{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:38:46Z","timestamp":1760150326944,"version":"build-2065373602"},"reference-count":155,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,8]],"date-time":"2023-11-08T00:00:00Z","timestamp":1699401600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"SESASA project (European Leap-Agri call)"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Ecosystem modeling is a complex and multidisciplinary modeling problem which emerged in the 1950s. It takes advantage of the computational turn in sciences to better understand anthropogenic impacts and improve ecosystem management. For that purpose, ecosystem simulation models based on difference or differential equations were built. These models were relevant for studying dynamical phenomena and still are. However, they face important limitations in data-poor situations. As a response, several formal and non-formal qualitative dynamical modeling approaches were independently developed to overcome some limitations of the existing methods. Qualitative approaches allow studying qualitative dynamics as relevant abstractions of those provided by quantitative models (e.g., response to press perturbations). Each modeling framework can be viewed as a different assemblage of properties (e.g., determinism, stochasticity or synchronous update of variable values) designed to satisfy some scientific objectives. Based on four stated objectives commonly found in complex environmental sciences ((1) grasping qualitative dynamics, (2) making as few assumptions as possible about parameter values, (3) being explanatory and (4) being predictive), our objectives were guided by the wish to model complex and multidisciplinary issues commonly found in ecosystem modeling. We then discussed the relevance of existing modeling approaches and proposed the ecological discrete-event networks (EDEN) modeling framework for this purpose. The EDEN models propose a qualitative, discrete-event, partially synchronous and possibilistic view of ecosystem dynamics. We discussed each of these properties through ecological examples and existing analysis techniques for such models and showed how relevant they are for environmental science studies.<\/jats:p>","DOI":"10.3390\/e25111526","type":"journal-article","created":{"date-parts":[[2023,11,8]],"date-time":"2023-11-08T01:54:30Z","timestamp":1699408470000},"page":"1526","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On the History of Ecosystem Dynamical Modeling: The Rise and Promises of Qualitative Models"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8353-5104","authenticated-orcid":false,"given":"Maximilien","family":"Cosme","sequence":"first","affiliation":[{"name":"UMR AMAP, INRAE, University of Montpellier (Facult\u00e9 des Sciences), IRD, CIRAD, CNRS, 34398 Montpellier, France"},{"name":"UMR DECOD, Institut Agro Rennes-Angers (Campus Rennes), 65 rue de Saint-Brieuc, 35042 Rennes, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7650-784X","authenticated-orcid":false,"given":"Colin","family":"Thomas","sequence":"additional","affiliation":[{"name":"IBISC, University of Evry, 91025 Evry, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4521-8914","authenticated-orcid":false,"given":"C\u00e9dric","family":"Gaucherel","sequence":"additional","affiliation":[{"name":"IBISC, University of Evry, 91025 Evry, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,8]]},"reference":[{"key":"ref_1","unstructured":"Golley, F.B. (1993). A History of the Ecosystem Concept in Ecology: More Than the Sum of the Parts, Yale University Press."},{"key":"ref_2","unstructured":"Varenne, F. (2016). Mod\u00e9lisation, Succ\u00e8s et Limites, French Academy of Technologies."},{"key":"ref_3","unstructured":"Patten, B.C. (1971). Systems Analysis and Simulation in Ecology, Elsevier."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"459","DOI":"10.2307\/2258730","article-title":"Stability of Grazing Systems: An Application of Predator-Prey Graphs","volume":"63","year":"1975","journal-title":"J. Ecol."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Innis, G.S. (1978). Grassland Simulation Model, Springer. Ecological Studies.","DOI":"10.1007\/978-1-4612-9929-5"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"McCallum, H. (1999). Population Parameters: Estimation for Ecological Models, Wiley. [1st ed.].","DOI":"10.1002\/9780470757468"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1146\/annurev.ecolsys.35.021103.105711","article-title":"Regime Shifts, Resilience, and Biodiversity in Ecosystem Management","volume":"35","author":"Folke","year":"2004","journal-title":"Annu. Rev. Ecol. Evol. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1280","DOI":"10.1016\/j.envsoft.2008.03.003","article-title":"Parameterization of a process-based tree-growth model: Comparison of optimisation, MCMC and Particle filtering algorithms","volume":"23","author":"Gaucherel","year":"2008","journal-title":"Environ. Model. Softw."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1111\/j.1749-6632.1974.tb20562.x","article-title":"Qualitative Analysis of Partially Specified Systems","volume":"231","author":"Levins","year":"1974","journal-title":"Ann. N. Y. Acad. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1007\/s10539-006-9049-3","article-title":"The strategy of \u201cThe strategy of model building in population biology\u201d","volume":"21","author":"Odenbaugh","year":"2006","journal-title":"Biol. Philos."},{"key":"ref_11","first-page":"421","article-title":"The strategy of model building on population biology","volume":"54","author":"Levins","year":"1966","journal-title":"Am. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Recknagel, F. (2006). Ecological Informatics: Scope, Techniques and Applications, Springer.","DOI":"10.1007\/3-540-28426-5"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Recknagel, F. (2006). Ecological Informatics: Scope, Techniques and Applications, Springer.","DOI":"10.1007\/3-540-28426-5"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1073\/pnas.1008204108","article-title":"A network model for plant\u2013pollinator community assembly","volume":"108","author":"Campbell","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1615","DOI":"10.1111\/2041-210X.13242","article-title":"Using discrete systems to exhaustively characterize the dynamics of an integrated ecosystem","volume":"10","author":"Gaucherel","year":"2019","journal-title":"Methods Ecol. Evol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1372","DOI":"10.1890\/0012-9658(2002)083[1372:ROCSIA]2.0.CO;2","article-title":"Relevance of Community Structure in Assessing Indeterminacy of Ecological Predictions","volume":"83","author":"Dambacher","year":"2002","journal-title":"Ecology"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"638","DOI":"10.2307\/1935352","article-title":"Qualitative Stability in Model Ecosystems","volume":"54","author":"May","year":"1973","journal-title":"Ecology"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Buis, R. (2019). Biology and Mathematics: History and Challenges, ISTE.","DOI":"10.1002\/9781119663416"},{"key":"ref_19","unstructured":"Odum, E.P. (1953). Fundamentals of Ecology, Saunders. [1st ed.]."},{"key":"ref_20","unstructured":"von Bertalanffy, L. (1969). General System Theory: Foundations, Development, Applications, G. Braziller."},{"key":"ref_21","unstructured":"Vernadski, V.I. (1926). Biosfera, Nauchnoe Khimiko-Techniche-Skoye Izdatel\u2019stvo."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"53","DOI":"10.2307\/1943255","article-title":"Limnological Studies in Connecticut","volume":"9","author":"Riley","year":"1939","journal-title":"Ecol. Monogr."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"291","DOI":"10.2307\/1943285","article-title":"Trophic Structure and Productivity of a Windward Coral Reef Community on Eniwetok Atoll","volume":"25","author":"Odum","year":"1955","journal-title":"Ecol. Monogr."},{"key":"ref_24","unstructured":"Euler, L. (1748). Introductio in Analysin Infinitorum, Apud Marcum-Michaelem Bousquet & Socios."},{"key":"ref_25","first-page":"113","article-title":"Notice sur la loi que la population poursuit dans son accroissement","volume":"Volume 10","author":"Quetelet","year":"1838","journal-title":"Correspondance Math\u00e9matique et Physique"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1126\/science.26.653.21.b","article-title":"Relation between Birth Rates and Death Rates","volume":"26","author":"Lotka","year":"1907","journal-title":"Science"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1080\/14786440408637050","article-title":"A problem in age-distribution","volume":"21","author":"Sharpe","year":"1911","journal-title":"London Edinburgh Dublin Philos. Mag. J. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Baca\u00ebr, N. (2011). A Short History of Mathematical Population Dynamics, Springer.","DOI":"10.1007\/978-0-85729-115-8"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1073\/pnas.6.7.410","article-title":"Analytical Note on Certain Rhythmic Relations in Organic Systems","volume":"6","author":"Lotka","year":"1920","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1038\/118558a0","article-title":"Fluctuations in the Abundance of a Species considered Mathematically","volume":"118","author":"Volterra","year":"1926","journal-title":"Nature"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"221","DOI":"10.2307\/1930032","article-title":"An Introduction to the Cybernetics of the Ecosystem: The Trophic-Dynamic Aspect","volume":"40","author":"Patten","year":"1959","journal-title":"Ecology"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TBME.1980.326685","article-title":"Compartmental System Analysis: State of the Art","volume":"27","author":"Brown","year":"1980","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_33","unstructured":"Patten, B.C. (1971). Systems Analysis and Simulation in Ecology, Academic Press."},{"key":"ref_34","unstructured":"Patten, B.C. (1971). Systems Analysis and Simulation in Ecology, Academic Press."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.ecolmodel.2003.08.020","article-title":"A Bayesian network of eutrophication models for synthesis, prediction, and uncertainty analysis","volume":"173","author":"Borsuk","year":"2004","journal-title":"Ecol. Model."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.ecoinf.2018.03.003","article-title":"Hidden variables in a Dynamic Bayesian Network identify ecosystem level change","volume":"45","author":"Uusitalo","year":"2018","journal-title":"Ecol. Inform."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2005WR004599","article-title":"A stochastic model of nitrate transport and cycling at basin scale","volume":"42","author":"Botter","year":"2006","journal-title":"Water Resour. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0304-3800(97)00156-7","article-title":"State-of-the-art in ecosystem theory","volume":"100","year":"1997","journal-title":"Ecol. Model."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/BF00209430","article-title":"Defining ecology: Ecological theories, mathematical models, and applied biology in the 1960s and 1970s","volume":"24","author":"Palladino","year":"1991","journal-title":"J. Hist. Biol."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Clements, F.E. (1916). Plant Succession; An Analysis of the Development of Vegetation, Carnegie Institution of Washington.","DOI":"10.5962\/bhl.title.56234"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.ecolmodel.2004.06.007","article-title":"Distributed control in ecological networks","volume":"179","author":"Fath","year":"2004","journal-title":"Ecol. Model."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1086\/283881","article-title":"The Cybernetic Nature of Ecosystems","volume":"118","author":"Patten","year":"1981","journal-title":"Am. Nat."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Innis, G.S. (1978). Grassland Simulation Model, Springer. Ecological Studies.","DOI":"10.1007\/978-1-4612-9929-5"},{"key":"ref_44","unstructured":"Patten, B.C. (1975). Systems Analysis and Simulation in Ecology: Volume III, Academic Press."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1038\/493295a","article-title":"Time to model all life on Earth","volume":"493","author":"Purves","year":"2013","journal-title":"Nature"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Harfoot, M.B.J., Newbold, T., Tittensor, D.P., Emmott, S., Hutton, J., Lyutsarev, V., Smith, M.J., Scharlemann, J.P.W., and Purves, D.W. (2014). Emergent Global Patterns of Ecosystem Structure and Function from a Mechanistic General Ecosystem Model. PLoS Biol., 12.","DOI":"10.1371\/journal.pbio.1001841"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/0304-3800(95)00112-3","article-title":"Development of a general ecosystem model for a range of scales and ecosystems","volume":"88","author":"Fitz","year":"1996","journal-title":"Ecol. Model."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Bartlett, L.J., Newbold, T., Purves, D.W., Tittensor, D.P., and Harfoot, M.B.J. (2016). Synergistic impacts of habitat loss and fragmentation on model ecosystems. Proc. R. Soc. B Biol. Sci., 283.","DOI":"10.1098\/rspb.2016.1027"},{"key":"ref_49","unstructured":"J\u00f8rgensen, S.E. (2016). Developments in Environmental Modelling, Elsevier."},{"key":"ref_50","unstructured":"Likens, G.E. (1992). Excellence in Ecology, Ecology Institute."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"562","DOI":"10.2307\/1937422","article-title":"Flow Analysis of Models of the Hubbard Brook Ecosystem","volume":"61","author":"Finn","year":"1980","journal-title":"Ecology"},{"key":"ref_52","unstructured":"Nielsen, S.N. (2020). A New Ecology: Systems Perspective, Elsevier."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1146\/annurev.es.04.110173.001553","article-title":"On the Principles of Thermodynamics in Ecology","volume":"4","author":"Gallucci","year":"1973","journal-title":"Annu. Rev. Ecol. Syst."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1126\/science.164.3877.262","article-title":"The Strategy of Ecosystem Development","volume":"164","author":"Odum","year":"1969","journal-title":"Science"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/0304-3800(94)00037-I","article-title":"Network integration of ecological extremal principles: Exergy, emergy, power, ascendency, and indirect effects","volume":"79","author":"Patten","year":"1995","journal-title":"Ecol. Model."},{"key":"ref_56","unstructured":"Odum, H.T. (1983). Systems Ecology: An Introduction, Wiley."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/0304-3800(77)90023-0","article-title":"Ecological buffer capacity","volume":"3","author":"Mejer","year":"1977","journal-title":"Ecol. Model."},{"key":"ref_58","unstructured":"Lotka, A.J. (1925). Elements of Physical Biology, Williams & Wilkins."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/BF02153597","article-title":"Biologie et thermodynamique des ph\u00e9nom\u00e8nes irr\u00e9versibles","volume":"2","author":"Prigogine","year":"1946","journal-title":"Experientia"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1006\/jtbi.2000.2234","article-title":"Complementarity of Ecological Goal Functions","volume":"208","author":"Fath","year":"2001","journal-title":"J. Theor. Biol."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"882","DOI":"10.1016\/j.rser.2015.10.048","article-title":"A review of emergy theory, its application and latest developments","volume":"54","author":"Amaral","year":"2016","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/978-3-642-50124-1_21","article-title":"Lorenzo Camerano\u2019s Contribution to Early Food Web Theory","volume":"Volume 100","author":"Levin","year":"1994","journal-title":"Frontiers in Mathematical Biology"},{"key":"ref_63","unstructured":"Levin, S.A. (1880). Frontiers in Mathematical Biology, Springer. Lecture Notes in Biomathematics."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1939452","article-title":"Perturbation Experiments in Community Ecology: Theory and Practice","volume":"65","author":"Bender","year":"1984","journal-title":"Ecology"},{"key":"ref_65","first-page":"557","article-title":"Correlation and Causation","volume":"20","author":"Wright","year":"1921","journal-title":"J. Agric. Res."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/S0304-3800(02)00295-8","article-title":"Qualitative predictions in model ecosystems","volume":"161","author":"Dambacher","year":"2003","journal-title":"Ecol. Model."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1086\/508099","article-title":"Qualitative Scientific Modeling and Loop Analysis","volume":"72","author":"Justus","year":"2005","journal-title":"Philos. Sci."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/978-1-4613-9072-5_6","article-title":"Qualitative Modeling in Ecology: Loop Analysis, Signed Digraphs, and Time Averaging","volume":"Volume 5","author":"Luker","year":"1991","journal-title":"Qualitative Simulation Modeling and Analysis"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1007\/s10539-006-9050-x","article-title":"Loop analysis and qualitative modeling: Limitations and merits","volume":"21","author":"Justus","year":"2007","journal-title":"Biol. Philos."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"530","DOI":"10.2307\/3546432","article-title":"Parsimonious Interpretation of the Impact of Vegetation, Food, and Predation on Snowshoe Hare","volume":"84","author":"Dambacher","year":"1999","journal-title":"Oikos"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"2651","DOI":"10.1016\/j.ecolmodel.2011.03.040","article-title":"Exploring alternative states in ecological systems with a qualitative analysis of community feedback","volume":"222","author":"Marzloff","year":"2011","journal-title":"Ecol. Model."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"836","DOI":"10.1890\/10-1354.1","article-title":"Predicting community responses to perturbations in the face of imperfect knowledge and network complexity","volume":"92","author":"Novak","year":"2011","journal-title":"Ecology"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1111\/2041-210X.12703","article-title":"Revealing beliefs: Using ensemble ecosystem modelling to extrapolate expert beliefs to novel ecological scenarios","volume":"8","author":"Bode","year":"2017","journal-title":"Methods Ecol. Evol."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.ecolind.2012.08.020","article-title":"Identifying keystone trophic groups in benthic ecosystems: Implications for fisheries management","volume":"25","author":"Ortiz","year":"2013","journal-title":"Ecol. Indic."},{"key":"ref_75","doi-asserted-by":"crossref","unstructured":"Ortiz, M., and Levins, R. (2017). Self-feedbacks determine the sustainability of human interventions in eco-social complex systems: Impacts on biodiversity and ecosystem health. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0176163"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.ecolmodel.2015.06.004","article-title":"Ecological non-monotonicity and its effects on complexity and stability of populations, communities and ecosystems","volume":"312","author":"Zhang","year":"2015","journal-title":"Ecol. Model."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0304-3800(91)90177-3","article-title":"Qualitative reasoning about an ecological process: Interpretation in hydroecology","volume":"59","author":"Guerrin","year":"1991","journal-title":"Ecol. Model."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.ecolmodel.2005.11.014","article-title":"Modelling population and community dynamics with qualitative reasoning","volume":"195","author":"Salles","year":"2006","journal-title":"Ecol. Model."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/0004-3702(86)90073-1","article-title":"Qualitative simulation","volume":"29","author":"Kuipers","year":"1986","journal-title":"Artif. Intell."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.ecoinf.2009.09.009","article-title":"Garp3\u2014Workbench for qualitative modelling and simulation","volume":"4","author":"Bredeweg","year":"2009","journal-title":"Ecol. Inform."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.agee.2012.09.011","article-title":"How do different agricultural management strategies affect bird communities inhabiting a savanna-forest mosaic? A qualitative reasoning approach","volume":"164","author":"Goulart","year":"2013","journal-title":"Agric. Ecosyst. Environ."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.ecoinf.2013.02.004","article-title":"How plants changed the world: Using qualitative reasoning to explain plant macroevolution\u2019s effect on the long-term carbon cycle","volume":"17","author":"Kansou","year":"2013","journal-title":"Ecol. Inform."},{"key":"ref_83","first-page":"229","article-title":"Botanical survey of Scotland: A general map of the highlands with a sketch of the history and methods","volume":"22","author":"Hardy","year":"1906","journal-title":"Scott. Geogr. Mag."},{"key":"ref_84","first-page":"271","article-title":"Successional Relations of the Vegetation about Yarmouth, Nova Scotia","volume":"12","author":"Transeau","year":"1909","journal-title":"Plant World"},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/BF02390895","article-title":"Successive mapping of dune slack vegetation","volume":"29","author":"Londo","year":"1974","journal-title":"Vegetatio"},{"key":"ref_86","first-page":"76","article-title":"Plant succession in relation to range management","volume":"Volume 791","author":"Sampson","year":"1919","journal-title":"Bulletin No. 791"},{"key":"ref_87","first-page":"593","article-title":"Succession as a Factor in Range Management","volume":"15","author":"Sampson","year":"1917","journal-title":"J. For."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"104","DOI":"10.2307\/3893680","article-title":"Condition and Management of Range Land Based on Quantitative Ecology","volume":"2","author":"Dyksterhuis","year":"1949","journal-title":"J. Range Manag."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"266","DOI":"10.2307\/3899492","article-title":"Opportunistic Management for Rangelands Not at Equilibrium","volume":"42","author":"Westoby","year":"1989","journal-title":"J. Range Manag."},{"key":"ref_90","first-page":"106","article-title":"State and transition modeling: An ecological process approach","volume":"56","author":"Stringham","year":"2003","journal-title":"Rangel. Ecol. Manag. Range Manag. Arch."},{"key":"ref_91","unstructured":"Mooney, H.A., and Conrad, C.E. (1977, January 1\u20135). Post fire succession of plants in Mediterranean ecosystems. Proceedings of the Symposium on the Environmental Consequences of Fire and Fuel Management in Mediterranean Ecosystems, Palo Alto, CA, USA."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1038\/2251160a0","article-title":"Transition Probabilities for a Forest","volume":"225","author":"Waggoner","year":"1970","journal-title":"Nature"},{"key":"ref_93","unstructured":"Horn, H.S. (1975). Ecology and Evolution of Communities, Harvard University Press."},{"key":"ref_94","first-page":"229","article-title":"The use of state and transition models for predicting vegetation change in rangelands","volume":"28","author":"Scanlan","year":"1994","journal-title":"Trop. Grasslands"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1177\/0309133315581700","article-title":"Boxing daze\u2014Using state-and-transition models to explore the evolution of socio-biophysical landscapes","volume":"39","year":"2015","journal-title":"Prog. Phys. Geogr. Earth Environ."},{"key":"ref_96","doi-asserted-by":"crossref","unstructured":"Briske, D.D. (2017). Rangeland Systems: Processes, Management and Challenges, Springer International Publishing.","DOI":"10.1007\/978-3-319-46709-2"},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1466-822X.2006.00212.x","article-title":"Novel ecosystems: Theoretical and management aspects of the new ecological world order","volume":"15","author":"Hobbs","year":"2006","journal-title":"Glob. Ecol. Biogeogr."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/j.ecolmodel.2010.10.010","article-title":"Combining state and transition models with dynamic Bayesian networks","volume":"222","author":"Nicholson","year":"2011","journal-title":"Ecol. Model."},{"key":"ref_99","doi-asserted-by":"crossref","unstructured":"Van Fraassen, B.C. (1980). The Scientific Image, Clarendon Press.","DOI":"10.1093\/0198244274.001.0001"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"art125","DOI":"10.1890\/ES11-00211.1","article-title":"The limits to prediction in ecological systems","volume":"2","author":"Beckage","year":"2011","journal-title":"Ecosphere"},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.jtbi.2004.10.011","article-title":"Random biochemical networks and the probability of self-sustaining autocatalysis","volume":"233","author":"Mossel","year":"2005","journal-title":"J. Theor. Biol."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0304-3800(89)90066-5","article-title":"Artificial intelligence and expert systems in ecology and natural resource management","volume":"46","author":"Rykiel","year":"1989","journal-title":"Ecol. Model."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"art83","DOI":"10.1890\/ES12-00415.1","article-title":"Toward rigorous use of expert knowledge in ecological research","volume":"4","author":"Drescher","year":"2013","journal-title":"Ecosphere"},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1086\/282272","article-title":"Graphical Representation and Stability Conditions of Predator-Prey Interactions","volume":"97","author":"Rosenzweig","year":"1963","journal-title":"Am. Nat."},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1146\/annurev-ecolsys-110411-160340","article-title":"Historical Contingency in Community Assembly: Integrating Niches, Species Pools, and Priority Effects","volume":"46","author":"Fukami","year":"2015","journal-title":"Annu. Rev. Ecol. Evol. Syst."},{"key":"ref_106","doi-asserted-by":"crossref","unstructured":"Song, C., Fukami, T., and Saavedra, S. (2021). Untangling the complexity of priority effects in multispecies communities. Ecol. Lett., 2301\u20132313.","DOI":"10.1111\/ele.13870"},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1046\/j.1365-2656.1998.00212.x","article-title":"Coexistence and collapse: An experimental investigation of the persistent communities of a protist species pool","volume":"67","author":"Weatherby","year":"1998","journal-title":"J. Anim. Ecol."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.agsy.2008.09.003","article-title":"Developing decision support tools for rangeland management by combining state and transition models and Bayesian belief networks","volume":"99","author":"Bashari","year":"2008","journal-title":"Agric. Syst."},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1016\/0022-5193(73)90247-6","article-title":"Boolean formalization of genetic control circuits","volume":"42","author":"Thomas","year":"1973","journal-title":"J. Theor. Biol."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/0022-5193(69)90015-0","article-title":"Metabolic stability and epigenesis in randomly constructed genetic nets","volume":"22","author":"Kauffman","year":"1969","journal-title":"J. Theor. Biol."},{"key":"ref_111","doi-asserted-by":"crossref","unstructured":"de Go\u00ebr de Herve, M., Thomas, C., Cosme, M., Warren, P.H., and Gaucherel, C. (2022). Is a community state reachable, and why?. Authorea.","DOI":"10.22541\/au.164301558.85072720\/v1"},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/0022-5193(63)90027-4","article-title":"Functional analysis of chemical systems in vivo using a logical circuit equivalent. II. The idea of a molecular automaton","volume":"4","author":"Sugita","year":"1963","journal-title":"J. Theor. Biol."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/s001099900023","article-title":"Gene expression profiling, genetic networks, and cellular states: An integrating concept for tumorigenesis and drug discovery","volume":"77","author":"Huang","year":"1999","journal-title":"J. Mol. Med."},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10928-017-9567-4","article-title":"Boolean Network Modeling in Systems Pharmacology","volume":"45","author":"Bloomingdale","year":"2018","journal-title":"J. Pharmacokinet. Pharmacodyn."},{"key":"ref_115","doi-asserted-by":"crossref","unstructured":"Della Dora, J., Demongeot, J., and Lacolle, B. (1981). Numerical Methods in the Study of Critical Phenomena, Springer.","DOI":"10.1007\/978-3-642-81703-8"},{"key":"ref_116","doi-asserted-by":"crossref","unstructured":"Thomas, R. (1979). Kinetic Logic A Boolean Approach to the Analysis of Complex Regulatory Systems, Proceedings of the EMBO Course \u201cFormal Analysis of Genetic Regulation\u201d, Springer. Lecture Notes in Biomathematics.","DOI":"10.1007\/978-3-642-49321-8"},{"key":"ref_117","doi-asserted-by":"crossref","unstructured":"Cordier, M.O., Largou\u00ebt, C., and Zhao, Y. (2014, January 10\u201312). Model-Checking an Ecosystem Model for Decision-Aid. Proceedings of the IEEE 26th International Conference 681 on Tools with Artificial Intelligence, Limassol, Cyprus.","DOI":"10.1109\/ICTAI.2014.87"},{"key":"ref_118","doi-asserted-by":"crossref","unstructured":"Cassandras, C.G., and Lafortune, S. (2008). Introduction to Discrete Event Systems, Springer. [2nd ed.].","DOI":"10.1007\/978-0-387-68612-7"},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1046\/j.1469-8137.1998.00208.x","article-title":"Germination and post-germination growth to carrot seedling emergence: Predictive threshold models and sources of variation between sowing occasions","volume":"139","author":"Steckel","year":"1998","journal-title":"New Phytol."},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"e03302","DOI":"10.1002\/ecs2.3302","article-title":"Potential for ecological nonlinearities and thresholds to inform Pacific salmon management","volume":"11","author":"Munsch","year":"2020","journal-title":"Ecosphere"},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"3878","DOI":"10.1038\/s41598-019-40349-4","article-title":"The prevalence of nonlinearity and detection of ecological breakpoints across a land use gradient in streams","volume":"9","author":"Rearick","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"1917","DOI":"10.1093\/bioinformatics\/btn336","article-title":"Synchronous versus asynchronous modeling of gene regulatory networks","volume":"24","author":"Garg","year":"2008","journal-title":"Bioinformatics"},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1006\/jtbi.1998.0701","article-title":"Dynamics of the genetic regulatory Network for Arabidopsis thaliana flower morphogenesis","volume":"193","author":"Mendoza","year":"1998","journal-title":"J. Theor. Biol."},{"key":"ref_124","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/s10699-017-9535-x","article-title":"How Future Depends on Past and Rare Events in Systems of Life","volume":"23","author":"Longo","year":"2018","journal-title":"Found. Sci."},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1111\/j.1365-2028.2006.00662.x","article-title":"A \u2018large infrequent disturbance\u2019 in an East African savanna","volume":"44","author":"Gillson","year":"2006","journal-title":"Afr. J. Ecol."},{"key":"ref_126","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1353\/sor.2008.0013","article-title":"Possibilistic Thinking: A New Conceptual Tool for Thinking about Extreme Events","volume":"75","author":"Clarke","year":"2008","journal-title":"Soc. Res."},{"key":"ref_127","doi-asserted-by":"crossref","first-page":"109122","DOI":"10.1016\/j.ecolmodel.2020.109122","article-title":"Predicting the ecosystem-wide impacts of eradication with limited information using a qualitative modelling approach","volume":"430","author":"Han","year":"2020","journal-title":"Ecol. Model."},{"key":"ref_128","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1111\/2041-210X.13179","article-title":"Dealing with high uncertainty in qualitative network models using Boolean analysis","volume":"10","author":"Kristensen","year":"2019","journal-title":"Methods Ecol. Evol."},{"key":"ref_129","doi-asserted-by":"crossref","first-page":"170","DOI":"10.3182\/20140514-3-FR-4046.00135","article-title":"Model Checking Logical Regulatory Networks","volume":"47","author":"Monteiro","year":"2014","journal-title":"IFAC Proc. Vol."},{"key":"ref_130","doi-asserted-by":"crossref","unstructured":"Giacobazzi, R., Berdine, J., and Mastroeni, I. (2013, January 20\u201322). Causality Checking for Complex System Models. Proceedings of the Verification, Model Checking, and Abstract Interpretation, Rome, Italy. Lecture Notes in Computer Science.","DOI":"10.1007\/978-3-642-35873-9"},{"key":"ref_131","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.oneear.2019.08.017","article-title":"Shortfalls in Conservation Evidence: Moving from Ecological Effects of Interventions to Policy Evaluation","volume":"1","author":"Adams","year":"2019","journal-title":"One Earth"},{"key":"ref_132","doi-asserted-by":"crossref","first-page":"101205","DOI":"10.1016\/j.ecoinf.2020.101205","article-title":"Discrete-event models for conservation assessment of integrated ecosystems","volume":"61","author":"Gaucherel","year":"2020","journal-title":"Ecol. Inform."},{"key":"ref_133","doi-asserted-by":"crossref","unstructured":"Cosme, M., H\u00e9ly, C., Pommereau, F., Pasquariello, P., Tiberi, C., Treydte, A., and Gaucherel, C. (2021). Qualitative Modeling for Bridging Expert-Knowledge and Social-Ecological Dynamics of an East African Savanna. Land, 11.","DOI":"10.20944\/preprints202111.0569.v1"},{"key":"ref_134","doi-asserted-by":"crossref","unstructured":"Thomas, C., Maximilien, C., C\u00e9dric, G., and Franck, P. (2022). Model-checking ecological state-transition graphs. PLoS Comput. Biol., 18.","DOI":"10.1371\/journal.pcbi.1009657"},{"key":"ref_135","doi-asserted-by":"crossref","first-page":"749","DOI":"10.2307\/5394","article-title":"The Assembly of Ecological Communities: A Minimalist Approach","volume":"62","author":"Luh","year":"1993","journal-title":"J. Anim. Ecol."},{"key":"ref_136","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1111\/ele.13702","article-title":"Tractable models of ecological assembly","volume":"24","author":"Allesina","year":"2021","journal-title":"Ecol. Lett."},{"key":"ref_137","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.ecolmodel.2007.02.011","article-title":"Modelling coral reef habitat trajectories: Evaluation of an integrated timed automata and remote sensing approach","volume":"205","year":"2007","journal-title":"Ecol. Model."},{"key":"ref_138","doi-asserted-by":"crossref","unstructured":"Yachie-Kinoshita, A., Onishi, K., Ostblom, J., Langley, M.A., Posfai, E., Rossant, J., and Zandstra, P.W. (2018). Modeling signaling-dependent pluripotency with Boolean logic to predict cell fate transitions. Mol. Syst. Biol., 14.","DOI":"10.15252\/msb.20177952"},{"key":"ref_139","doi-asserted-by":"crossref","unstructured":"Papadimitriou, C.H., and Vishnoi, N.K. (2015). On the Computational Complexity of Limit Cycles in Dynamical Systems. arXiv.","DOI":"10.1145\/2840728.2840752"},{"key":"ref_140","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.agee.2017.10.009","article-title":"Rangeland vegetation diversity and transition pathways under indigenous pastoralist management regimes in southern Ethiopia","volume":"252","author":"Liao","year":"2018","journal-title":"Agric. Ecosyst. Environ."},{"key":"ref_141","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.catena.2017.02.009","article-title":"State-and-transition models in geomorphology","volume":"153","author":"Phillips","year":"2017","journal-title":"Catena"},{"key":"ref_142","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1890\/0012-9658(2003)084[1001:MTAOPC]2.0.CO;2","article-title":"Mapping the Assembly of Protist Communities in Microcosms","volume":"84","author":"Warren","year":"2003","journal-title":"Ecology"},{"key":"ref_143","doi-asserted-by":"crossref","unstructured":"Abou-Jaoud\u00e9, W., Monteiro, P.T., Naldi, A., Grandclaudon, M., Soumelis, V., Chaouiya, C., and Thieffry, D. (2015). Model Checking to Assess T-Helper Cell Plasticity. Front. Bioeng. Biotechnol., 2.","DOI":"10.3389\/fbioe.2014.00086"},{"key":"ref_144","doi-asserted-by":"crossref","unstructured":"Clarke, E.M., Henzinger, T.A., Veith, H., and Bloem, R. (2018). Handbook of Model Checking, Springer International Publishing.","DOI":"10.1007\/978-3-319-10575-8"},{"key":"ref_145","doi-asserted-by":"crossref","first-page":"025114","DOI":"10.1063\/1.4809783","article-title":"Dynamical modeling and analysis of large cellular regulatory networks","volume":"23","author":"Chaouiya","year":"2013","journal-title":"Chaos Interdiscip. J. Nonlinear Sci."},{"key":"ref_146","doi-asserted-by":"crossref","unstructured":"Diop, O., Tourniel, L., and Fromion, V. (2019, January 25\u201328). Summarizing complex asynchronous Boolean attractors, application to the analysis of a mammalian cell cycle model. Proceedings of the 2019 18th European Control Conference (ECC), Naples, Italy.","DOI":"10.23919\/ECC.2019.8795712"},{"key":"ref_147","doi-asserted-by":"crossref","first-page":"85","DOI":"10.3166\/isi.16.3.85-111","article-title":"EcoMata, un logiciel d\u2019aide \u00e0 la d\u00e9cision pour am\u00e9liorer la gestion des \u00e9cosyst\u00e8mes","volume":"16","author":"Zhao","year":"2011","journal-title":"Ing\u00e9nierie Syst\u00e8mes d\u2019Inform."},{"key":"ref_148","unstructured":"Largou\u00ebt, C. (2000). Aide \u00e0 l\u2019Interpr\u00e9tation d\u2019une S\u00e9quence d\u2019Images par la Mod\u00e9lisation de l\u2019\u00c9volution du Syst\u00e8me Observ\u00e9: Application \u00e0 la Reconnaissance de l\u2019Occupation du Sol. [Ph.D. Thesis, Universit\u00e9 de Rennes]."},{"key":"ref_149","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF00121013","article-title":"The use of vital attributes to predict successional changes in plant communities subject to recurrent disturbances","volume":"43","author":"Noble","year":"1980","journal-title":"Vegetatio"},{"key":"ref_150","doi-asserted-by":"crossref","first-page":"968","DOI":"10.1002\/lno.10713","article-title":"Insights into the ecology of the Black Sea through the qualitative loop analysis of the community structure","volume":"63","author":"Bodini","year":"2018","journal-title":"Limnol. Oceanogr."},{"key":"ref_151","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1177\/0048393119894897","article-title":"Model Pluralism","volume":"50","author":"Veit","year":"2020","journal-title":"Philos. Soc. Sci."},{"key":"ref_152","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1089\/10665270252833208","article-title":"Modeling and Simulation of Genetic Regulatory Systems: A Literature Review","volume":"9","year":"2002","journal-title":"J. Comput. Biol."},{"key":"ref_153","doi-asserted-by":"crossref","unstructured":"Bartocci, E., and Li\u00f3, P. (2016). Computational Modeling, Formal Analysis, and Tools for Systems Biology. PLoS Comput. Biol., 12.","DOI":"10.1371\/journal.pcbi.1004591"},{"key":"ref_154","doi-asserted-by":"crossref","first-page":"4256","DOI":"10.1038\/s41467-020-18112-5","article-title":"Reconciling qualitative, abstract, and scalable modeling of biological networks","volume":"11","author":"Chatain","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_155","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1140\/epjnbp\/s40366-016-0031-y","article-title":"A comparative study of qualitative and quantitative dynamic models of biological regulatory networks","volume":"4","author":"Saadatpour","year":"2016","journal-title":"EPJ Nonlinear Biomed. Phys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/11\/1526\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:19:06Z","timestamp":1760131146000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/11\/1526"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,8]]},"references-count":155,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["e25111526"],"URL":"https:\/\/doi.org\/10.3390\/e25111526","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,11,8]]}}}