Skip to main content
SpringerLink
Log in

A review on the use of entropy in landscape ecology: heterogeneity, unpredictability, scale dependence and their links with thermodynamics

  • Review Article
  • Published:
Landscape Ecology Aims and scope Submit manuscript

Abstract

The identification of a universal law that can predict the spatiotemporal structure of any entity at any scale has long been pursued. Thermodynamics have targeted this goal, and the concept of entropy has been widely applied for various disciplines and purposes, including landscape ecology. Within this discipline, however, the uses of the entropy concept and its underlying assumptions are various and are seldom described explicitly. In addition, the link between this concept and thermodynamics is unclear. The aim of this paper is to review the various interpretations and applications of entropy in landscape ecology and to sort them into clearly defined categories. First, a retrospective study of the concept genesis from thermodynamics to landscape ecology was conducted. Then, 50 landscape ecology papers that use or discuss entropy were surveyed and classified by keywords, variables and metrics identified as related to entropy. In particular, the thermodynamic component of entropy in landscape ecology and its various interpretations related to landscape structure and dynamics were considered. From the survey results, three major definitions (i.e., spatial heterogeneity, the unpredictability of pattern dynamics and pattern scale dependence) associated with the entropy concept in landscape ecology were identified. The thermodynamic interpretations of these definitions are based on different theories. The thermodynamic interpretation of spatial heterogeneity is not considered relevant. The thermodynamic interpretation related to scale dependence is also questioned by complexity theory. Only unpredictability can be thermodynamically relevant if appropriate measurements are used to test it.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

The marked references indicate the 50 papers used for the survey. *: Spatial heterogeneity, #: unpredictability, °: scale dependence, ‘:thermodynamic relationship

  • * Antrop M (1998) Landscape change: Plan or chaos? Landsc Urban Plann 41:7

  • * Antrop M (2004) From holistic landscape synthesis to transdisciplinary landscape management. Frontis Workshop, 2004/06/01/6 2004. Springer, The Netherlands

  • * Antrop M, Van Eetvelde V (2000) Holistic aspects of suburban landscapes: visual image interpretation and landscape metrics. Landsc Urban Plan 50:16

  • Baas ACW (2002) Chaos, fractals and self-organization in coastal geomorphology: simulating dune landscapes in vegetated environments. Geomorphology 48:309–328

    Article  Google Scholar 

  • Baudry J (1991) Ecological consequences of grazing extensification and land abandonment: role of interactions between environment, society and techniques. Options Mediterraneennes. Serie A: Seminaires Mediterraneens (CIHEAM)

  • Benatti F (2003) Classical and quantum entropies: dynamics and information. In: Greven A, Keller G, Warnecke G, Kellerare G (eds) Entropy. Princeton University Press, Princeton, pp 279–298

    Google Scholar 

  • * Benson MJ, Mackenzie MD (1995) Effects of sensor spatial resolution on landscape structure parameters. Landscape Ecol 10:8

  • Benson H (1996) Entropy and the second law of thermodynamics. University Physics, Wiley, New York, pp 417–439

    Google Scholar 

  • ‘* Bogaert J, Farina A, Ceulemans R (2005) Entropy increase of fragmented habitats: a sign of human impact? Ecol Indic 5:6

  • *# Bolliger J, Lischke H, Green DG (2005) Simulating the spatial and temporal dynamics of landscapes using generic and complex models. Ecol Complex 2:107–116

  • Cale P, Hobbs RJ (1994) Landscape heterogeneity indices: problems of scale and applicability, with particular reference to animal habitat description. Pac Conserv Biol 1:183–193

  • * Carranza ML, Acosta A, Ricotta C (2007) Analyzing landscape diversity in time: the use of Renyi’s generalized entropy function. Ecol Indic 7:6

  • Chakraborty A, Li BL (2011) Contribution of biodiversity to ecosystem functioning: a non-equilibrium thermodynamic perspective. J Arid Land 3:71–74

    Article  Google Scholar 

  • ‘# Corona P (1993) Applying biodiversity concepts to plantation forestry in northern Mediterranean landscapes. Landsc Urban Plan 24:23–31

  • Cushman SA, Littell J, Mcgarigal K (2010) The problem of ecological scaling in spatially complex, nonequilibrium ecological systems. Spatial Complexity, Informatics, and Wildlife Conservation. Springer, New York, pp 43–63

  • Cushman SA, Mcgarigal K (2003) Landscape-level patterns of avian diversity in the Oregon Coast Range. Ecol Monogr 73:259–281

    Article  Google Scholar 

  • Depondt P (2002) L’entropie et tout ça. Le roman de la thermodynamique, Paris, Cassini

    Google Scholar 

  • ‘# Dorney RS, Hoffman DW (1979) Development of landscape planning concepts and management strategies for an urbanizing agricultural region. Landsc Plan 6:151–177

  • * Ernoult A, Bureau F, Poudevigne A (2003) Patterns of organisation in changing landscapes: implications for the management of biodiversity. Landscape Ecol 18:13

  • Fahrig L, Baudry J, Brotons L (2011) Functional landscape heterogeneity and animal biodiversity in agricultural landscapes. Ecol Lett 14:101–112

    Article  PubMed  Google Scholar 

  • Fahrig L, Nuttle WK (2005) Population ecology in spatially heterogeneous environments. In: Lovett GM, Turner MG, Jones CG, Weathers KC (eds) Ecosystem function in heterogeneous landscapes. Springer, New York, pp 95–118

    Chapter  Google Scholar 

  • Farina A (ed) (2000) Methods in landscape ecology. In: Principles and methods in landscape ecology. Kluwer Academic, Dordrecht, p 65

  • ‘* Forman RTT (1995) Land mosaics: the ecology of landscapes and regions. Cambridge University Press, Cambridge, MA

  • ‘* Forman RTT, Godron M (1986a) Heterogeneity and typology. In: Forman RTT, Godron M (eds) Landscape ecology. Wiley, New York, pp 463–493

  • Forman RTT, Godron M (1986) Overall structure. In: Forman RTT, Godron M (eds) Landscape ecology. Wiley, New York, pp 191–225

    Google Scholar 

  • * Gaucherel C (2007) Multiscale heterogeneity map and associated scaling profile for landscape analysis. Landsc Urban Plan 82:8

  • Gini C (1921) Measurement of inequality of incomes. Econ J 31:124–126

    Article  Google Scholar 

  • ‘# Gobattoni F, Pelorosso R, Lauro G, Leone A, Monaco R (2011) A procedure for mathematical analysis of landscape evolution and equilibrium scenarios assessment. Landsc Urban Plan 103:289–302

  • Green DG, Sadedin S (2005) Interactions matter—complexity in landscapes and ecosystems. Ecol Complex 2:117–130

    Article  Google Scholar 

  • Halley J, Hartley S, Kallimanis A, Kunin W, Lennon J, Sgardelis S (2004) Uses and abuses of fractal methodology in ecology. Ecol Lett 7:254–271

    Article  Google Scholar 

  • Harte J (2011) Entropy, information and the concept of maximum entropy. In: Harte J (ed) Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press, Oxford, pp 117–129

    Chapter  Google Scholar 

  • Hartonen T, Annila A (2012) Natural networks as thermodynamic systems. Complexity 18:53–62

    Article  Google Scholar 

  • ‘# Ingegnoli V (2011) Non-equilibrium thermodynamics, landscape ecology and vegetation science. In: Moreno-Piraján JC (ed) Thermodynamics—systems in equilibrium and non-equilibrium. InTech, Rijeka, pp 139–172. http://www.intechopen.com/books/thermodynamics-systems-in-equilibrium-and-non-equilibrium/non-equilibrium-thermodynamics-landscape-ecology-and-vegetation-science

  • * Jaeger JAG (2000) Landscape division, splitting index, and effective mesh size: new measures of landscape fragmentation. Landscape Ecol 15:115–130

  • ° Johnson GD, Myers WL, Patil GP, Taillie C (1999) Multiresolution fragmentation profiles for assessing hierarchically structured landscape patterns. Ecol Model 116:9

  • ° Johnson GD, Myers WL, Patil GP, Taillie C (2001) Characterizing watershed-delineated landscapes in Pennsylvania using conditional entropy profiles. Landscape Ecol 16:597–610

  • °* Johnson GD, Patil GP (2007) Methods for quantitative characterization of landscape pattern. Landscape pattern analysis for assessing ecosystem. Springer, Berlin, pp 13–22

  • * Joshi PK, Lele N, Agarwal SP (2006) Entropy as an indicator of fragmented landscape. Curr Sci 91:3

  • Jost L (2006) Entropy and diversity. Oikos 113:363–375

    Article  Google Scholar 

  • Kenkel N, Walker D (1996) Fractals in the biological sciences. Coenoses 11:77–100

    Google Scholar 

  • * Kilgore MA, Snyder SA, Block-Torgerson K, Taff SJ (2013) Challenges in characterizing a parcelized forest landscape: Why metric, scale, threshold, and definitions matter. Landsc Urban Plan 110:36–47

  • Krummel J, Gardner R, Sugihara G, O’neill R and Coleman P (1987) Landscape patterns in a disturbed environment. Oikos 321–324

  • ‘# Lee BJ (1982) An ecological comparison of the McHarg method with other planning initiatives in the Great Lakes Basin. Landsc Plan 9:147–169

  • Legendre P, Legendre L (2012) Numerical ecology. Elsevier Science, Amsterdam

    Google Scholar 

  • * Leibocivi DG (2009) Defining spatial entropy from multivariate distributions of co-occurrences. In: Hornsby KS, Claramunt C, Denis M, Ligozat G (eds) 9th international conference on spatial information theory, 2009 Aber Wrac’h. Springer, Berlin

  • ‘# Leuven RSEW, Poudevigne I (2002) Riverine landscape dynamics and ecological risk assessment. Freshw Biol 47:845–865

  • Levin SA (1992) The problem of pattern and scale in ecology: the Robert H. MacArthur award lecture. Ecology 73:1943–1967

    Article  Google Scholar 

  • Li B-L (2002) A theoretical framework of ecological phase transitions for characterizing tree-grass dynamics. Acta Biotheor 50:141–154

    Article  PubMed  Google Scholar 

  • Li B-L (2000) Fractal geometry applications in description and analysis of patch patterns and patch dynamics. Ecol Model 132:33–50

    Article  Google Scholar 

  • ‘# Li B-L (2000b) Why is the holistic approach becoming so important in landscape ecology? Landsc Urban Plan 50:27–41

  • * Li H, Reynolds J (1993) A new contagion index to quantify spatial patterns of landscapes. Landscape Ecol 8:155–162

  • Li J, Zhang J, Ge W, Liu X (2004) Multi-scale methodology for complex systems. Chem Eng Sci 59:1687–1700

    Article  CAS  Google Scholar 

  • Macarthur R (1955) Fluctuations of animal populations and a measure of community stability. Ecology 36:533–536

    Article  Google Scholar 

  • Maldague M (2004) Le deuxième principe de la thermodynamique et la gestion de la biosphère. Application à l’environnement et au développement. In: Eraift MM, Unesco (eds) Traité de gestion de l’environnement tropical. Les Classiques des Sciences Sociales, Saguenay, pp 10.1–10.21

    Google Scholar 

  • Mandelbrot BB (1983) The fractal geometry of nature. Henry Holt and Company

  • # Mander Ü, Jongman RHG (1998) Human impact on rural landscapes in central and northern Europe. Landsc Urban Plan 41:149–153

  • Margalef R (1958) Information theory in ecology. Gen Syst 3:36–72

    Google Scholar 

  • Maroney O (2009) Information processing and thermodynamic entropy. In: Zalta EN (ed) The Stanford Encyclopedia of Philosophy, Stanford University, Stanford. http://stanford.library.usyd.edu.au/entries/information-entropy/

  • # Martín MJJ, Pablo CL, Agar PM (2006) Landscape changes over time: comparison of land uses, boundaries and mosaics. Landscape Ecol 21:1075–1088

  • Mcgarigal K, Cushman SA, Ene E (2012) FRAGSTATS v4: spatial pattern analysis program for categorical and continuous maps. University of Massachusetts, Amherst

    Google Scholar 

  • ‘# Mcharg IL (1981) Human ecological planning at Pennsylvania. Landsc Plan 8:109–120

  • Moran MJ, Shapiro HN, Boettner DD, Bailey M (2010) Using entropy. Fundamentals of engineering thermodynamics. Wiley, Hoboken, pp 281–358

    Google Scholar 

  • ‘# Naveh Z (1982) Mediterranean landscape evolution and degradation as multivariate biofunctions: theoretical and practical implications. Landsc Plan 9:125–146

  • ‘# Naveh Z (1987) Biocybernetic and thermodynamic perspectives of landscape functions and land use patterns. Landscape Ecol 1:75–83

  • Neel MC, Mcgarigal K, Cushman SA (2004) Behavior of class-level landscape metrics across gradients of class aggregation and area. Landscape Ecol 19:435–455

    Article  Google Scholar 

  • ‘# Newman PWG (1999) Sustainability and cities: extending the metabolism model. Landsc Urban Plan 44:219–226

  • ‘° O’neill RV, Johnson AR, King AW (1989) A hierarchical framework for the analysis of scale. Landscape Ecol 3:13

  • Orloci L (1991) Entropy and information. The Hague, SPB Academic Publishing

  • * Pablo CL, Agar PM, Sal AG, Pineda FD (1988) Descriptive capacity and indicative value of territorial variables in ecological cartography. Landscape Ecol 1:203–211

  • * Palang H, Mander Ü, Naveh Z (2000) Holistic landscape ecology in action. Landsc Urban Plan 50:1–6

  • Parrott L (2010) Measuring ecological complexity. Ecol Indic 10:1069–1076

    Article  Google Scholar 

  • ° Patil GP, Myers WL, Luo Z, Johnson GD, Taillie C (2000) Multiscale assessment of landscapes and watersheds with synoptic multivariate spatial data in environmental and ecological statistics. Math Comput Model 32:257–272

  • * Phillips SJ, Anderson RP, Shapire RE 2006. Maximum entropy modeling of species geographic distributions. Ecol Model 190:29

  • * Phipps M (1981) Entropy and community pattern analysis. J Theor Biol 93:253–273

  • Pielou EC (1975) Ecological diversity. Wiley, New York

    Google Scholar 

  • Pimm SL (1984) The complexity and stability of ecosystems. Nature 307:321–326

    Article  Google Scholar 

  • * Powell M, Accad A, Austin MP, Choy SL, Williams KJ, Shapcott A (2010) Predicting loss and fragmentation of habitat of the vulnerable subtropical rainforest tree Macadamia integrifolia with models developed from compiled ecological data. Biol Conserv 143:12

  • * Proulx R, Fahrig L (2010) Detecting human-driven deviations from trajectories in landscape composition and configuration. Landscape Ecol 25:1479–1467

  • * Rahman A, Aggarwal SP, Netzband M, Fazal S (2011) Monitoring urban sprawl using remote sensing and GIS techniques of a fast growing urban centre, India. IEEE J Sel Top Appl Earth Obs Remote Sens 4:56–64

  • Renyi A (1961) On measures of entropy and information. In: Fourth Berkeley symposium on mathematical statistics and probability, 1961 Berkeley. University of California Press

  • * Ricotta C (2000) From theoretical ecology to statistical physics and back: self-similar landscape metrics as a synthesis of ecological diversity and geometrical complexity. Ecol Model 125:245–253

  • Ricotta C, Corona P, Marchetti M (2003) Beware of contagion! Landsc Urban Plan 62:173–177

    Article  Google Scholar 

  • * Riiters KH, O’neill RV, Wickham JD, Jones BK (1996) A note on contagion indices for landscape analysis. Landscape Ecol 11:197–202

  • ° Riitters KH, O’neill RV, Hunsaker CT, Wickham JD, Yankee DH, Timmins SP, Jones KB, Jackson BL (1995) A factor analysis of landscape pattern and structure metrics. Landscape Ecol 10:23–39

    Article  Google Scholar 

  • Romme WH (1982) Fire and landscape diversity in subalpine forests of Yellowstone National Park. Ecol Monogr 52:199–221

    Article  Google Scholar 

  • Ryszkowski L, Kędziora A (1987) Impact of agricultural landscape structure on energy flow and water cycling. Landscape Ecol 1:85–94

    Article  Google Scholar 

  • Sanov IN (1958) On the probability of large deviations of random variables. Math Sb 42:11–44

    Google Scholar 

  • Shannon CE, Weaver W (1948) A mathematical theory of communication. American Telephone and Telegraph Company

  • Stonier T (1996) Information as a basic property of the universe. BioSystems 38:135–140

    Article  CAS  PubMed  Google Scholar 

  • * Sudhira HS, Ramachandra TV, Jagadish KS (2004) Urban sprawl: metrics, dynamics and modelling using GIS. Int J Appl Earth Obs Geoinf 5:29–39

  • Tews J, Brose U, Grimm V, Tielbörger K, Wichmann M, Schwager M, Jeltsch F (2004) Animal species diversity driven by habitat heterogeneity/diversity: the importance of keystone structures. J Biogeogr 31:79–92

    Article  Google Scholar 

  • Turner MG (1989) Landscape ecology: the effect of pattern on process. Annu Rev Ecol Evolut Syst 20:171–187

    Article  Google Scholar 

  • Turner MG, O’neill RV, Gardner RH, Milne BT (1989) Effects of changing spatial scale on the analysis of landscape pattern. Landscape Ecol 3:153–162

    Article  Google Scholar 

  • Ulanowicz RE (2001) Information theory in ecology. Comput Chem 25:393–399

    Article  CAS  PubMed  Google Scholar 

  • Ulanowicz RE (2004) On the nature of ecodynamics. Ecol Complex 1:341–354

    Article  Google Scholar 

  • Whittaker RH (1960) Vegetation of the Siskiyou mountains, Oregon and California. Ecol Monogr 30:279–338

    Article  Google Scholar 

  • ‘# Wilkin DC (1996) Accounting for sustainability: challenges to landscape professionals in an increasingly unsustainable world. Landsc Urban Plan 36:217–227

  • Wilkinson DM (1999) The disturbing history of intermediate disturbance. Oikos 84:145–147

    Article  Google Scholar 

  • Wu J, David JL (2002) A spatially explicit hierarchical approach to modeling complex ecological systems: theory and applications. Ecol Model 153:7–26

    Article  Google Scholar 

  • Wu J, Marceau D (2002) Modeling complex ecological systems: an introduction. Ecol Model 153:1–6

    Article  Google Scholar 

  • Wurtz P, Annila A (2010) Ecological succession as an energy dispersal process. Biosystems 100:70–80

    Article  PubMed  Google Scholar 

  • Xu T, Moore ID, Gallant JC (1993) Fractals, fractal dimensions and landscapes—a review. Geomorphology 8:245–262

    Article  Google Scholar 

  • Yarrow MM, Salthe SN (2008) Ecological boundaries in the context of hierarchy theory. BioSystems 92:233–244

    Article  PubMed  Google Scholar 

  • * Yeh AGO, Li X (1999) An entropy method to analyze urban sprawl in a rapid growing region using TM images. In: Sensing AAOR (ed) Asian conference on remote sensing, 1999 Hong Kong. GISdevelopment

  • # Zaccarelli N, Li B-L, Petrosillo I, Zurlini G (2013) Order and disorder in ecological time-series: Introducing normalized spectral entropy. Ecol Indic 28:22–30

  • ‘# Zhang Y, Yang Z, Li W (2006) Analyses of urban ecosystem based on information entropy. Ecol Model 197:1–12

  • # Zurlini G, Petrosillo I, Jones BK, Zaccarelli N (2013) Highlighting order and disorder in social–ecological landscapes to foster adaptive capacity and sustainability. Landscape Ecol 28:1161–1173

Download references

Acknowledgments

Isabelle Vranken is a research fellow at the FNRS, Belgium. Thanks to Prof. G. Zurlini and Dr N. Zaccarelli for their complementary explanations. Thanks for the thoughtful remarks of the Editor.

Author information

Authors and Affiliations

  1. Research Unit of Landscape Ecology and Plant Production Systems, ULB, CP 264/2, Campus de la Plaine, Boulevard du Triomphe, 1050, Brussels, Belgium

    Isabelle Vranken & Marjolein Visser

  2. UP980: Sad-paysage, INRA, rue de Saint-Brieuc, 65, 35042, Rennes Cedex, France

    Jacques Baudry

  3. Unit of Biosystem Physics, Gembloux Agro-Bio Tech (ULg), passage des Déportés, 2, 5030, Gembloux, Belgium

    Marc Aubinet

  4. Biodiversity and Landscape Unit, Gembloux Agro-Bio Tech (ULg), passage des Déportés, 2, 5030, Gembloux, Belgium

    Isabelle Vranken & Jan Bogaert

Authors
  1. Isabelle Vranken
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jacques Baudry
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marc Aubinet
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marjolein Visser
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jan Bogaert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Isabelle Vranken.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vranken, I., Baudry, J., Aubinet, M. et al. A review on the use of entropy in landscape ecology: heterogeneity, unpredictability, scale dependence and their links with thermodynamics. Landscape Ecol 30, 51–65 (2015). https://doi.org/10.1007/s10980-014-0105-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10980-014-0105-0

Keywords

Search

Navigation