1=Panikkar |first1=Preetha |last2=Khan |first2=M. Feroz }}</ref><ref>{{cite journal |doi=10.1016/j.ecolmodel.2009.05.020 |title=Assessment of impacts of invasive fishes on the food web structure and ecosystem properties of a tropical reservoir in India |journal=Ecological Modelling |volume=220 |issue=18 |pages=2281–2290 |year=2009 |last1=Feroz Khan |first1=M. |last2=Panikkar |first2=Preetha }}</ref>

==Model design==
[[File:Silver Spring Model.jpg|thumb|right|300px|Diagram of the Silver Springs model (Odum, 1971). Note the aggregation into functional groups such as "herbivores" or "decomposers".<ref>Odum, H.T. (1971). Environment, Power, and Society. Wiley-Interscience New York, N.Y.</ref>]]

The process of model design begins with a specification of the problem to be solved, and the objectives for the model.<ref>{{cite book|author=Soetaert, Karline|author2=Herman, Peter M.J.|name-list-style=amp|title=A practical guide to ecological modelling: using R as a simulation platform|publisher=Springer|year=2009|isbn=978-1-4020-8623-6|page=11|url=https://books.google.com/books?id=aVjDtSmJqhAC&pg=PA11}}</ref>

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]], [[ecosystem]] 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.<ref>{{cite book|author=Gillman, Michael|author2=Hails, Rosemary|name-list-style=amp|title=An introduction to ecological modelling: putting practice into theory|publisher=Wiley-Blackwell|year=1997|isbn=978-0-632-03634-9|page=4|url=https://books.google.com/books?id=7U8Uf10TpyIC&pg=PA4}}</ref><ref>{{cite book|author=Müller, Felix|chapter=What are the General Conditions Under Which Ecological Models Can Be Applied|editor=Jopp, Fred|display-editors=etal|title=Modeling Complex Ecological Dynamics|publisher=Springer|year=2011|isbn=978-3-642-05028-2|pages=13–14|chapter-url=https://books.google.com/books?id=AEgIo-BOzF0C&pg=PA13|display-authors=etal}}</ref>

The process of simplification typically reduces an ecosystem to a small number of [[state variable]]s and [[Function (mathematics)|mathematical functions]] that describe the nature of the relationships between them.<ref>Hall & Day, 1990: p. 21</ref> 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.<ref>Hall & Day, 1990: p. 19</ref><ref>{{cite journal |doi=10.5733/afin.052.0112 |title=Functional Feeding Groups as a Taxonomic Surrogate for a Grassland Arthropod Assemblage |journal=African Invertebrates |volume=52 |pages=217–228 |year=2011 |last1=Buschke |first1=Falko T. |last2=Seaman |first2=Maitland T. |doi-access=free }}</ref>

After establishing the components to be modeled 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. 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.<ref>{{cite book|author=McCallum, Hamish|chapter=Spatial Parameters|title=Population parameters: estimation for ecological models|publisher=Wiley-Blackwell|year=2000|isbn=978-0-86542-740-2|page=184|chapter-url=https://books.google.com/books?id=mFKIbI4cLUEC&pg=PA184}}</ref><ref>{{cite book|editor=Tenhunen, John D.|display-editors=etal|title=Ecosystem approaches to landscape management in Central Europe|publisher=Springer|year=2001|isbn=978-3-540-67267-8|pages=586–587|url=https://books.google.com/books?id=WSanEfM25uAC&pg=PA586}}</ref><ref>{{cite book|author=Ball, George L.|chapter=Ecological modeling|title=Encyclopedia of environmental science|publisher=Springer|year=1999|isbn=978-0-412-74050-3|pages=154|chapter-url=https://books.google.com/books?id=Y0iX2z48qkUC&pg=PA154}}</ref> 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.<ref>{{cite book|author=Sklar, Fred H.|author2=Hunsaker, Carolyn T.|name-list-style=amp|chapter=The Use and Uncertainties of Spatial Data for Landscape Models: An Overview with Examples from the Florida Everglades|editor=Hunsaker, Carolyn T.|title=Spatial uncertainty in ecology: implications for remote sensing and GIS applications|publisher=Springer|year=2001|isbn=978-0-387-95129-4|page=15|chapter-url=https://books.google.com/books?id=HbczI9mw2v8C&pg=PA15}}</ref>

==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.<ref>{{cite book|author=Jørgensen, Sven Erik|author2=Bendoricchio, G.|name-list-style=amp|title=Fundamentals of ecological modelling|publisher=Gulf Professional Publishing|year=2001|isbn=978-0-08-044028-6|page=79|url=https://books.google.com/books?id=geNPWdVBbDYC&pg=PA79}}</ref><ref>{{cite book|author=Pastorok, Robert A.|chapter=Introduction|title=Ecological modeling in risk assessment: chemical effects on populations, ecosystems, and landscapes|publisher=CRC Press|year=2002|isbn=978-1-56670-574-5|page=[https://archive.org/details/ecologicalmodeli0000unse/page/22 22]|chapter-url=https://books.google.com/books?id=LNdRGbpDWgUC&pg=PA22|url=https://archive.org/details/ecologicalmodeli0000unse/page/22}}</ref><ref>{{cite book|author=Shifley, S.R.|editor=Millspaugh, Joshua J.|editor2=Thompson, Frank Richard|chapter=Validation of Landscape-Scale Decision Support Models That Predict Vegetation and Wildlife Dynamics|title=Models for planning wildlife conservation in large landscapes|publisher=Academic Press|year=2008|isbn=978-0-12-373631-4|page=419|chapter-url=https://books.google.com/books?id=GLtcJs2f810C&pg=PA419}}</ref><ref>{{cite book|author=Voinov, Alexey|title=Systems Science and Modeling for Ecological Economics|year=2008|publisher=Academic Press|isbn=978-0-12-372583-7|page=131|url=https://books.google.com/books?id=Nol8DOt-qe8C&pg=PA131}}</ref><ref>{{cite book|author=Reuter, Hauke|chapter=How Valid Are Model Results? Assumptions, Validity Range and Documentation|editor=Jopp, Fred|display-editors=etal|title=Modeling Complex Ecological Dynamics|publisher=Springer|year=2011|isbn=978-3-642-05028-2|pages=325|chapter-url=https://books.google.com/books?id=AEgIo-BOzF0C&pg=PA325|display-authors=etal}}</ref>

==Examples==
===The Lotka–Volterra equations===
[[File:Lotka Volterra dynamics.svg|thumb|300px|right|A sample [[Time series|time-series]] of the [[Lotka–Volterra equation|Lotka-Volterra model]].  Note that the two populations exhibit [[Limit cycle|cyclic behaviour]], and that the predator cycle lags behind that of the prey.]]
One of the earliest,<ref>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</ref> and most well-known, ecological models is the [[predation|predator-prey]] model of [[Alfred J. Lotka]] (1925)<ref>{{cite book | last=Lotka | first=A. J. | year=1925 | title=The Elements of Physical Biology | publisher=Williams & Williams Co., Baltimore, USA }}</ref> and [[Vito Volterra]] (1926).<ref>{{cite journal |doi=10.1038/118558a0 |title=Fluctuations in the Abundance of a Species considered Mathematically |journal=Nature |volume=118 |issue=2972 |pages=558–560 |year=1926 |last1=Volterra |first1=Vito |bibcode=1926Natur.118..558V |doi-access=free }}</ref>  This model takes the form of a pair of [[ordinary differential equation]]s, one representing a prey [[species]], the other its predator.

: <math>\frac{dX}{dt} = \alpha . X - \beta . X . Y</math>
: <math>\frac{dY}{dt} = \gamma . \beta . X . Y - \delta . Y</math>

where,
{| style="background-color: transparent margin: 1em auto; width: 90%"
| width="50%" align="left" valign="top" |
* <math>X</math> is the number/concentration of the prey species;
* <math>Y</math> is the number/concentration of the predator species;
* <math>\alpha</math> is the prey species' growth rate;
| width="50%" align="left" valign="top" |
* <math>\beta</math> is the predation rate of <math>Y</math> upon <math>X</math>;
* <math>\gamma</math> is the [[Assimilation (biology)|assimilation]] efficiency of <math>Y</math>;
* <math>\delta</math> 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 [[fishery|fishing]] was curtailed).  However, the equations have subsequently been applied more generally.<ref>{{cite book | last1=Begon | first=M. | last2=Harper | first2=J. L. | last3=Townsend | first3=C. R. | year=1988 | title=Ecology: Individuals, Populations and Communities | publisher=Blackwell Scientific Publications Inc., Oxford, UK | title-link=Ecology: Individuals, Populations and Communities }}</ref> Although simple, they illustrate some of the salient features of ecological models:  modelled biological [[population]]s experience [[Malthusian growth model|growth]], interact with other populations (as either predators, prey or [[Competitive Lotka-Volterra equations|competitors]]) and suffer [[mortality rate|mortality]].{{Citation needed|date=April 2011}}

A credible, simple alternative to the Lotka-Volterra predator-prey model and its common prey dependent generalizations is the ratio dependent or [[Arditi-Ginzburg equations|Arditi-Ginzburg]] model.<ref>{{cite journal |doi=10.1016/S0022-5193(89)80211-5 |title=Coupling in predator-prey dynamics: Ratio-Dependence |journal=Journal of Theoretical Biology |volume=139 |issue=3 |pages=311–326 |year=1989 |last1=Arditi |first1=Roger |last2=Ginzburg |first2=Lev R. |bibcode=1989JThBi.139..311A }}</ref> 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.<ref>Arditi, R. and Ginzburg, L.R. (2012) [https://books.google.com/books?id=c2m6XspGs-cC&dq=%22How+Species+Interact:+Altering+the+Standard+View+on+Trophic+Ecology%22&pg=PP2 ''How Species Interact: Altering the Standard View on Trophic Ecology''] Oxford University Press. {{ISBN|9780199913831}}.</ref>

===Others===

The [[Theoretical ecology|theoretical ecologist]] [[Robert Ulanowicz]] has used [[information theory]] tools to describe the structure of ecosystems, emphasizing [[mutual information]] (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]].<ref>{{cite book|last=Ulanowicz|first=Robert E.|title=Ecology, the Ascendent Perspective|url=https://books.google.com/books?id=jSKDw_zAMJUC&pg=PP1|year=1997|publisher=Columbia University Press|isbn=978-0-231-10829-4}}</ref>

[[Conway's Game of Life]] and its variations model ecosystems where [[Distance|proximity]] of the members of a population are factors in population growth.

==See also==
{{Portal|Environment|Ecology|Earth sciences}}
{{Refbegin|2}}
* [[Compartmental models in epidemiology]]
* [[Dynamic global vegetation model]]
* [[Ecological forecasting]]
* [[Gordon Arthur Riley]]
* [[Land Surface Model (LSM version 1.0)]]
* [[Liebig's law of the minimum]]
* [[Mathematical biology]]
* [[Population dynamics]]
* [[Population ecology]]
* [[Rapoport's rule]]
* [[Scientific modelling]]
* [[System dynamics]]
{{Refend}}

==References==
{{Reflist|colwidth=35em}}

==Further reading==
*{{cite journal |doi=10.1111/fme.12134 |title=Modelling the food web for assessment of the impact of stock supplementation in a reservoir ecosystem in India |journal=Fisheries Management and Ecology |volume=22 |issue=5 |pages=359–370 |year=2015 |last1=Khan |first1=M. F. |last2=Preetha |first2=P. |last3=Sharma |first3=A. P. }}
*{{cite journal |doi=10.1007/s10641-014-0255-6 |title=Characterizing trophic interactions of a catfish dominated tropical reservoir ecosystem to assess the effects of management practices |journal=Environmental Biology of Fishes |volume=98 |pages=237–247 |year=2014 |last1=Panikkar |first1=Preetha |last2=Khan |first2=M. Feroz |last3=Desai |first3=V. R. |last4=Shrivastava |first4=N. P. |last5=Sharma |first5=A. P. |s2cid=16992082 }}
*{{cite journal |doi=10.1016/j.ecolmodel.2007.10.029 |title=Comparative mass-balanced trophic models to assess the impact of environmental management measures in a tropical reservoir ecosystem |journal=Ecological Modelling |volume=212 |issue=3–4 |pages=280–291 |year=2008 |last1=Panikkar |first1=Preetha |last2=Khan |first2=M. Feroz }}
*{{cite journal |doi=10.1016/j.ecolmodel.2009.05.020 |title=Assessment of impacts of invasive fishes on the food web structure and ecosystem properties of a tropical reservoir in India |journal=Ecological Modelling |volume=220 |issue=18 |pages=2281–2290 |year=2009 |last1=Feroz Khan |first1=M. |last2=Panikkar |first2=Preetha }}

==External links==
* [http://ecobas.org/ Ecological modelling resources] (ecobas.org)
* [http://www.epa.gov/ceampubl/ Exposure Assessment Models] United States Environmental Protection Agency
* [http://www.ecotoxmodels.org/ Ecotoxicology & Models] (ecotoxmodels.org)

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{{modelling ecosystems}}

[[Category:Biological systems]]
[[Category:Environmental terminology]]
[[Category:Fisheries science]]
[[Category:Habitat]]
[[Category:Mathematical and theoretical biology]]
[[Category:Population models]]
[[Category:Systems ecology]]