With the rise of computers, simulation models have emerged beside the more traditional statistical and mathematical models as a third pillar for ecological analysis. Broadly speaking, a simulation model is an algorithm, typically implemented as a computer program, which propagates the states of a system forward. Unlike in a mathematical model, however, this propagation does not employ the methods of calculus but rather a set of rules or formulae that directly prescribe the next state. Such an algorithmic model specification is particularly suited for describing systems that are difficult to capture or analyze with differential equations such as: (a) systems that are highly nonlinear or chaotic; (b) discrete systems, for example networks or groups of distinct individuals; (c) systems that are stochastic; and (d) systems that are too complex to be successfully treated with classical calculus. As these situations are frequently encountered in ecology, simulation models are now widely applied across the discipline. They have been instrumental in developing new insights into classical questions of species’ coexistence, community assembly, population dynamics, biogeography, and many more. The methods for this relatively young field are still being actively developed, and practical work with simulation models requires ecologists to learn new skills such as coding, sensitivity analysis, calibration, validation, and forecasting uncertainties. Moreover, scientific inquiry with complex systems has led to subtle changes to the philosophical and epistemological views regarding simplicity, reductionism, and the relationship between prediction and understanding.
Three short overview articles that jointly paint a good picture of the field are Jackson, et al. 2000 on ecological modeling, Pascual 2005 on computational approaches in ecology, and Black and McKane 2012 on stochastic simulations in ecology. Huston, et al. 1988 is another short piece that not only provides a good overview about questions and aims of simulation models in ecology but also an explanation of why these aims cannot be realized with simpler mathematical models (about mathematical models, see also the separate Oxford Bibliographies article Mathematical Ecology). Two useful textbooks on ecological modeling are Jørgensen and Bendoricchio 2001 and Grimm and Railsback 2005. Jørgensen and Bendoricchio 2001 provides an introduction to ecological modeling, leaning toward system analysis and system models, a topic also reviewed in the separate Oxford Bibliographies article Systems Ecology. Grimm and Railsback 2005 focuses on individual-based models in ecology. Two further technical references are Zeigler, et al. 2000, a comprehensive general introduction to simulation modeling, and Wilkinson 2011, an excellent technical reference on stochastic simulations. Finally, a note: simulations are also frequently employed in statistical methods, for example in statistical null models (e.g., Gotelli 2000). Such approaches, however, which only resample or simulate data without describing an explicit ecological process, are not covered in this article.
Black, A. J., and A. J. McKane. 2012. Stochastic formulation of ecological models and their applications. Trends in Ecology & Evolution 27.6: 337–345.
A recent review on stochastic simulation models in ecology, with a focus on individual-based simulations.
Gotelli, N. J. 2000. Null model analysis of species co‐occurrence patterns. Ecology 81.9: 2606–2621.
A classic reference on statistical null models that employ simulation or resampling algorithms to compare an observed pattern to a null expectation.
Grimm, V., and S. F. Railsback. 2005. Individual-based modeling and ecology. Princeton, NJ: Princeton Univ. Press.
This standard textbook provides an excellent introduction to the field of individual-based models in ecology.
Huston, M., D. DeAngelis, and W. Post. 1988. New computer models unify ecological theory. BioScience 38.10: 682–691.
A short piece that not only provides a good overview about questions and aims of complex simulation models in ecology but also an explanation of why these aims cannot be realized with simpler mathematical models.
Jackson, L. J., A. S. Trebitz, and K. L. Cottingham. 2000. An introduction to the practice of ecological modeling. BioScience 50.8: 694–706.
A short and gentle introduction into the topics of ecological modeling (mathematical and simulation models).
Jørgensen, S. E., and G. Bendoricchio. 2001. Fundamentals of ecological modelling. 4th ed. Amsterdam, The Netherlands: Elsevier.
A classic textbook on ecological modeling, with a focus on system analysis and system models.
Pascual, M. 2005. Computational ecology: From the complex to the simple and back. PLoS Computational Biology 1.2: e18.
A short introduction to the field of computation ecology, with tree examples that show how simulation models can help to understand complex adaptive ecological systems.
Wilkinson, D. J. 2011. Stochastic modelling for systems biology. Boca Raton, Florida: CRC Press.
Although this book is written primarily for system biologists, it will also be useful to ecologists, through its thorough introduction to the field of stochastic simulations techniques.
Zeigler, B. P., H. Praehofer, and T. G. Kim. 2000. Theory of modeling and simulation: Integrating discrete event and continuous complex dynamic systems. Cambridge, Massachusetts, United States: Academic Press.
A classic textbook on simulation models in science in general.
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- Accounting for Ecological Capital
- Allocation of Reproductive Resources in Plants
- Animals, Functional Morphology of
- Animals, Reproductive Allocation in
- Animals, Thermoregulation in
- Antarctic Environments and Ecology
- Applied Ecology
- Aquatic Conservation
- Aquatic Nutrient Cycling
- Archaea, Ecology of
- Assembly Models
- Bacterial Diversity in Freshwater
- Benthic Ecology
- Biodiversity and Ecosystem Functioning
- Biodiversity Patterns in Agricultural Systms
- Biological Chaos and Complex Dynamics
- Biome, Alpine
- Biome, Boreal
- Biome, Desert
- Biome, Grassland
- Biome, Savanna
- Biome, Tundra
- Biomes, African
- Biomes, East Asian
- Biomes, Mountain
- Biomes, North American
- Biomes, South Asian
- Bryophyte Ecology
- Butterfly Ecology
- Carson, Rachel
- Chemical Ecology
- Classification Analysis
- Coastal Dune Habitats
- Communities and Ecosystems, Indirect Effects in
- Communities, Top-Down and Bottom-Up Regulation of
- Community Concept, The
- Community Ecology
- Community Genetics
- Community Phenology
- Competition and Coexistence in Animal Communities
- Competition in Plant Communities
- Complexity Theory
- Conservation Biology
- Conservation Genetics
- Coral Reefs
- Darwin, Charles
- De-Glaciation, Ecology of
- Disease Ecology
- Drought as a Disturbance in Forests
- Early Explorers, The
- Earth’s Climate, The
- Eco-Evolutionary Dynamics
- Ecological Dynamics in Fragmented Landscapes
- Ecological Informatics
- Ecology, Microbial (Community)
- Ecosystem Engineers
- Ecosystem Multifunctionality
- Ecosystem Services
- Ecosystem Services, Conservation of
- Elton, Charles
- Endophytes, Fungal
- Energy Flow
- Environments, Extreme
- Ethics, Ecological
- Facilitation and the Organization of Communities
- Fern and Lycophyte Ecology
- Fire Ecology
- Food Webs
- Foraging Behavior, Implications of
- Foraging, Optimal
- Forests, Temperate Coniferous
- Forests, Temperate Deciduous
- Freshwater Invertebrate Ecology
- Genetic Considerations in Plant Ecological Restoration
- Genomics, Ecological
- Geographic Range
- Gleason, Henry
- Greig-Smith, Peter
- Gymnosperm Ecology
- Habitat Selection
- Harper, John L.
- Heavy Metal Tolerance
- Himalaya, Ecology of the
- Host-Parasitoid Interactions
- Human Ecology
- Human Ecology of the Andes
- Hutchinson, G. Evelyn
- Insect Ecology, Terrestrial
- Introductory Sources
- Invasive Species
- Island Biogeography Theory
- Island Biology
- Kin Selection
- Landscape Dynamics
- Landscape Ecology
- Laws, Ecological
- Legume-Rhizobium Symbiosis, The
- Leopold, Aldo
- Lichen Ecology
- Life History
- Literature, Ecology and
- MacArthur, Robert H.
- Mangrove Zone Ecology
- Marine Fisheries Management
- Mathematical Ecology
- Mating Systems
- Maximum Sustainable Yield
- Metabolic Scaling Theory
- Metacommunity Dynamics
- Metapopulations and Spatial Population Processes
- Mutualisms and Symbioses
- Mycorrhizal Ecology
- Natural History Tradition, The
- Networks, Ecological
- Niche Versus Neutral Models of Community Organization
- Nutrient Foraging in Plants
- Odum, Eugene and Howard
- Old Fields
- Ordination Analysis
- Organic Agriculture, Ecology of
- Parental Care, Evolution of
- Patch Dynamics
- Phenotypic Selection
- Philosophy, Ecological
- Phylogenetics and Comparative Methods
- Physiological Ecology of Nutrient Acquisition in Animals
- Physiological Ecology of Photosynthesis
- Physiological Ecology of Water Balance in Terrestrial Anim...
- Plant Disease Epidemiology
- Plant Ecological Responses to Extreme Climatic Events
- Polar Regions
- Pollination Ecology
- Population Dynamics, Density-Dependence and Single-Species
- Population Dynamics, Methods in
- Population Ecology, Plant
- Population Fluctuations and Cycles
- Population Genetics
- Population Viability Analysis
- Populations and Communities, Dynamics of Age- and Stage-St...
- Predation and Community Organization
- Predator-Prey Interactions
- Reductionism Versus Holism
- Religion and Ecology
- Remote Sensing
- Restoration Ecology
- Ricketts, Edward Flanders Robb
- Seed Ecology
- Serpentine Soils
- Shelford, Victor
- Simulation Modeling
- Soil Biogeochemistry
- Soil Ecology
- Spatial Pattern Analysis
- Spatial Patterns of Species Biodiversity in Terrestrial En...
- Species Extinctions
- Species Responses to Climate Change
- Species-Area Relationships
- Stability and Ecosystem Resilience, A Below-Ground Perspec...
- Stoichiometry, Ecological
- Stream Ecology
- Systems Ecology
- Tansley, Sir Arthur
- Terrestrial Resource Limitation
- Thermal Ecology of Animals
- Tragedy of the Commons
- Trophic Levels
- Vegetation Classification
- Vegetation Mapping
- Weed Ecology
- Whittaker, Robert H.
- Wildlife Ecology