Skip to main content
SpringerLink
Log in

Ascribing Ecological Meaning to Habitat Shape by Means of a Piecewise Regression Approach to Fractal Domains

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

Abstract

A fractal dimension (FD) indicates the ability of a set of structures to fill the Euclidean space where it is embedded. For habitat boundaries, FD is bound to a plane, thus 1 ≤ FD  ≤ 2. FD is low for simple shapes and increases as patches become more irregular. Some authors have found that FD metric delineating area-perimeter relation (APR) is best fitted through piecewise linear curves, where the slope of each line segment is one-half the FD over the corresponding scaling region. The detection of shifts in boundary FD of landscape habitats is a significant issue in ecology, since discontinuities could be an index of a substantial modification of the processes and dynamics that generate and maintain habitats. This work makes use of fractal analysis to examine the relationship between anthropogenic processes and habitat spatial patterns. It proposes two goals (1) suggesting Multivariate Adaptive Regression Splines (MARS®) as a fast and effective approach to discover shifts in APR of landscape patches; (2) explaining the substantial existence of such shifts using a set of human-related predictor variables. MARS methodology has been applied to 6 types of habitats within the Baganza stream watershed (Parma, Italy) and the discovered patterns have been correlated with anthropogenic variables that could influence APR. A standardized linear discriminant analysis (DA) has been used to predict FDs from the set of the employed predictors. DA corroborated the existence of breakpoints in APR and explained the contribute of predictor variables in determining the discovered shifts.

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

Similar content being viewed by others

References

  • E.Z. Baskent (1999) ArticleTitleControlling spatial structure of forested landscapes: a case study towards landscape management Landscape Ecol. 14 83–97 Occurrence Handle10.1023/A:1008071307848

    Article  Google Scholar 

  • M. Buechner (1989) ArticleTitleAre small-scale landscape features important factors for field studies of small mammal dispersal sinks? Landscape Ecol. 2 191–199 Occurrence Handle10.1007/BF00126018

    Article  Google Scholar 

  • C.E.C. (Commission of European Community) 1991. CORINE Biotopes Manual, habitats of the European Community. A method to identify and describe consistently sites of major importance for nature conservation. EUR 12587/3, Bruxelles, Belgium.

  • J. Chen J.F. Franklin T.A. Spies (1992) ArticleTitleVegetation responses to edge environments in old-growth Douglas-fir forests Ecol. Appl. 2 387–396

    Google Scholar 

  • J. Cohen (1988) Statistical power analysis for the behavioural sciences Lawrence Erlbaum Associates New Jersey, USA

    Google Scholar 

  • P. Craven G. Wabha (1979) ArticleTitleSmoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation Numer. Math. 31 317–403

    Google Scholar 

  • R.D. Veaux ParticleDe D.C. Psichogios L.H. Ungar (1993a) ArticleTitleA comparison of two nonparametric estimation schemes: MARS and neural networks Comp. Chem. Eng. 17 819–837 Occurrence Handle10.1016/0098-1354(93)80066-V

    Article  Google Scholar 

  • R.D. Veaux ParticleDe A.L. Gordon J.C. Comiso N.E. Bacherer (1993b) ArticleTitleModelling of topographic effects on Antartic Sea Ice using multivariate adaptive regression splines J. Geophys. Res. 98 307–319

    Google Scholar 

  • A. Ferrarini P. Rossi N. Zaccarelli (2002) ArticleTitleHigh accurated vegetation mapping: neural networks applied to MIVIS sensor data Ital. J. Remote Sens. 22 13–22

    Google Scholar 

  • R.T. Forman (1995) Land Mosaics, the Ecology of Landscapes and Regions Cambridge University Press CambridgeUK

    Google Scholar 

  • R.T. Forman M. Godron (1986) Landscape Ecology John Wiley & Sons New York, USA

    Google Scholar 

  • I. E. Frank (1995) ArticleTitleModern nonlinear regression methods Chemometr. Intell. Lab. Syst. 27 1–9 Occurrence Handle10.1016/0169-7439(94)00005-4

    Article  Google Scholar 

  • J.H. Friedman (1991) ArticleTitleMultivariate adaptive regression splines Annal Stat. 19 1–141

    Google Scholar 

  • S. Frontier (1987) Applications of fractal theory to ecology P. Legendre L. Legendre (Eds) Developments in Numerical Ecology Springer-Verlag Berlin, Germany 335–378

    Google Scholar 

  • L. Grossi G. Zurlini O. Rossi (2001) ArticleTitleStatistical detection of multiscale landscape patterns Environ. Ecol. Stat. 8 253–267 Occurrence Handle10.1023/A:1011391608285

    Article  Google Scholar 

  • R.A. Hardt R.T.T. Forman (1989) ArticleTitleBoundary form effects on woody colonization of reclaimed surface mines Ecology 70 1252–1260

    Google Scholar 

  • L.D. Harris P. Kangas (1979) Designing future landscapes from principles of form and function G.H. Pilsner R.C. Smardon (Eds) Our National Landscape: Applied Techniques for Analysis and Management of the Visual Resource US Forest Service Washington D.C., USA 725–729

    Google Scholar 

  • H.M. Hastings G. Sugihara (1993) Fractals: a User's Guide for the Natural Sciences Oxford University Press OxfordUK

    Google Scholar 

  • L.R. Iverson (1989) ArticleTitleLand use changes in Illinois, USA: the influence of landscape attributes on current and historic land use Landscape Ecol. 2 45–61 Occurrence Handle10.1007/BF00138907

    Article  Google Scholar 

  • P.M. Kuhnert K. Do R. McClure (2000) ArticleTitleCombining non-parametric models with logistic regression: an application to motor vehicle injury data Comput. Stat. Data Anal. 34 371–386 Occurrence Handle10.1016/S0167-9473(99)00099-7

    Article  Google Scholar 

  • J.R. Krummel R.H. Gardner G. Sugihara R.V. O’Neill (1987) ArticleTitleLandscape patterns in a disturbed environment Oikos 48 321–324

    Google Scholar 

  • P.A.W. Lewis J.G. Stevens (1991) ArticleTitleNonlinear modelling of time series using multivariate adaptive regression splines (MARS) J. Am. Stat. Assoc. 86 864–877

    Google Scholar 

  • A.J. Liu G.N. Cameron (2001) ArticleTitleAnalysis of landscape patterns in coastal wetlands of Galveston Bay, Texas (USA) Landscape Ecol. 16 581–595 Occurrence Handle10.1023/A:1013139525277

    Article  Google Scholar 

  • B.B. Mandelbrot (1982) The Fractal Geometry of Nature W.H. Freeman San FranciscoUSA

    Google Scholar 

  • J.N. Miller R.P. Brooks M.J. Croonquist (1997) ArticleTitleEffects of landscape patterns on biotic communities Landscape Ecol. 12 137–153 Occurrence Handle10.1023/A:1007970716227

    Article  Google Scholar 

  • Mladeno D.J. and DeZonia B. 2001. Apack 2.17 Analysis Software. User’s guide, pp. 52.

  • R.V. O'9Neill J.R. Krummel R.H. Gardner G. Sugihara B. Jackson D.L. DeAngelis B.T. Milne M.G. Turner B. Zygmunt S.W. Christensen V.H. Dale R.L. Graham (1988) ArticleTitleIndices of landscape pattern Landscape Ecol. 1 153–162 Occurrence Handle10.1007/BF00162741

    Article  Google Scholar 

  • O. Rossi G. Zurlini (1993) ArticleTitlePrimi elementi conoscitivi essenziali per la realizzazione della Carta della Natura (Leggen. 394 del 6/12/1991) Bull. Ital. Ecol. Soc. 14 46–56

    Google Scholar 

  • P. Rossi A. Ferrarini N. Zaccarelli (2001) ArticleTitleCORINE habitats recognition inside Baganza stream watershed (ParmaItaly) through MIVIS sensor data Ital. J. Remote Sens. 20 41–48

    Google Scholar 

  • P. Rossi (1999) Analisi della diversitá vegetazionale in Val Baganza mediante la classificazione CORINE Biotopes University of Parma ParmaItaly 250

    Google Scholar 

  • C.M. Schonewald-Cox J.W. Bayless (1986) ArticleTitleThe boundary model: a geographic analysis of design and conservation of nature reserves Biol. Conserv. 38 305–322 Occurrence Handle10.1016/0006-3207(86)90057-1

    Article  Google Scholar 

  • S. Sekulic B.R. Kowalski (1992) ArticleTitleMARS: a tutorial J. Chemometr. 6 199–216 Occurrence Handle10.1002/cem.1180060405

    Article  Google Scholar 

  • G. Sugihara R.M. May (1990) ArticleTitleApplications of fractals in ecology Trend. Res. Ecol. Evol. 5 79–86 Occurrence Handle10.1016/0169-5347(90)90235-6

    Article  Google Scholar 

  • D. Steinberg B. Bernstein P. Colla K. Martin (1999) MARS User Guide Salford Systems San Diego, CA

    Google Scholar 

  • D.W. Thompson (1961) On Growth and Form Cambridge University Press CambridgeUK

    Google Scholar 

  • M.G. Turner C.L. Ruscher (1988) ArticleTitleChanges in the spatial patterns of lands use in Georgia Landscape Ecol. 1 241–251 Occurrence Handle10.1007/BF00157696

    Article  Google Scholar 

  • M.B. Usher (1991) Habitat structure and the design of nature reserves S.S. Bell E.D. McCoy H.R. Mushinsky (Eds) Habitat Structure – the Physical Arrangement of Objects in Space Chapman and Hall London 373–391

    Google Scholar 

  • J.A. Wiens C.S. Crawford R. Gosz (1985) ArticleTitleBoundary dynamics: a conceptual framework for studying landscape ecosystems Oikos 45 421–427

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Environmental Science, University of Parma, Science Avenue, 11/a, 43100, Parma, Italy

    Alessandro Ferrarini, Pierfrancesca Rossi & Orazio Rossi

Authors
  1. Alessandro Ferrarini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pierfrancesca Rossi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Orazio Rossi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Orazio Rossi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ferrarini, A., Rossi, P. & Rossi, O. Ascribing Ecological Meaning to Habitat Shape by Means of a Piecewise Regression Approach to Fractal Domains. Landscape Ecol 20, 799–809 (2005). https://doi.org/10.1007/s10980-005-0065-5

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10980-005-0065-5

Keywords

Search

Navigation