Ecological Model
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An ecosystem model is an
abstract Abstract may refer to: * ''Abstract'' (album), 1962 album by Joe Harriott * Abstract of title a summary of the documents affecting title to parcel of land * Abstract (law), a summary of a legal document * Abstract (summary), in academic publishi ...
, usually
mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, representation of an
ecological system An ecosystem (or ecological system) consists of all the organisms and the physical environment with which they interact. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy enters the syst ...
(ranging in scale from an individual
population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using ...
, to an
ecological community In ecology, a community is a group or association of populations of two or more different species occupying the same geographical area at the same time, also known as a biocoenosis, biotic community, biological community, ecological community, ...
, or even an entire
biome A biome () is a biogeographical unit consisting of a biological community that has formed in response to the physical environment in which they are found and a shared regional climate. Biomes may span more than one continent. Biome is a broader ...
), 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 process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities. Some of this chemical energy is stored in ...
rate, or that between predator and prey populations—are derived, and these are combined to form
ecosystem An ecosystem (or ecological system) consists of all the organisms and the physical environment with which they interact. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy enters the syst ...
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, community, ecosystem, and biosphere levels. Ecotoxicology is a multidisciplinary field, which integrates toxicology and ecology. T ...
and
environmental health Environmental health is the branch of public health concerned with all aspects of the natural and built environment affecting human health. In order to effectively control factors that may affect health, the requirements that must be met ...
,
agriculture Agriculture or farming is the practice of cultivating plants and livestock. Agriculture was the key development in the rise of sedentary human civilization, whereby farming of domesticated species created food surpluses that enabled peop ...
, and
wildlife conservation Wildlife conservation refers to the practice of protecting wild species In biology, a species is the basic unit of Taxonomy (biology), classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often ...
. 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 characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, leading to nonlinearity, randomness, collective dynamics, hierarchy, and emergence. The term is generally used to c ...
,
ecosystem An ecosystem (or ecological system) consists of all the organisms and the physical environment with which they interact. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy enters the syst ...
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 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 behaviour in the absence of a ...
s and mathematical functions 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 the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually con ...
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 Predation is a biological interaction where one organism, the predator, kills and eats another organism, its prey. It is one of a family of common feeding behaviours that includes parasitism and micropredation (which usually do not kill t ...
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 biology and integral equations, being one of the founders of functional analysis. Biography Born in An ...
(1926). This model takes the form of a pair of
ordinary differential equation In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contras ...
s, one representing a prey
species In biology, a species is the basic unit of Taxonomy (biology), classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of ...
, 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 Fish are aquatic, craniate, gill-bearing animals that lack limbs with digits. Included in this definition are the living hagfish, lampreys, and cartilaginous and bony fish as well as various extinct related groups. Approximately 95% ...
and
shark Sharks are a group of elasmobranch fish characterized by a cartilaginous skeleton, five to seven gill slits on the sides of the head, and pectoral fins that are not fused to the head. Modern sharks are classified within the clade Selachi ...
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 Sea) ...
after the
First World War World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fig ...
(when
fishing Fishing is the activity of trying to catch fish. Fish are often caught as wildlife from the natural environment, but may also be caught from stocked bodies of water such as ponds, canals, park wetlands and reservoirs. Fishing techniques ...
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 typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using ...
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, indivi ...
) 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 scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and 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 dependence between the two variables. More specifically, it quantifies the " amount of information" (in units such as ...
(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 the process by which an entire body of water, or parts of it, becomes progressively enriched with minerals and nutrients, particularly nitrogen and phosphorus. It has also been defined as "nutrient-induced increase in phytopla ...
.
Conway's Game of Life The Game of Life, also known simply as 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 state, requiring no furt ...
and its variations model ecosystems where
proximity Proximity may refer to: * Distance, a numerical description of how far apart objects are * Proxemics, the study of human spatial requirements and the effects of population density * Proximity (2000 film), ''Proximity'' (2000 film), an action/thril ...
of the members of a population are factors in population growth.


See also

*
Compartmental models in epidemiology Compartmental models are a very general modelling technique. They are often applied to the mathematical modelling of infectious diseases. The population is assigned to compartments with labels – for example, S, I, or R, (Susceptible, Infectious ...
* Dynamic global vegetation model * Ecological forecasting * Gordon Arthur Riley *
Land Surface Model (LSM version 1.0) The National Center for Atmospheric Research Land Surface Model (LSM) is a unidimensional computational model developed by Gordon Bonan that describes ecological processes joined in many ecosystem models, hydrological processes found in Hydrological ...
* 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 the living organisms to investigate the principles that govern the structure, development a ...
*
Population dynamics Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. History Population dynamics has traditionally been the dominant branch of mathematical biology, which has ...
*
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, such as birth and death rates, and by immigration and emigration. The discipline is impor ...
* Rapoport's rule *
Scientific modelling Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted ...
*
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 mathematic ...


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