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Landscape Stability, Instability and Civilization Collapse

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Modelling Landscape Dynamics

Abstract

Aside of the mathematical notions of stability which is briefly introduced here, the landscape-ecological approach to landscape stability is distinct from the geomorphological: the two are different, yet complementary to one another. Their main difference consists in that, while the geomorphological perspective focuses on hillslope processes and climate-soil-vegetation systems, the ecological approach focuses on ecosystem dynamics. Using as example the collapse of the Mycenean civilization in late Helladic IIIB, it can be suggested that long-term landscape instability may be associated with the collapse of a civilization. It is therefore essential to monitor and assess landscape stability over long time intervals. Yet, it is shown here that the mathematical and the ecological approaches to landscape stability may not always converge: although a system of ordinary differential equations describing landscape dynamics may be stable, the landscape changes may be “unstable” in the ecological sense.

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References

  • Aimers, J., & Hodell, D. (2011). “Societal collapse”: Drought and the Maya. Nature, 479(7371), 44–45.

    Article  Google Scholar 

  • Arbesman, S. (2011). The life-spans of empires. Historical Methods: A Journal of Quantitative and Interdisciplinary History, 44(3), 127–129.

    Article  Google Scholar 

  • Arnold, V., Varchenko, A., & Goussein-Zade, S. (1986). Singularites des applications Differentiables. Mir.

    Google Scholar 

  • Austin, P. M., & Cook, B. G. (1974). Ecosystem stability. A result from an abstract simulation. Journal of Theoretical Biology, 45, 435–458.

    Article  Google Scholar 

  • Balcer, J. M. (1974). The mycenean dam at Tiryns. American Journal of Archaeology, 78, 141–149.

    Article  Google Scholar 

  • Bel, G., Hagberg, A., & Meron, E. (2012). Gradual regime shifts in spatially extended ecosystems. Theoretical Ecology, 5(4), 591–604.

    Article  Google Scholar 

  • Bintliff, J. L. (1977). Natural environment and human settlement in prehistoric Greece. Oxford British Archaeology Supplement Series, Part I. 28 (I).

    Google Scholar 

  • Bologna, M., Chandia, K., & Flores, J. C. (2016). A non-linear mathematical model for a three-species ecosystem: Hippos in Lake Edward. Journal of Theoretical Biology, 389, 83–87.

    Article  Google Scholar 

  • Brunsden, D., & Thornes, J. (1977). Geomorphology and time. Methuen.

    Google Scholar 

  • Bryson, R. A., Lamb, H. H., & Donley, D. L. (1974). Drought and the decline of the Mycene. Antiquity, 48, 46–50.

    Article  Google Scholar 

  • Butzer, K. W. (2012). Collapse, environment, and society. Proceedings of the National Academy of Sciences, 6(109), 10, 3632–3639.

    Google Scholar 

  • Carpenter, R. (1966). Discontinuity in Greek civilizations. Cambridge University Press.

    Google Scholar 

  • Chorley, R. J., & Kennedy, B. A. (1971). Physical geography-a systems approach. Prentice Hall.

    Google Scholar 

  • Coombes, P., & Barber, K. (2005). Environmental determinism in Holocene research: Causality or coincidence? Area, 37(3), 303–311.

    Article  Google Scholar 

  • Das, K., Shiva Reddy, K., Srinivas, M. N., & Gazi, N. H. (2014). Chaotic dynamics of a three species prey-predator competition model with noise in ecology. Applied Mathematics and Computation, 231, 117–133.

    Article  Google Scholar 

  • Das, K. P., Chatterjee, S., & Jchattopadhyay, J. (2009). Disease in prey population and body size of intermediate predator reduce the prevalence of chaos-conclusion drawn from hastings-powell model. Ecological Complexity, 6, 363–374.

    Article  Google Scholar 

  • Davidson, D. A. (1980). Erosion in Greece during the first and second millenia b.C. In R. Cullingford & D.A. Davidson (eds) Timescales in Geomorphology (pp. 143–158). Wiley.

    Google Scholar 

  • Davis, W. N. (1924). Die Erklarende Beschreibung der Landformen. Teubner.

    Google Scholar 

  • De Angelis, D. L. (1975). Global asymptotic stability criteria for models of density-dependent population growth. Journal of Theoretical Biology, 50(1), 35–43.

    Article  Google Scholar 

  • Demitrack, A. (1986). Late quaternary geologic history of the larissa plain (Thessaly, Greece)- tectonic, climatic and human impact on the landscape. Ph.D. dissertation, Stanford University.

    Google Scholar 

  • Diamond, J. (2005). Collapse: How societies choose to fail or succeed. Penguin.

    Google Scholar 

  • Ehrlich, P. R., & Ehrlich, A. H. (2013). Can a collapse of global civilization be avoided? Proceedings of the Royal Society B, 280(2012), 2845.

    Google Scholar 

  • Findlay, S., & Zheng, L. (1993). Structural correlates of Stability and resilience in strong hierarchies. Bulletin of Mathematical Biology, 55(3), 543–560.

    Article  Google Scholar 

  • Gakkhar, S., Priyadashi, A., & Banerjee, S. (2012). Complex behaviour in four species food-web model. Journal of Biological Dynamics, 6(2), 440–556.

    Article  Google Scholar 

  • Gardner, M. R., & Ashby, W. R. (1970). Connectance of large dynamic (cybernetic) systems: critical values for stability. Nature, 228(5273), 784–784.

    Google Scholar 

  • Gibbon, E. (1994). The history of the decline and fall of the Roman Empire. Penguin.

    Google Scholar 

  • Goh, B. S. (1987). Global stability in many-species ecosystems. American Naturalist, 111(977), 135–143.

    Article  Google Scholar 

  • Gomes, A. A., Manica, E., & Varriale, M. C. (2008). Applications of chaos control techniques to a three-species food chain. Chaos Solitons and Fractals, 35, 432–441.

    Article  Google Scholar 

  • Gounand, I., Mouquet, N., Canard, E., Guichard, F., Hauzy, C., & Gravel, D. (2014). The paradox of enrichment in metaecosystems. American Naturalist, 184, 752–763.

    Article  Google Scholar 

  • Grant, M. (1990). The fall of the Roman empire. Weidenfeld and Nicolson.

    Google Scholar 

  • Grant, M. (1999). The collapse and recovery of the Roman empire. Routledge.

    Google Scholar 

  • Gravel, D., Guichard, F., Loreau, M., & Mouquet, N. (2010). Source and sink dynamics in meta ecosystems. Ecology, 91, 2172–2184.

    Article  Google Scholar 

  • Hack, J. T. (1960). Interpretation of erosional topography in humid temperate regions. American Journal of Science, 258(A), 80–97.

    Google Scholar 

  • Hack, J. T. (1965). Geomorphology of the Shenandoah valley, Virginia and West Virginia, and origin of the residual ore deposits. U.S. Geological Survey Professional Paper 484.

    Google Scholar 

  • Hack, J. T. (1966). Interpretation of the Cumberland escarpment and highland rim, south-central Tennessee and north-east Alabama. U.S. Geological Survey Professional Paper 524–526, 16.

    Google Scholar 

  • Hastings, A., & Powell, T. (1991). Chaos in a three-species food chain. Ecology, 2(3), 896–903.

    Article  Google Scholar 

  • Haug, G. H., Gunther, D., Peterson, L. C., Sigman, D. M., Hughen, K. A., & Aeschlimann, B. (2003). Climate and the collapse of Maya civilization. Science, 299(5613), 1731.

    Article  Google Scholar 

  • Iooss, G., & Joseph, D. (1990). Elementary stability and bifurcation theory. Springer.

    Book  Google Scholar 

  • Jacobsen, T. (1969). Excavations at Porto-Heli and vicinity. report 1-The Franchthi cave. Hesperia, 38, 343–381.

    Article  Google Scholar 

  • Jacobsen, T. (1973). Excavations at the Franchthi cave. part 1 and 2, Hesperia, 42, 45–88 and 253–283.

    Google Scholar 

  • Khmaladze, E., Brownrigg, R., & Haywood, J. (2007). Brittle power: On Roman emperors and exponential lengths of rule. Statistics & Probability Letters, 77, 1248–1257.

    Article  Google Scholar 

  • Kilian, K. (1978). Ausgrabungen in Tiryns—1976. Archaeologisches Anzeiger, 4, 449–470.

    Google Scholar 

  • Klebanoff, A., & Hastings, A. (1994). Chaos in three species food chains. Journal of Mathematical Biology, 32, 427–451.

    Article  Google Scholar 

  • Kutzbach, J. E. (1981). Monsoon climate of the early Holocene—Climatic experiment with the Earth’s orbital parameters for 9000 years ago. Science, 214, 59–61.

    Article  Google Scholar 

  • Lefschetz, S. (1977). Differential equations-geometric theory. Dover.

    Google Scholar 

  • Leopold, L., & Langbein, L. (1962). The concept of entropy in landscape evolution. U.S. Geological Survey Professional Paper 500A, 3–20.

    Google Scholar 

  • Leroux, S. J., & Loreau, M. (2012). Dynamics of reciprocal pulsed subsidies in local and meta. 569 Ecosystems, 15, 48–59.

    Google Scholar 

  • Lin, J., & Kahn, P. B. (1977). Qualitative behaviour of predator-prey communities. Journal of Theoretical Biology, 65, 101–132.

    Article  Google Scholar 

  • Loehle, C. (1989a). Catastrophe theory in ecology. Acritical review and an example of the butterfly catastrophe. Ecological Modelling, 49, 125–152.

    Article  Google Scholar 

  • Loehle, C. (1989b). Forest-level analysis of stability under exploitation. Depensation responses and catastrophe theory. Vegetatio, 79, 109–115.

    Article  Google Scholar 

  • Loreau, M., Mouquet, N., & Holt, R. D. (2003). Meta-ecosystems: A theoretical framework for a spatial ecosystem ecology. Ecology Letters, 6(8), 673–679.

    Article  Google Scholar 

  • Lowe, J. W. G. (1985). The dynamics of apocalypse: A systems simulation of the classic Maya collapse. University of New Mexico Press.

    Google Scholar 

  • Marleau, J. N., Guichard, F., & Loreau, M. (2014). Meta-ecosystem dynamics and functioning on finite spatial networks. Proceedings of the Royal Society B: Biological Sciences, 281(1777), 20132094.

    Article  Google Scholar 

  • May, R. M., & Leonard, W. J. (1975). Nonlinear aspects of competition between three species. SIAM Journal of Applied Mathematics, 29, 243–253.

    Article  Google Scholar 

  • May, R. (1972). Will a large complex system be stable? Nature, 238, 413–414.

    Article  Google Scholar 

  • May, R. (1973). Stability and complexity in model ecosystems. Princeton University Press.

    Google Scholar 

  • McCann, K., & Hastings, A. (1997). Re-evaluating the omnivory-stability relationship in food webs. Proceedings of the London Royal Society, B, 264, 1249–1254.

    Article  Google Scholar 

  • McCann, K. S., Cazelles, K., MacDougall, A. S., Fussmann, G. F., Bieg, C., & Cristescu, M. (2021). Landscape modification and nutrient-driven instability at a distance. Ecology Letters, 600(24), 398–414.

    Article  Google Scholar 

  • McMurthie, R. F. (1975). Determinants of stability of large, randomly-connected systems. Journal of Theoretical Biology, 40, 1–11.

    Article  Google Scholar 

  • Ott, E., Grebogi, C., & Yorke, A. (1990). Controlling chaos. Physics Review Letters, 64, 1196–1199.

    Google Scholar 

  • Paine, A. D. M. (1985). Ergodic reasoning in Geomorphology—Time for a review of the term. Progress in Physical Geography, 9, 1–15.

    Article  Google Scholar 

  • Papadimitriou, F. (1998). Landscape Sustainability. In P. Mairota, J. Thornes, & N. Geeson (eds.), Atlas of mediterranean environments in Europe. (pp. 72–74). Wiley.

    Google Scholar 

  • Papadimitriou, F. (2009). Modelling spatial landscape complexity using the Levenshtein algorithm. Ecological Informatics, 4, 48–55.

    Article  Google Scholar 

  • Papadimitriou, F. (2010a). Mathematical modelling of spatial-ecological complex systems: An evaluation. Geography, Environment, Sustainability, 1(3), 67–80.

    Article  Google Scholar 

  • Papadimitriou, F. (2010b). Conceptual modelling of landscape complexity. Landscape Research, 35(5), 563–570.

    Article  Google Scholar 

  • Papadimitriou, F. (2012a). The algorithmic complexity of landscapes. Landscape Research, 37(5), 599–611.

    Article  Google Scholar 

  • Papadimitriou, F. (2012b). Modelling landscape complexity for land use management in Rio de Janeiro, Brazil. Land Use Policy, 29(4), 855–861.

    Article  Google Scholar 

  • Papadimitriou, F. (2012c). Artificial intelligence in modelling the complexity of mediterranean landscape transformations. Computers and Electronics in Agriculture, 81, 87–96.

    Article  Google Scholar 

  • Papadimitriou, F. (2013). Mathematical modelling of land use and landscape complexity with ultrametric topology. Journal of Land Use Science, 8(2), 234–254.

    Article  Google Scholar 

  • Papadimitriou, F. (2020a). Modelling and visualization of landscape complexity with braid topology. In D.Edler, C.Jenal & O. Kühne (Eds.), Modern approaches to the visualization of landscapes (pp. 79–101). Springer VS.

    Google Scholar 

  • Papadimitriou, F. (2020b). Spatial complexity, visual complexity and aesthetics. In F. Papadimitriou (Ed.), Spatial complexity: Theory, mathematical methods and applications (pp. 243–261). Springer.

    Google Scholar 

  • Papadimitriou, F. (2020c). Spatial complexity: Theory, mathematical methods and applications. Springer Nature.

    Google Scholar 

  • Papadimitriou, F. (2022a). Emergence, sustainability and cyber-physical landscapes. In F. Papadimitriou (Ed.), Spatial entropy and landscape analysis (pp. 123–139). Springer VS.

    Google Scholar 

  • Papadimitriou, F. (2022b). Spatial negentropy and social self-organization in simulated landscapes. In F. Papadimitriou (Ed.), Spatial entropy and landscape analysis (pp. 75–86). Springer VS.

    Google Scholar 

  • Papadimitriou, F. (2022c). Spatial entropy of landscapes simulated with artificial life and swarm intelligence. In F. Papadimitriou (Ed.), Spatial entropy and landscape analysis (pp. 57–73). Springer VS.

    Google Scholar 

  • Papadimitriou, F. (2022d). Spatial entropy and landscape analysis. Springer VS.

    Book  Google Scholar 

  • Parshad, R. D., Kumari, N., Kasimov, A. R., & Abderrahmane, H. A. (2014). Turing patterns and long-time behavior in a three-species food-chain model. Mathematical Biosciences, 254, 83–102.

    Article  Google Scholar 

  • Patten, B. C. (1975). Ecosystem linearization: An evolutionary design problem. The American Naturalist, 109(969), 529–539.

    Article  Google Scholar 

  • Penck, W. (1924). Die geomorphologische Analyse. J. Engelhorns Nachfolger.

    Google Scholar 

  • Rai, V., & Sreenivasan, R. (1993). Period-doubling bifurcations leading to chaos in a model food chain. Ecological Modelling, 69(1–2), 63–77.

    Article  Google Scholar 

  • Redman, C. L. (1999). Human impact on ancient environments. University of Arizona Press.

    Google Scholar 

  • Reuveny, R., & Decker, C. S. (2000). Easter Island: Historical anecdote or warning for the future? Ecological Economics, 350(2), 271–287.

    Article  Google Scholar 

  • Rotenberg, M. (1975). Equilibrium and stability in populations whose interactions are age-specific. Journal of Theoretical Biology, 54, 207–224.

    Article  Google Scholar 

  • Rutter, J. B. (1983). Some observations on the cyclades in the later third and early second millenia. American Journal of Archeology, 87, 69–78.

    Article  Google Scholar 

  • Scheidegger, A. E. (1991). Theoretical geomorphology. Springer.

    Book  Google Scholar 

  • Schumm, S. A. (1963). Disparity between present rates of denudation and orogeny. U.S. Geological Survey Professional Paper, 454, 13.

    Google Scholar 

  • Schumm, S. A. (1965). Quaternary palaeohydrology. In H. E. Whright & D. G. Frey (Eds.), The quaternary of the United States (pp. 783–794). Princeton University Press.

    Google Scholar 

  • Schumm, S. A. (1979). Geomorphic thresholds—The concepts and its applications. Transactions of the Institute of British Geographers, 4, 485–515.

    Article  Google Scholar 

  • Schuster, P., Sigmund, K., Hofbauer, J., & Wolff, R. (1981). Self-regulation of behaviour in animal societies. Biological Cybernetics, 40, 1–25.

    Article  Google Scholar 

  • Shiao, L., & Wu, Y. (1977). The stability of ecosystems—A finite time approach. Journal of Theoretical Biology, 66, 345–359.

    Article  Google Scholar 

  • Taagepera, R. (1978). Size and duration of empires: Growth-decline curves, 3000 to 600 B.C. Social Science Research, 7, 180–196.

    Article  Google Scholar 

  • Tainter, J. A. (1988). The collapse of complex societies. Cambridge University Press.

    Google Scholar 

  • Thornes, J. (1980). Structural instability and ephemeral channel behaviour. Zeitschrieft Fur Geomorphologie, n.f. Suppl-Bd, 36, 233–244.

    Google Scholar 

  • Turchin, P. (2003). Historical dynamics: Why states rise and fall. Princeton University Press.

    Google Scholar 

  • Upadhyay, R. K., & Rai, V. (1997). Why chaos is rarely observed in natural populations? Chaos, Solitons and Fractals, 8(12), 1933–1939.

    Article  Google Scholar 

  • Upadhyay, R. K., Iyengar, S. R. K., & Rai, V. (1998). Chaos: An ecological reality? International Journal of Bifurcations and Chaos, 8, 1325–1333.

    Article  Google Scholar 

  • Ur, J. (2010a). Cycles of civilization in northern mesopotamia, 4400–2000 BC. Journal of Archaeological Research, 18(4), 387–431.

    Article  Google Scholar 

  • Ur, J. (2010b). Urbanism and cultural landscapes in Northeastern Syria: The Tell Hamoukar Survey 1999–2001. Oriental Institute Publications 137. Oriental Institute of the University of Chicago.

    Google Scholar 

  • Van Andel, T. H., Runnels, C. N., & Pope, K. O. (1986). Five thousands[sic] years of land use and abuse in the southern Argolid, Greece. Hesperia, 55(1), 103–128.

    Article  Google Scholar 

  • Verhulst, F. (1990). Non-linear differential equations and dynamical systems. Springer.

    Book  Google Scholar 

  • Vita-Finzi, C. (1969). The mediterranean valleys-geological changes in historical times. Cambridge University Press.

    Google Scholar 

  • Vogl, R. J. (1982). Chaparral succession. In: Proceedings of the symposium on the dynamics and management of mediterranean—Type ecosystems, June 22–26, 1981, San Diego. 81–85.

    Google Scholar 

  • Von-Der-Muhll, G. (2007). Ecology, culture, and rationality: Toynbee and diamond on the growth and collapse of civilizations. Comparative Civilizations Review, 57(57), 5.

    Google Scholar 

  • Weiss, H., & Courty, M. A. (1993). The genesis and collapse of the Akkadian Empire: The accidental refraction of historical law. In M. Liverani (ed.), Akkad, the first world empire (pp. 131–155). Springer.

    Google Scholar 

  • Weiss, H., Courty, M. A., Wellerstrom, W., Guichard, F., Senior, L., Meadow, R., & Currow, A. (1993). The genesis and collapse of third millennium north Mesopotamian civilization. Science, 261(5124), 995–1004.

    Article  Google Scholar 

  • Wenxiang, W., & Tungsheng, L. (2004). Possible role of the “Holocene Event 3” on the collapse of Neolithic cultures around the central plain of China. Quaternary International, 117(1), 153–166.

    Article  Google Scholar 

  • Wiener, M. H. (2014). The interaction of climate change and agency in the collapse of civilizations ca. 2300–2000 BC. Tree-Ring Research, 70(3), S1–S16.

    Google Scholar 

  • Willey, G. R. (1974). The classic Maya hiatus: A ‘rehearsal’ for the collapse? In N. Hammond (ed.), Mesoamerican archeology: New approaches (pp. 417–30). Duckworth.

    Google Scholar 

  • Willey, G. R., & Shimkin, D. B. (1973). The Maya collapse: A summary view. In T. P. Culbert (ed.), The classic Maya collapse (pp. 457–501). University of New Mexico Press.

    Google Scholar 

  • Write, H. E. (1968). Climatic change in Mycenean Greece. Antiquity, XLII, 123–127.

    Google Scholar 

  • Yasuda, Y. (2013). Decline of the Yangtze River civilization. In Y. Yasuda (ed.), Water civilization: From Yangtze to Khmer civilizations (pp. 47–63). Advances in Asian Human–Environment Research. Springer.

    Google Scholar 

  • Yasur-Landau, A. (2010). The philistines and aegean migration at the end of the late Bronze Age. Cambridge University Press.

    Book  Google Scholar 

  • Yoffee, N., & Cowgill, G. (Eds.). (1988). The collapse of ancient states and civilizations. University of New Mexico Press.

    Google Scholar 

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Papadimitriou, F. (2023). Landscape Stability, Instability and Civilization Collapse. In: Modelling Landscape Dynamics. RaumFragen: Stadt – Region – Landschaft. Springer VS, Wiesbaden. https://doi.org/10.1007/978-3-658-42496-1_3

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