A procedure for mathematical analysis of landscape evolution and equilibrium scenarios assessment

Abstract The need for suitable planning strategies to reduce landscape fragmentation favoring energy and matter fluxes between ecosystems and preserving biodiversity, is a key issue of nature conservation and sustainable development. Human interventions may represent obstacles to such fluxes between ecosystems and they may affect landscape evolution and equilibrium conditions in terms of biodiversity reduction, accelerated erosion phenomena, hydrological instability and flood events that are well recognized consequences of anthropic impact. In this work an innovative procedure, called PANDORA, Procedure for mAthematical aNalysis of lanDscape evOlution and equilibRium scenarios Assessment, is presented to assess the effects of different planning strategies on final possible equilibrium states that are energetically stable. It provides a tool for the evaluation of landscape functionality and its resilience. PANDORA, linking together thermodynamic concepts, mathematical equilibrium, metabolic theory and landscape metrics, allows to model landscape evolution in time under the impact of external constraints and giving a unique response from it in terms of energy. An application of PANDORA is here proposed as a Decision Support System for choosing among possible urban planning strategies in a Mediterranean watershed of Central Italy. PANDORA model, allows to evaluate an analytical solution of landscape time-evolution problem and to study its stability depending on parameters obtained from GIS data, available, usually, by land managers. Such a model aims to provide a large applicability tool for “what if” scenarios evaluation in territorial planning as afforestation, deforestation, urban and road network development.

[1]  Tommaso Ruggeri,et al.  Asymptotic Methods in Nonlinear Wave Phenomena , 2007 .

[2]  Sven E. Jørgensen,et al.  Tentative Fourth Law of Thermodynamics, Applied to Description of Ecosystem Development , 1999 .

[3]  R. O'Neill,et al.  A revised concept of landscape equilibrium: Disturbance and stability on scaled landscapes , 1993, Landscape Ecology.

[4]  R. Forman.  Land Mosaics: The Ecology of Landscapes and Regions , 1995 .

[5]  Robert S Schick,et al.  Graph models of habitat mosaics. , 2009, Ecology letters.

[6]  E. D. Schneider,et al.  Complexity and thermodynamics: Towards a new ecology , 1994 .

[7]  A. J. Lotka.  Contribution to the Energetics of Evolution. , 1922, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Roberto Monaco,et al.  A mathematical procedure for the evolution of future landscape scenarios , 2010 .

[9]  James H. Brown,et al.  Toward a metabolic theory of ecology , 2004 .

[10]  A. Kleidon,et al.  Optimized stomatal conductance of vegetated land surfaces and its effects on simulated productivity and climate , 2004 .

[11]  Barbara Barletta,et al.  Space‐based formaldehyde measurements as constraints on volatile organic compound emissions in east and south Asia and implications for ozone , 2007 .

[12]  D. DeAngelis,et al.  Equilibrium and Nonequilibrium Concepts in Ecological Models , 1987 .

[13]  E. D. Schneider,et al.  Life as a manifestation of the second law of thermodynamics , 1994 .

[14]  Giorgia Servente,et al.  Un modello per la valutazione di energia biologica in un sistema ambientale , 2010 .

[15]  Christian Wissel,et al.  Babel, or the ecological stability discussions: an inventory and analysis of terminology and a guide for avoiding confusion , 1997, Oecologia.

[16]  Vivek Sharma,et al.  Natural process--natural selection. , 2007, Biophysical chemistry.

[17]  J. Vallino.  Ecosystem biogeochemistry considered as a distributed metabolic network ordered by maximum entropy production , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[18]  Veerle Van Eetvelde,et al.  Holistic aspects of suburban landscapes: visual image interpretation and landscape metrics , 2000 .

[19]  Axel Kleidon,et al.  Optimized stomatal conductance and the climate sensitivity to carbon dioxide , 2007 .

[20]  Santiago Saura,et al.  A new habitat availability index to integrate connectivity in landscape conservation planning : Comparison with existing indices and application to a case study , 2007 .

[21]  K. Michaelian,et al.  Thermodynamic stability of ecosystems. , 2004, Journal of theoretical biology.

[22]  Rafael L. Bras,et al.  A maximum hypothesis of transpiration , 2007 .

[23]  Vittorio Ingegnoli,et al.  Landscape Ecology: A Widening Foundation , 2002 .

[24]  Roberto Monaco,et al.  A Model for the Evolution of Bioenergy in an Environmental System , 2007 .

[25]  Z. Naveh.  Ten major premises for a holistic conception of multifunctional landscapes , 2001 .

[26]  Antonio Leone,et al.  Land cover and land use change in the Italian central Apennines: A comparison of assessment methods , 2009 .

[27]  Zev Naveh,et al.  Biocybernetic and thermodynamic perspectives of landscape functions and land use patterns , 1987, Landscape Ecology.

[28]  Brian D. Fath,et al.  Application of thermodynamic principles in ecology , 2004 .

[29]  George L. W. Perry,et al.  Landscapes, space and equilibrium: shifting viewpoints , 2002 .

[30]  Koyel Ghosh,et al.  Maximum-entropy principle: ecological organization and evolution , 2010, Journal of biological physics.

[31]  J. Wahr,et al.  Elastic uplift in southeast Greenland due to rapid ice mass loss , 2007 .

[32]  James D. Murray.  Mathematical Biology: I. An Introduction , 2007 .

[33]  Cr. Paltineanu,et al.  Relationships between the De Martonne aridity index and water requirements of some representative crops: A case study from Romania** , 2007 .

[34]  Arto Annila,et al.  Ecological succession as an energy dispersal process , 2010, Biosyst..

[35]  Duccio Rocchini,et al.  Landscape change and the dynamics of open formations in a natural reserve , 2006 .

[36]  Bai-Lian Li,et al.  Why is the holistic approach becoming so important in landscape ecology , 2000 .

[37]  Richard T. T. Forman,et al.  Landscape graphs: Ecological modeling with graph theory to detect configurations common to diverse landscapes , 1993, Landscape Ecology.

[38]  Vittorio Ingegnoli,et al.  An innovative contribution of landscape ecology to vegetation science , 2005 .

[39]  Michael K. Tippett,et al.  Measuring the potential utility of seasonal climate predictions , 2004 .

[40]  Yadvinder Malhi,et al.  Maximum entropy production in environmental and ecological systems , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[41]  D. Mishra,et al.  Change detection and landscape metrics for inferring anthropogenic processes in the greater EFMO area , 2004 .

[42]  C. H. Waddington,et al.  Evolution and Consciousness: Human Systems in Transition , 1976 .

[43]  Nathaniel A. Brunsell,et al.  Quantifying the thermodynamic entropy budget of the land surface: is this useful? , 2011 .

[44]  T. Saaty.  How to Make a Decision: The Analytic Hierarchy Process , 1990 .

[45]  Arto Annila,et al.  Physical foundations of evolutionary theory , 2010 .

[46]  Jochen A. G. Jaeger,et al.  Suitability criteria for measures of urban sprawl , 2010 .

[47]  Zev Naveh,et al.  What is holistic landscape ecology? A conceptual introduction , 2000 .

[48]  J. Vallino.  Differences and implications in biogeochemistry from maximizing entropy production locally versus globally , 2011 .