Scaling properties in landscape patterns: New Zealand experience

In this paper we present a case study of spatial structure in landscape patterns for the North and South Islands of New Zealand. The aim was to characterise quantitatively landscape heterogeneity and investigate its possible scaling properties. The study examines spatial heterogeneity, in particular patchiness, at a range of spatial scales, to help build understanding on the effects of landscape heterogeneity on water movement in particular, and landscape ecology in general.We used spatial information on various landscape properties (soils, hydrogeology, vegetation, topography) generated from the New Zealand Land Resource Inventory. To analyse this data set we applied various methods of fractal analyses following the hypothesis that patchiness in selected landscape properties demonstrates fractal scaling behaviour at two structural levels: (1) individual patches; and (2) mosaics (sets) of patches.Individual patches revealed scaling behaviour for both patch shape and boundary. We found self-affinity in patch shape with Hurst exponent H from 0.75 to 0.95. We also showed that patch boundaries in most cases were self-similar and in a few cases of large patches were self-affine. The degree of self-affinity was lower for finer patches. Similarly, when patch scale decreases the orientation of patches tends to be uniformly distributed, though patch orientation on average is clearly correlated with broad scale geological structures. These results reflect a tendency to isotropic behaviour of individual patches from broad to finer scales. Mosaics of patches also revealed fractal scaling in the total patch boundaries, patch centers of mass, and in patch area distribution. All these reflect a special organisation in patchiness represented in fractal patch clustering. General relationships which interconnect fractal scaling exponents were derived and tested. These relationships show how scaling properties of individual patches affect those for mosaics of patches and vice-versa. To explain similarity in scaling behaviour in patchiness of different types we suggest that the Self-Organised Criticality concept should be used. Also, potential applications of our results in landscape ecology are discussed, especially in relation to improved neutral landscape models.

[1]  Monica G. Turner,et al.  Interactions between the fractal geometry of landscapes and allometric herbivory , 1992 .

[2]  Nathan H. Schumaker,et al.  Using Landscape Indices to Predict Habitat Connectivity , 1996 .

[3]  R. Gardner,et al.  Quantitative Methods in Landscape Ecology , 1991 .

[4]  D. Noever,et al.  Fractal geometry of individual river channels and its computer simulation , 1993 .

[5]  Bruce T. Milne,et al.  Spatial Aggregation and Neutral Models in Fractal Landscapes , 1992, The American Naturalist.

[6]  Olivier Bour,et al.  Connectivity of random fault networks following a power law fault length distribution , 1997 .

[7]  M. Seyfried,et al.  Scale and the Nature of Spatial Variability: Field Examples Having Implications for Hydrologic Modeling , 1995 .

[8]  Shunji Ouchi,et al.  Measurement of self-affinity on surfaces as a trial application of fractal geometry to landform analysis , 1992 .

[9]  Monica G. Turner,et al.  Ecological implications of landscape fragmentation , 1993 .

[10]  Bruce T. Milne,et al.  Lessons from applying fractal models to landscape patterns , 1991 .

[11]  Robert Lee Schooley,et al.  Patchy Landscapes and Animal Movements: Do Beetles Percolate? , 1997 .

[12]  A. King.  Translating models across scales in the landscape , 1991 .

[13]  C. Pearson,et al.  Regional frequency analysis of annual maximum streamflow drought , 1995 .

[14]  M. Matsushita,et al.  On the self-affinity of various curves , 1989 .

[15]  Per Bak,et al.  How Nature Works , 1996 .

[16]  C. Pearson,et al.  Regional flood frequency analysis for small New Zealand basins. II: Flood frequency groups , 1991 .

[17]  J. Lagro.  Assessing patch shape in landscape mosaics , 1991 .

[18]  Monica G. Turner,et al.  Landscape connectivity and population distributions in heterogeneous environments , 1997 .

[19]  Jianguo Wu,et al.  A patch-based spatial modeling approach: conceptual framework and simulation scheme , 1997 .

[20]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[21]  L. Liebovitch,et al.  A fast algorithm to determine fractal dimensions by box counting , 1989 .

[22]  Robert V. O'Neill,et al.  Neutral models for the analysis of broad-scale landscape pattern , 1987, Landscape Ecology.

[23]  Efi Foufoula-Georgiou,et al.  Study of self-similar and self-affine objects using logarithmic correlation integral , 1995 .

[24]  M. Goodchild,et al.  The Fractal Nature of Geographic Phenomena , 1987 .

[25]  Anthony W. King,et al.  The Use and Misuse of Neutral Landscape Models in Ecology , 1997 .

[26]  C. P. Pearson.  Regional frequency analysis of low flows in New Zealand Rivers , 1995 .

[27]  C. Sparrow.  The Fractal Geometry of Nature , 1984 .

[28]  A. Mckerchar.  Regional flood frequency analysis for small New Zealand basins. I: Mean annual flood estimation , 1991 .

[29]  R. O'Neill,et al.  Landscape patterns in a disturbed environment , 1987 .