Advertisement

Acta Applicandae Mathematicae

, Volume 125, Issue 1, pp 173–192 | Cite as

Mathematical Models in Landscape Ecology: Stability Analysis and Numerical Tests

  • Federica Gobattoni
  • Giuliana Lauro
  • Roberto Monaco
  • Raffaele Pelorosso
Article

Abstract

In the present paper a review of some mathematical models for the ecological evaluation of environmental systems is considered. Moreover a new model, capable to furnish more detailed information at the level of landscape units, is proposed. Numerical tests are then performed for a case study in the province of Viterbo (central Italy).

Keywords

Landscape ecology Mathematical models Stability analysis 

Mathematics Subject Classification (2000)

34D05 92F05 

References

  1. 1.
    Council of Europe: European Landscape Convention. Treaty Series no. 176, Florence, 2000 October 20th (2000) Google Scholar
  2. 2.
    Naveh, Z., Lieberman, A.: Landscape Ecology: Theory and Applications. Springer, New York (1984) Google Scholar
  3. 3.
    Turner, M.G., Gardnerl, R.H.: Quantitative Methods in Landscape Ecology. Springer, New York (1990) Google Scholar
  4. 4.
    Ingegnoli, V.: Landscape Ecology: A Widening Foundation. Springer, New York (2002) CrossRefGoogle Scholar
  5. 5.
    Fabbri, P.: Principi Ecologici per la Progettazione del Paesaggio. Franco Angeli Editore, Milano (2007) Google Scholar
  6. 6.
    Turner, M.G., Romme, V.H., Gardnerl, R.H., O’Neil, R.V., Kratz, T.K.: A revised concept of landscape equilibrium: disturbance and stability on scaled landscapes. Landsc. Ecol. 8(3), 213–227 (1993) CrossRefGoogle Scholar
  7. 7.
    Pelorosso, R., Della Chiesa, S., Tappeiner, U., Leone, A., Rocchini, D.: Stability analysis for defining management strategies in abandoned mountain landscapes of the Mediterranean basin. Landsc. Urban Plan. 103, 335–346 (2011) CrossRefGoogle Scholar
  8. 8.
    Petit, C., et al. (eds.): Landscape Analysis and Visualisation-Spatial Models for Natural and Resources an Planning. Springer, New York (2008) Google Scholar
  9. 9.
    Vermaat, J.E., Eppink, F., Van den Bergh, J.C., Barendregt, A., Van Belle, J.: Matching of scales in spatial economic and ecological analysis. Ecol. Econ. 52, 229–237 (2005) CrossRefGoogle Scholar
  10. 10.
    Fabbri, P.: Paesaggio, Pianificazione, Sostenibilità. Alinea, Firenze (2003) Google Scholar
  11. 11.
    Urban, D.L., Minor, E.S., Treml, E.A., Schick, R.S.: Graph models of habitat mosaics. Ecol. Lett. 12, 260–273 (2009) CrossRefGoogle Scholar
  12. 12.
    Lauro, G., Monaco, R., Servente, G.: A model for the evolution of bioenergy in an environmental system. In: Sammartino, M., Ruggeri, T. (eds.) Asymptotic Methods in Non-linear Wave Phenomena, pp. 96–106. World Scientific, Singapore (2007) CrossRefGoogle Scholar
  13. 13.
    Lauro, G., Lisi, M., Monaco, R.: A modeling framework for analysis of landscape stability and bifurcation phenomena. Rend. Sem. Mat. Univ. Politec. Torino 68(4), 399–413 (2010) MathSciNetGoogle Scholar
  14. 14.
    Finotto, F., Monaco, R., Servente, G.: Un modello per la valutazione della produzione e della diffusività di energia biologica in un sistema ambientale. Sci. Reg. 9(3), 61–84 (2010) Google Scholar
  15. 15.
    Gobattoni, F., Lauro, G., Leone, A., Monaco, R., Pelorosso, R.: A procedure for mathematical analysis of landscape evolution and equilibrium scenarios assessment. Landsc. Urban Plan. 103, 289–302 (2011) CrossRefGoogle Scholar
  16. 16.
    Monaco, R., Servente, G.: Introduzione ai Modelli Matematici nelle Scienze Territoriali, 2nd edn. Celid, Torino (2011) Google Scholar
  17. 17.
    Ingegnoli, V., Giglio, E.: Ecologia del Paesaggio. Manuale per conservare, gestire e pianificare l’ambiente. Esselibri, Napoli (2005) Google Scholar
  18. 18.
    Jordan, D.W., Smith, P.: Nonlinear Ordinary Differential Equations. Clarendon Press, Oxford (1977) zbMATHGoogle Scholar
  19. 19.
    Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions. Dover, New York (1980) Google Scholar
  20. 20.
    O’Neill, R.V., Johnson, A.R., King, A.W.: A hierarchical framework for the analysis of scale. Landsc. Ecol. 3, 193–205 (1989) CrossRefGoogle Scholar
  21. 21.
    Navino, D.: Valutazione della BTC mediante un modello dinamico relativo al grafo ecologico. Graduate Thesis in Urban Planning, Politecnico di Torino (2010) Google Scholar
  22. 22.
    Li, B.: Why is the holistic approach becoming so important in landscape ecology? Landsc. Urban Plan. 50, 27–41 (2000) CrossRefGoogle Scholar
  23. 23.
    Naveh, Z.: Ten major premises for a holistic conception of multifunctional landscapes. Landsc. Urban Plan. 57, 269–284 (2001) CrossRefGoogle Scholar
  24. 24.
    Finotto, F.: Landscape assessment: the ecological profile. In: Cassatella, C., Peano, A. (eds.) Landscape Indicators. Assessing and Monitoring Landscape Quality, pp. 47–75. Springer, Dordrecht (2011) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Federica Gobattoni
    • 1
  • Giuliana Lauro
    • 2
  • Roberto Monaco
    • 3
  • Raffaele Pelorosso
    • 1
  1. 1.Dipartimento DAFNEUniversità della TusciaViterboItaly
  2. 2.Dipartimento di Ingegneria CivileSeconda Università di NapoliAversaItaly
  3. 3.Dipartimento Interateneo di Scienze, Progetto e Politiche del TerritorioPolitecnico di TorinoTorinoItaly

Personalised recommendations