Abstract
The use of spatially explicit models (SEMs) in ecology has grown enormously in the past two decades. One major advancement has been that fine-scale details of landscapes, and of spatially dependent biological processes, such as dispersal and invasion, can now be simulated with great precision, due to improvements in computer technology. Many areas of modeling have shifted toward a focus on capturing these fine-scale details, to improve mechanistic understanding of ecosystems. However, spatially implicit models (SIMs) have played a dominant role in ecology, and arguments have been made that SIMs, which account for the effects of space without specifying spatial positions, have an advantage of being simpler and more broadly applicable, perhaps contributing more to understanding. We address this debate by comparing SEMs and SIMs in examples from the past few decades of modeling research. We argue that, although SIMs have been the dominant approach in the incorporation of space in theoretical ecology, SEMs have unique advantages for addressing pragmatic questions concerning species populations or communities in specific places, because local conditions, such as spatial heterogeneities, organism behaviors, and other contingencies, produce dynamics and patterns that usually cannot be incorporated into simpler SIMs. SEMs are also able to describe mechanisms at the local scale that can create amplifying positive feedbacks at that scale, creating emergent patterns at larger scales, and therefore are important to basic ecological theory. We review the use of SEMs at the level of populations, interacting populations, food webs, and ecosystems and argue that SEMs are not only essential in pragmatic issues, but must play a role in the understanding of causal relationships on landscapes.
Similar content being viewed by others
References
Abrams PA. 1992. Predators that benefit prey and prey that harm predators: unusual effects of interacting foraging adaptation. Am Nat 140:573–600.
Accatino F, Wiegand K, Ward D, De Michele C. 2016. Trees, grass, and fire in humid savannas—the importance of life history traits and spatial processes. Ecol Model 320:135–44.
Adams TP, Purves DW, Pacala SW. 2007. Understanding height-structured competition in forests: is there an R* for light? Proc R Soc B 274:3039–48.
Adler P, Raff D, Lauenroth W. 2001. The effect of grazing on the spatial heterogeneity of vegetation. Oecologia 128:465–79.
Ager AA, Finney MA, Kerns BK, Maffei H. 2007. Modeling wildfire risk to northern spotted owl (Strix occidentalis caurina) habitat in Central Oregon, USA. For Ecol Manag 246:45–56.
Ahearn SC, Smith JL, Joshi AR, Ding J. 2001. TIGMOD: an individual-based spatially explicit model for simulating tiger/human interaction in multiple use forests. Ecol Model 140:81–97.
Alexander RB, Boyer EW, Smith RA, Schwarz GE, Moore RB. 2007. The role of headwater streams in downstream water quality. J Am Water Res Assoc 43:41–59.
Auchincloss AH, Roux AV. 2008. A new tool for epidemiology: the usefulness of dynamic-agent models in understanding place effects on health. Amer J Epidem 168:1–8.
Balkenhol N, Gugerli F, Cushman SA, Waits LP, Coulon A, Arntzen JW, Holderegger R, Wagner HH. 2009. Identifying future research needs in landscape genetics: where to from here? Landsc Ecol 24:455–63.
Bartsch J, Brander K, Heath M, Munk P, Richardson K, Svendsen E. 1989. Modeling the advection of herring larvae in the North Sea. Nature 340:632–6.
Bascompte J, Solé RV, Martí N. 1997. Population cycles and spatial patterns in snowshoe hares: an individual-oriented simulation. J Theor Biol 187:213–22.
Basset A, Fedele M, DeAngelis DL. 2002. Optimal exploitation of spatially distributed trophic resources and population stability. Ecol Model 151:245–60.
Bennett DA, Tang W. 2006. Modelling adaptive, spatially aware, and mobile agents: elk migration in Yellowstone. Intern J Geogr Inform Sci 20:1039–66.
Berger U, Hildenbrandt H. 2000. A new approach to spatially explicit modelling of forest dynamics: spacing, ageing and neighbourhood competition of mangrove trees. Ecol Model 132:287–302.
Berger U, Hildenbrandt H, Grimm V. 2002. Towards a standard for the individual-based of plant populations: self-thinning and the field-of-neighborhood approach. Nat Res Model 15:39–54.
Bertuzzo E, Casagrandi R, Gatto M, Rodriguez-Iturbe I, Rinaldo A. 2009. On spatially explicit models of cholera epidemics. J R Soc Interface. doi:10.1098/rsif.2009.0204.
Blanchart E, Marilleau N, Chotte JL, Drogoul A, Perrier E, Cambier C. 2009. SWORM: an agent-based model to simulate the effect of earthworms on soil structure. Eur J Soil Sci 60(1):13–21.
Blaine TW, DeAngelis DL. 1997. The effects of spatial scale on predator-prey functional response. Ecol Model 95:319–28.
Blanco CC, Scheiter S, Sosinski E, Fidelis A, Anand M, Pillar VD. 2014. Feedbacks between vegetation and disturbance processes promote long-term persistence of forest–grassland mosaics in south Brazil. Ecol Model 291:224–32.
Bonachela JA, Pringle RM, Sheffer E, Coverdale TC, Guyton JA, Caylor KK, Levin SA, Tarnita CE. 2015. Termite mounds can increase the robustness of dryland ecosystems to climatic change. Science 347:651–5.
Botkin DB, Janak JF, Wallis JR. 1972. Some ecological consequences of a computer model of forest growth. J Ecol 60:849–72.
Braunisch V, Segelbacher G, Hirzel AH. 2010. Modelling functional landscape connectivity from genetic population structure: a new spatially explicit approach. Molec Ecol 19:3664–78.
Brown JL, Weber JJ, Alvarado-Serrano DF, Hickerson MJ, Franks SJ, Carnaval AC. 2016. Predicting the genetic consequences of future climate change: the power of coupling spatial demography, the coalescent, and historical landscape changes. Amer J Bot 103:153–63.
Buchmann SL, Nabhan GP. 2012. The forgotten pollinators. Washington: Island Press.
Bugmann HKM. 1996. A simplified forest model to study species composition along climate gradients. Ecology 77:2055–74.
Bugmann H. 2001. A review of forest gap models. Clim Change 51:259–305.
Bugmann H, Lindner M, Lasch P, Flechsig M, Ebert B, Cramer W. 2000. Scaling issues in forest succession modelling. Clim Change 44:265–89.
Burchill CA, Kenkel NC. 1991. Vegetation-environment relationships of an inland boreal salt pan. Can J Bot 69:722–32.
Busing RT, Mailly D. 2004. Advances in spatial, individual-based modelling of forest dynamics. J Veg Sci 15:831–42.
Calabrese JM, Vazquez F, Lopez C, San Miguel M, Grimm V. 2010. The independent and interactive effects of tree–tree establishment competition and fire on savanna structure and dynamics. Am Nat 175:E44–65.
Callaway RM, Ridenour WM. 2004. Novel weapons: invasive success and the evolution of increased competitive ability. Front Ecol Environ 2:436–43.
Canham CD, Finzi AC, Pacala SW, Burbank DH. 1994. Causes and consequences of resource heterogeneity in forests: interspecific variation in light transmission by canopy trees. Can J For Res 24:337–49.
Canham CD, LePage PT, Coates KD. 2004. A neighborhood analysis of canopy tree competition: effects of shading versus crowding. Can J For Research. 34:778–87.
Cantrell RS, Cosner C. 2001. Spatial heterogeneity and critical patch size: area effects via diffusion in closed environments. J Theor Biol 209:161–71.
Cantrell RS, Cosner C. 2003. Spatial Ecology via Reaction-Diffusion Equations. Chichester: Wiley. p 411.
Carter J, Finn JT. 1999. MOAB: a spatially explicit, individual-based expert system for creating animal foraging models. Ecol Model 119:29–41.
Carter N, Levin S, Barlow A, Grimm V. 2015. Modeling tiger population and territory dynamics using an agent-based approach. Ecol Model 312:347–62.
Chesson P. 2000. General theory of competitive coexistence in spatially-varying environments. Theor Pop Biol 58:211–37.
Coates KD, Canham CD, Beaudet M, Sachs DL, Messier C. 2003. Use of a spatially explicit individual-tree model (SORTIE/BC) to explore the implications of patchiness in structurally complex forests. For Ecol Manag 186:297–310.
Costanza R, Sklar FH, White ML. 1990. Modeling coastal landscape dynamics. BioScience 40:91–107.
Cuddington K, Yodzis P. 2002. Predator-prey dynamics and movement in fractal environments. Am Nat 160:119–34.
D’Alpaos A, Lanzoni S, Marani M, Rinaldo A. 2007. Landscape evolution in tidal embayments: modeling the interplay of erosion, sedimentation, and vegetation dynamics. J Geophys Res. doi:10.1029/2006JF000537.
Darby P, DeAngelis DL, Romañach S, Suir K, Bridevaux J. 2015. Apple snail population dynamics on the Everglades landscape. Lands Ecol 30:1497–510.
DeAngelis DL, Gross LJ, Huston MA, Wolff WF, Fleming DM, Comiskey EJ, Sylvester SM. 1998. Landscape modeling for Everglades ecosystem restoration. Ecosystems 1:64–75.
De Roos AM, Mccauley E, Wilson WG. 1991. Mobility versus density-limited predator–prey dynamics on different spatial scales. Proc R Soc B 246:117–22.
Dion E, Van Schalkwyk L, Lambin EF. 2011. The landscape epidemiology of foot-and-mouth disease in South Africa: a spatially explicit multi-agent simulation. Ecol Model 222:2059–72.
Dunning JB Jr, Stewart DJ, Danielson BJ, Noon BR, Root TL, Lamberson RH, Stevens EE. 1995. Spatially explicit population models: current forms and future uses. Ecol Appl 5:3–11.
Durrett R, Levin S. 1994. The importance of being discrete (and spatial). Theor Pop Biol 46:363–94.
Ehrenfeld JG, Ravit B, Elgersma K. 2005. Feedback in the plant-soil system. Annu Rev Environ Resour 30:75–115.
Elderd BD, Nott MP. 2008. Hydrology, habitat change and population demography: an individual-based model for the endangered Cape Sable seaside sparrow Ammodramus maritimus mirabilis. J Appl Ecol 45:258–68.
Elkin C, Reineking B, Bigler C, Bugmann H. 2012. Do small-grain processes matter for landscape scale questions? sensitivity of a forest landscape model to the formulation of tree growth rate. Landsc Ecol 27:697–711.
Ellison AM, Bedford BL. 1995. Response of a wetland vascular plant community to disturbance: a simulation study. Ecol Appl 1:109–23.
Encinas-Viso F, Revilla TA, Velzen E, Etienne RS. 2014. Frugivores and cheap fruits make fruiting fruitful. J Evol Biol 27:313–24.
Fahrig L. 2003. Effects of habitat fragmentation on biodiversity. Annu Rev Ecol Evol System 34:487–515.
Feng Z, Alfaro-Murillo JA, DeAngelis DL, Schmidt J, Barga M, Zheng Y, Olson M, Glaser T, Kielland K, Chapin FSIII. 2012. Plant toxins and trophic cascades alter fire regime and succession on a boreal forest landscape. Ecol Model 244:79–92.
Fischer R, Bohn F, Dantas de Paula M, Dislich C, Groeneveld J, Gutiérrez AG, Kazmierczak M, Knapp N, Lehmann S, Paulick S, Pütz S, Rödig E, Taubert F, Köhler P, Huth A. 2016. Lessons learned from applying a forest gap model to understand ecosystem and carbon dynamics of complex tropical forests. Ecol Model 326:124–33.
Follows MJ, Dutkiewicz S, Grant S, Chisholm SW. 2007. Emergent biogeography of microbial communities in a model ocean. Science 315:1843–6.
Fretwell SD. 1987. Food chain dynamics: the central theory of ecology? Oikos 50:291–301.
Fretwell SD, Lucas HL Jr. 1970. On territorial behavior and other factors influencing habitat distributions in birds. I. Theoretical development. Acta Biotheor 19:16–36.
Gaff H, DeAngelis DL, Gross LJ, Salinas R, Shorrosh M. 2000. A dynamics landscape model for fish in the Everglades and its application to restoration. Ecol Model 127:33–52.
Gardner RH, Engelhardt KA. 2008. Spatial processes that maintain biodiversity in plant communities. Persp Plant Ecol Evol Syst 9:211–28.
Ginzburg LR, Jensen CX. 2008. From controversy to consensus: the indirect interference functional response. Intern Verein Theor Angew Limn Verh 30:297–301.
Gratzer G, Canham C, Dieckmann U, Fischer A, Iwasa Y, Law R, Lexer MJ, Sandmann H, Spies TA, Splechtna BE, Szwagrzyk J. 2004. Spatio-temporal development of forests–current trends in field methods and models. Oikos 107:3–15.
Green DG, Sadedin S. 2005. Interactions matter—complexity in landscapes and ecosystems. Ecol Complex 2:117–30.
Grimm V, Railsback SF. 2005. Individual-Based Modeling and Ecology. Princeton: Princeton University Press. p 428.
Grimm V, Berger U, Bastiansen F, Eliassen S, Ginot V, Giske J, Goss-Custard J, Grand T, Heinz SK, Huse G, Huth A, Jepsen JU, Jørgensen C, Mooij WM, Müller B, Pe’er G, Piou C, Railsback SF, Robbins AM, Robbins MA, Rossmanith E, Rüger N, Strand E, Souissi S, Stillmann R, Vabø R, Visser U, DeAngelis DL. 2006. A standard protocol for describing individual-based and agent-based models. Ecol Model 198:115–26.
Grimm V, Revilla E, Berger U, Jeltsch F, Mooij WM, Railsback SF, Thulke HH, Weiner J, Wiegand T, DeAngelis DL. 2005. Pattern-oriented modeling of agent-based complex systems: lessons from ecology. Science 310:987–91.
Groffman PM, Butterbach-Bahl K, Fulweiler RW, Gold AJ, Morse JL, Stander EK, Tague C, Tonitto C, Vidon P. 2009. Challenges to incorporating spatially and temporally explicit phenomena (hotspots and hot moments) in denitrification models. Biogeochem 93:49–77.
Grosshans RE, Kenkel NC. 1997. Dynamics of emergent vegetation along natural gradients of water depth and salinity in a prairie marsh: delayed influences of competition. UFS (Delta Marsh) Annu Rep 32:83–93.
Gustafson EJ, Gardner RH. 1996. The effect of landscape heterogeneity on the probability of patch colonization. Ecology 77:94–107.
Hanski I, Thomas CD. 1994. Metapopulation dynamics and conservation: a spatially explicit model applied to butterflies. Biol Conserv 68:167–80.
Hanski I. 1999. Metapopulation Ecology. New York: Oxford University Press. p 313.
Hanski I. 2001. Spatially realistic theory of metapopulation ecology. Naturwissenschaften 88:372–81.
Hanski I, Ovaskainen O. 2003. Metapopulation theory for fragmented landscapes. Theor Pop Biol 64:119–27.
Hastings A. 1996. Models of spatial spread. Biol Cons 78:43–148.
Hellweger FL, Bucci V. 2009. A bunch of tiny individuals—individual-based modeling for microbes. Ecol Model 220:8–22.
Hendry R, Bacon PJ, Moss R, Palmer SC, McGlade J. 1997. A two-dimensional individual-based model of territorial behaviour: possible population consequences of kinship in red grouse. Ecol Model 105:23–39.
Hinckley S, Hermann AJ, Megrey BA. 1996. Development of a spatially explicit, individual-based model of marine fish early life history. Mar Ecol Prog Ser 139:47–68.
Hogeweg P. 1988. Cellular automata as a paradigm for ecological modeling. Appl Math Comput 27:81–100.
Holderegger R, Wagner HH. 2008. Landscape genetics. BioScience 58:199–207.
Hölker F, Breckling B. 2002. Influence of activity in a heterogeneous environment on the dynamics of fish growth: an individual-based model of roach. J Fish Biol 60:1170–89.
Houde ED. 2008. Emerging from Hjort’s shadow. J Northw Atl Fish Sci 41:53–70.
Hubbell SP. 2001. The Unified Neutral Theory of Biodiversity and Biogeography Monographs in Population Biology 32. Princeton: Princeton University Press. p 375.
Hui C, Li Z, Yue DX. 2004. Metapopulation dynamics and distribution, and environmental heterogeneity induced by niche construction. Ecol Model 177:107–18.
Huse G, Railsback S, Feronö A. 2002. Modelling changes in migration pattern of herring: collective behaviour and numerical domination. J Fish Biol 60:571–82.
Jeltsch F, Milton SJ, Dean WRJ, van Rooyen N. 1996. Tree spacing and coexistence in semiarid savannas. J Ecol 84:583–95.
Jeltsch F, Moloney KA, Schurr FM, Köchy M, Schwager M. 2008. The state of plant population modelling in light of environmental change. Persp Plant Ecol Evol Syst 9:171–89.
Jiang J, DeAngelis DL, Smith TJIII, Teh SY, Koh HL. 2012. Spatial pattern formation of coastal vegetation in response to hydrodynamics of soil porewater salinity: a model study. Landsc Ecol 27:109–19.
Jiang J, DeAngelis DL. 2013. Strong species-environment feedback shapes plant community assembly along environmental gradients. Ecol Evol 3:4119–28.
Jones CG, Lawton JH, Shachak M. 1997. Positive and negative effects of organisms as physical ecosystem engineers. Ecology 78:1946–57.
Kéfi S, Rietkerk M, van Baalen M, Loreau M. 2007. Local facilitation, bistability and transitions in arid ecosystems. Theor Pop Biol 71:367–79.
Kéfi S, Berlow EL, Wieters EA, Navarrete SA, Petchey OL, Wood SA, Boit A, Joppa LN, Lafferty KD, Williams RJ, Martinez ND. 2012. More than a meal… integrating non-feeding interactions into food webs. Ecol Lett 15:291–300.
Kierstead H, Slobodkin LB. 1953. The size of water masses containing plankton blooms. J Mar Res 12:141–7.
Kinahan AA, Pimm SL, Van Aarde RJ. 2007. Ambient temperature as a determinant of landscape use in the savanna elephant, Loxodonta Africana. J Therm Biol 32:47–58.
Kirwan ML, Murray AB. 2007. A coupled geomorphic and ecological model of tidal marsh evolution. Proc Natl Acad Sci 104:6118–22.
Klausmeier CA. 1999. Regular and irregular patterns in semiarid vegetation. Science 284:1826–8.
Kohyama T. 1993. Size-structured tree populations in gap-dynamic forest–the forest architecture hypothesis for the stable coexistence of species. J Ecol 81:131–43.
Kramer-Schadt ST, Revilla E, Wiegand T, Breitenmoser UR. 2004. Fragmented landscapes, road mortality and patch connectivity: modelling influences on the dispersal of Eurasian lynx. J Appl Ecol 41:711–23.
Kreft JU, Picioreanu C, Wimpenny JW, van Loosdrecht MC. 2001. Individual-based modelling of biofilms. Microbiology 147:2897–912.
Kreft JU, Booth G, Wimpenny JW. 1998. BacSim, a simulator for individual-based modelling of bacterial colony growth. Microbiology 144:3275–87.
Kreft JU. 2004. Biofilms promote altruism. Microbiology 150:2751–60.
Lawton JH. 1999. Are there general laws in ecology? Oikos 84:177–92.
Lee HL, DeAngelis DL. 1997. A simulation study of the spatio temporal dynamics of the Unionid mussels. Ecol Model 95:171–80.
Leibold MA, Holyoak M, Mouquet N, Amarasekare P, Chase JM, Hoopes MF, Holt RD, Shurin JB, Law R, Tilman D, Loreau M. 2004. The metacommunity concept: a framework for multi-scale community Ecology. Ecol Lett 7:601–13.
Letcher BH, Priddy JA, Walters JR, Crowder LB. 1998. An individual-based, spatially-explicit simulation model of the population dynamics of the endangered red-cockaded woodpecker, Picoides borealis. Biol Conserv 86:1–4.
Levin SA, Segel LA. 1976. Hypothesis for origin of planktonic patchiness. Nature 259:659.
Levin SA. 1992. The problem of pattern and scale in ecology: the Robert H. MacArthur award lecture. Ecology 73:1943–67.
Levins R, Culver D. 1971. Regional coexistence of species and competition between rare species. Proc Natl Acad Sci 68:1246–8.
Lewison RL, Carter J. 2004. Exploring behavior of an unusual megaherbivore: a spatially explicit foraging model of the hippopotamus. Ecol Modell 171:127–38.
Lindenmayer DB, Burgman MA, Akçakaya HR, Lacy RC, Possingham HP. 1995. A review of the generic computer programs ALEX, RAMAS/space and VORTEX for modelling the viability of wildlife metapopulations. Ecol Model 82:161–74.
Lindsay R, Rigall J, Burd F. 1985. The use of small-scale surface patterns in the classification of British peatlands. Aquilo Serie Bot 21:67–79.
Liu J, Ashton PS. 1998. FORMOSAIC: an individual-based spatially explicit model for simulating forest dynamics in landscape mosaics. Ecol Model 106:177–200.
Liu J, Dunning JB, Pulliam HR. 1995. Potential effects of a forest management plan on Bachman’s sparrows (Aimophila aestivalis): linking a spatially explicit model with GIS. Conserv Biol 9:62–75.
Loreau M, Holt RD. 2004. Spatial flows and the regulation of ecosystems. Am Nat 163:606–15.
Mao JC, Chen QW, Chen YC. 2008. Three-dimensional eutrophication model and application to Taihu Lake, China. J Environ Sci 20:278–84.
Marani M, Da Lio C, D’Alpaos A. 2013. Vegetation engineers marsh morphology through multiple competing stable states. Proc Natl Acad Sci 110:3259–63.
Martin JF, Reddy KR. 1997. Interaction and spatial distribution of wetland nitrogen processes. Ecol Model 105:1–21.
May F, Grimm V, Jeltsch F. 2009. Reversed effects of grazing on plant diversity: the role of below-ground competition and size symmetry. Oikos 118:1830–43.
McCann KS, Rasmussen JB, Umbanhowar J. 2005. The dynamics of spatially coupled food webs. Ecol Lett 8:513–23.
McKelvey K, Croker J, Noon BR. 1992. A spatially explicit life-history simulator for the northern spotted owl. In: Roseburg District resource management plan and environmental impact statement.
Mennechez G, Schtickzelle N, Baguette M. 2003. Metapopulation dynamics of the bog fritillary butterfly: comparison of demographic parameters and dispersal between a continuous and a highly fragmented landscape. Landsc Ecol 18:279–91.
Meron E. 2015. Nonlinear Physics of Ecosystems. Boca Raton: CRC Press.
Miller TJ. 2007. Contribution of individual-based coupled physico-biological models to understanding recruitment in marine fish populations. Mar Ecol Prog Ser 347:127–38.
Mitchell GC. 1986. Vampire bat control on Latin America. In: Orians GH et al., Eds. Ecological Knowledge and Environmental Problem Solving. Washington: National Academy Press.
Mladenoff DJ. 2004. LANDIS and forest landscape models. Ecol Model 180:7–19.
Moen R, Pastor J, Cohen Y. 1997. A spatially explicit model of moose foraging and energetics. Ecology 78:505–21.
Mollison D. 1977. Spatial contact models for ecological and epidemic spread. J R Statist Soc B 39:283–326.
Mooij WM, Bennetts RE, Kitchens WM, DeAngelis DL. 2002. Exploring the effect of drought extent and interval on the Florida snail kite: interplay between spatial and temporal scales. Ecol Model 149:25–39.
Moorcroft PR, Hurtt GC, Pacala SW. 2001. A method for scaling vegetation dynamics. Ecol Monogr 7:557–86.
Moorcroft PR, Lewis MA, Crabtree RL. 2006. Mechanistic home range models capture spatial patterns and dynamics of coyote territories in Yellowstone. Proc R Soc B 273:1651–9.
Morales Y, Weber LJ, Mynett AE, Newton TJ. 2006. Mussel dynamics model: a hydroinformatics tool for analyzing the effects of different stressors on the dynamics of freshwater mussel communities. Ecol Model 197:448–60.
Nolet BA, Mooij WM. 2002. Search paths of swans foraging on spatially autocorrelated tubers. J Anim Ecol 71:451–62.
Okubo A. 1980. Diffusion and Ecological Problems: Mathematical Models Biomathematics, Vol. 10Berlin: Springer-Verlag.
Orians GH, Buckley J, Clark W, Gilpin M, Jordan C, Lehman J, May R, Robilliard G, Simberloff D, Erckmann W, Policansky D, Grossblatt N. 1986. Ecological Knowledge and Environmental Problem Solving. Washington: National Academy Press.
Ovaskainen O. 2004. Habitat-specific movement parameters estimated using mark-recapture data and a diffusion model. Ecology 85:242–57.
Pacala SW, Silander JA Jr. 1985. Neighborhood models of plant population dynamics. I. Single-species models of annuals. Am Nat 125:385–411.
Pacala SW, Silander JA Jr. 1990. Field tests of neighborhood population dynamic models of two annual weed species. Ecol Monogr 60:113–34.
Pacala SW, Canham CD, Silander JA Jr. 1993. Forest models defined by field measurements: I. the design of a northeastern forest simulator. Can J For Res 23:1980–8.
Pacala SW, Deutschman DH. 1995. Details that matter: the spatial distribution of individual trees maintains forest ecosystem function. Oikos 74:357–65.
Paruelo JM, Pütz S, Weber G, Bertiller M, Golluscio RA, Aguiar MR, Wiegand T. 2008. Long-term dynamics of a semiarid grass steppe under stochastic climate and different grazing regimes: a simulation analysis. J Arid Environ 72:2211–31.
Parry HR, Evans AJ, Morgan D. 2006. Aphid population response to agricultural landscape change: a spatially explicit, individual-based model. Ecol Model 199:451–63.
Pastor J, Cohen Y, Moen R. 1999. Generation of spatial patterns in boreal forest landscapes. Ecosystems 2:439–50.
Perry GL, Millington JD. 2008. Spatial modelling of succession-disturbance dynamics in forest ecosystems: concepts and examples. Persp Plant Ecol Evol Syst 9:191–210.
Peters DP, Herrick JE, Urban DL, Gardner RH, Breshears DD. 2004. Strategies for ecological extrapolation. Oikos 106:627–36.
Petersen JH, DeAngelis DL. 2000. Dynamics of prey moving through a predator field: a model of migrating juvenile salmon. Math Biosc 165:97–114.
Pettifor RA, Caldow RW, Rowcliffe JM, Goss-Custard JD, Black JM, Hodder KH, Houston AI, Lang A, Webb J. 2000. Spatially explicit, individual-based, behavioural models of the annual cycle of two migratory goose populations. J Appl Ecol 37:103–35.
Pitt JP, Worner SP, Suarez AV. 2009. Predicting argentine ant spread over the heterogeneous landscape using a spatially explicit stochastic model. Ecol Appl 19:1176–86.
Poff NL, Nelson-Baker K. 1997. Habitat heterogeneity and algal–grazer interactions in streams: explorations with a spatially explicit model. J North Amer Benth Soc 1:263–76.
Polis GA, Power ME, Huxel GR, Eds. 2004. Food Webs at the Landscape Level. Chicago: University of Chicago Press. p 548.
Porté A, Bartelink HH. 2002. Modelling mixed forest growth: a review of models for forest management. Ecol Model 150:141–88.
Potthoff M, Johst K, Gutt J, Wissel C. 2006. Clumped dispersal and species coexistence. Ecol Model 198:247–54.
Pulliam HR. 1988. Sources, sinks, and population regulation. Am Nat 132:652–61.
Railsback SF, Stauffer HB, Harvey BC. 2003. What can habitat preference models tell us? tests using a virtual trout population. Ecol Appl 13:1580–94.
Reuter H, Breckling B. 1999. Emerging properties on the individual level: modelling the reproduction phase of the European robin Erithacus rubecula. Ecol Model 121:199–219.
Richards PM, Mooij WM, DeAngelis DL. 2004. Evaluating the effect of salinity on a simulated American crocodile (Crocodylus acutus) population with applications to conservation and Everglades restoration. Ecol Model 180:371–94.
Rietkerk M, Dekker SC, Wassen MJ, Verkroost AWM, Bierkens MFP. 2004. A putative mechanism for bog patterning. Am Nat 163:699–708.
Robles C, Desharnais R. 2002. History and current development of a paradigm of predation in rocky intertidal communities. Ecology 83:1521–36.
Roughgarden J. 1997. Production functions from ecological populations: a survey with emphasis on spatially implicit models. In: Tilman D, Kareiva P, Eds. Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions. Princeton: Princeton University Press. p 296–316.
Ruel JJ, Ayres MP. 1999. Jensen’s inequality predicts effects of environmental variation. Trends Ecol Evol 14:361–6.
Rupp TS, Starfield AM, Chapin FSIII. 2000. A frame-based spatially explicit model of subarctic vegetation response to climatic change: comparison with a point model. Landsc Ecol 15:383–400.
Rupp TS, Chapin FSIII, Starfield AM. 2001. Modeling the influence of topographic barriers on treeline advance at the forest-tundra ecotone in northwestern Alaska. Clim Change 48:399–416.
Schertzer E, Staver AC, Levin SA. 2015. Implications of the spatial dynamics of fire spread for the bistability of savanna and forest. J Math Biol 70:329–41.
Schmitz OJ, Booth G. 1997. Modelling food web complexity: the consequences of individual-based, spatially explicit behavioural ecology on trophic interactions. Evol Ecol 11:379–98.
Schmitz OJ. 2000. Combining field experiments and individual-based modeling to identify the dynamically relevant organizational scale in a field system. Oikos 89:471–84.
Schneider FD, Kefi S. 2016. Spatially heterogeneous pressure raises risk of catastrophic shifts. Theor Ecol. doi:10.1007/s12080-015-0289-1.
Schweitzer JA, Juric I, Voorde TF, Clay K, Putten WH, Bailey JK. 2014. Are there evolutionary consequences of plant–soil feedbacks along soil gradients? Funct Ecol 28:55–64.
Schwinning S, Parsons AJ. 1996. Analysis of the coexistence mechanisms for grasses and legumes in grazing systems. J Ecol 84:799–813.
Seidl R, Fernandes PM, Fonseca TF, Gillet F, Jönsson AM, Merganičová K, Netherer S, Arpaci A, Bontemps JD, Bugmann H, González-Olabarria JR. 2011. Modelling natural disturbances in forest ecosystems: a review. Ecol Model 222:903–24.
Semeniuk CA, Musiani M, Hebblewhite M, Grindal S, Marceau DJ. 2012. Incorporating behavioral–ecological strategies in pattern-oriented modeling of caribou habitat use in a highly industrialized landscape. Ecol Model 243:18–32.
Shrader-Frechett KS, McCoy ED. 1993. Method in Ecology: Strategy for Conservation. Cambridge: Cambridge University Press. p 328.
Shugart HH. 1984. A Theory of Forest Dynamics. New York: Springer. p 278.
Shugart HH. 1998. Terrestrial Ecosystems in Changing Environments. Cambridge: Cambridge University Press.
Shuman JK, Shugart HH, O’Halloran TL. 2011. Sensitivity of Siberian larch forests to climate change. Glob Change Biol 17:2370–84.
Skellam JG. 1951. Random dispersal in theoretical populations. Biometrika 38:196–218.
Sklar FH, Fitz HC, Wu Y, Van Zee R, McVoy C. 2001. South Florida: the reality of change and the prospects for sustainability: the design of ecological landscape models for Everglades restoration. Ecol Econ 37:379–401.
Spencer M. 1997. The effects of habitat size and energy on food web structure: an individual-based cellular automata model. Ecol Model 94:299–316.
Staver AC, Archibald S, Levin SA. 2011. Tree cover in sub-Saharan Africa: rainfall and fire constrain forest and savanna as alternative stable states. Ecology 92:1063–72.
Sternberg LDSL, Teh SY, Ewe SM, Miralles-Wilhelm F, DeAngelis DL. 2007. Competition between hardwood hammocks and mangroves. Ecosystems 10:648–60.
Stillman RA, Railsback SF, Giske J, Berger U, Grimm V. 2015. Making predictions in a changing world: the benefits of individual-based ecology. BioScience 65:140–50.
Strigul N, Pristinski D, Purves D, Dushoff J, Pacala S. 2008. Scaling from trees to forests: tractable macroscopic equations for forest dynamics. Ecol Monogr 78:523–45.
Teh SY, DeAngelis DL, Sternberg LSL, Miralles-Wilhelm FR, Smith TJIII, Koh HL. 2008. A simulation model for projecting changes in salinity concentrations and species dominance in the coastal margin habitats of the Everglades. Ecol Model 213:245–56.
Thorbek P, Topping CJ. 2005. The influence of landscape diversity and heterogeneity on spatial dynamics of agrobiont linyphiid spiders: an individual-based model. Biocontrol 50:1–33.
Tilman D. 1994. Competition and biodiversity in spatially structured habitats. Ecology 75:2–16.
Tilman D, Kareiva P, Eds. 1997. Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions. Princeton: Princeton University Press. p 368.
Tischendorf L, Bender DJ, Fahrig L. 2003. Evaluation of patch isolation metrics in mosaic landscapes for specialist vs. generalist dispersers. Landsc Ecol 18:41–50.
Tonini F, Hochmair HH, Scheffrahn RH, DeAngelis DL. 2013. Simulating the effects of an invasive termite in an urban environment using a stochastic individual-based model. Environ Entom 42:412–23.
Topping CJ, Sibly RM, Akcakaya HR, Smith GC, Crocker DR. 2005. Risk assessment of UK skylark populations using life-history and individual-based landscape models. Ecotoxicology 14:925–36.
Topping CJ, Hansen TS, Jensen TS, Jepsen JU, Nikolajsen F, Odderskær P. 2003. ALMaSS, an agent-based model for animals in temperate European landscapes. Ecol Model 167:65–82.
Travis JM, Dytham C. 1999. Habitat persistence, habitat availability and the evolution of dispersal. Proc Roy Soc Lond B 266:723–8.
Turner MG, Gardner RH, Eds. 1989. Quantitative Methods in Landscape Ecology. New York: Springer.
Turner MG, Arthaud GJ, Engstrom RT, Hejl SJ, Liu J, Loeb S, McKelvey K. 1995. Usefulness of spatially explicit population models in land management. Ecol Appl 5:12–16.
Turner MG, Wu Y, Romme WH, Wallace LL. 1994. A landscape simulation model of winter foraging by large ungulates. Ecol Model 69:163–84.
Tyre AJ, Possingham HP, Lindenmayer DB. 2001. Inferring process from pattern: can territory occupancy provide information about life history parameters? Ecol Appl 11:1722–37.
Urban DL. 2005. Modeling ecological processes across scales. Ecology 86:1996–2006.
Urban DL, Bonan GB, Smith TM, Shugart HH. 1991. Spatial applications of gap models. For Ecol Manag 42:95–110.
van de Koppel J, van der Heide T, Altieri AH, Eriksson BK, Bouma TJ, Olff H, Silliman BR. 2015. Long-distance interactions regulate the structure and resilience of coastal ecosystems. Annu Rev Marine Sci 7:139–58.
van der Zee et al. 2016. How habitat-modifying organisms structure the food web of two coastal ecosystems. Proc R Soc B. doi:10.1098/rspb.2015.2326.
Walters JR. 1991. Application of ecological principles to the management of endangered species: the case of the red-cockaded woodpecker. Annu Rev Ecol Syst 22:505–23.
Wang M, Grimm V. 2007. Home range dynamics and population regulation: an individual-based model of the common shrew Sorex araneus. Ecol Model 205:397–409.
Weiner J, Stoll P, Muller-Landau H, Jasentuliyana A. 2001. The effects of density, spatial pattern, and competitive symmetry on size variation in simulated plant populations. Am Nat 158:438–50.
Weiss L, Pfestorf H, May F, Körner K, Boch S, Fischer M, Müller J, Prati D, Socher SA, Jeltsch F. 2014. Grazing response patterns indicate isolation of semi-natural European grasslands. Oikos 123:599–612.
Werner FE, Quinlan JA, Lough RG, Lynch DR. 2001. Spatially-explicit individual based modeling of marine populations: a review of the advances in the 1990s. Sarsia 86:411–21.
West DC, McLaughlin SB, Shugart HH. 1980. Simulated forest response to chronic air pollution stress. J Environ Qual 9:43–9.
White TCR. 2005. Why Does the World Stay Green: Nutrition and the Survival of Plants. Collingwood: CSIRO Press. p 120.
Wiegand T, Knauer F, Kaczensky P, Naves J. 2004a. Expansion of brown bears (Ursus arctos) into the eastern Alps: a spatially explicit population model. Biodiv Conserv 13:79–114.
Wiegand T, Revilla E, Knauer F. 2004b. Dealing with uncertainty in spatially explicit population models. Biodiv Conserv 13:53–78.
Wilson JB, Agnew AD. 1992. Positive-feedback switches in plant communities. London: Academic Press.
Wolff WF. 1994. An individual-oriented model of a wading bird nesting colony. Ecol Model 72:75–114.
Wu J, Levin SA. 1997. A patch-based spatial modeling approach: conceptual framework and simulation scheme. Ecol Model 101:325–46.
Xi W, Coulson RN, Birt AG, Shang ZB, Waldron JD, Lafon CW, Cairns DM, Tchakerian MD, Klepzig KD. 2009. Review of forest landscape models: types, methods, development and applications. Acta Ecol Sin 29:69–78.
Xu C, Van Nes EH, Holmgren M, Kéfi S, Scheffer M. 2015. Local facilitation may cause tipping points on a landscape level preceded by early-earning indicators. Am Nat 186:E81–90.
Yniguez A, DeAngelis DL, McManus J. 2008. Allowing macroalgae growth forms to emerge: use of an agent-based model to understand the growth and spread of macroalgae in Florida coral reefs, with emphasis on Halimeda tuna. Ecol Model 216:60–74.
Yurek S, DeAngelis DL, Trexler JC, Jopp F, Donalson DD. 2013. Simulating mechanisms for dispersal, production and stranding of small forage fish in temporary wetland habitats. Ecol Modell. doi:10.1016/j.ecolmodel.2012.11.001.
Zhu L, Qualls WA, Marshall JM, Arheart KL, DeAngelis DL, McManus JW, Traore SF, Doumbia S, Schlein Y, Müller GC, Beier JC. 2015. A spatial individual-based model predicting a great impact of copious sugar sources and resting sites on survival of Anopheles gambiae and malaria parasite transmission. Malar J 14:59.
Acknowledgements
The Authors appreciate the helpful comments of two anonymous reviewers. DLD and SY were supported in part by the USGS Greater Everglades Priority Ecosystems Science program, and SY was supported in part by the University of Miami McLamore Fellowship in Tropical Biology.
Author information
Authors and Affiliations
Corresponding author
Additional information
Author Contributions
Don DeAngelis conceived and designed the study. The research involved reviewing papers and work on the topic of the review. This was divided evenly between the two authors, Don DeAngelis and Simeon Yurek. Don DeAngelis wrote most sections of the paper. Simeon Yurek wrote some sections and reviewed and edited the whole paper.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
DeAngelis, D.L., Yurek, S. Spatially Explicit Modeling in Ecology: A Review. Ecosystems 20, 284–300 (2017). https://doi.org/10.1007/s10021-016-0066-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10021-016-0066-z