The distribution of blackberry (Rubus hirtus W. K.) in different scales: the fractal analysis

Gazda, Anna

doi:ISSN 1505-2249

$The distribution of blackberry (Rubus hirtus W. K.) in different scales: the fractal analysis$

Download

Title: The distribution of blackberry (Rubus hirtus W. K.) in different scales: the fractal analysis

Abstract:

The scale dependence of natural patterns provides an opportunity to apply fractal geometry to diverse problems in "spatial" ecology so as to integrate the spatial and temporal characteristics of complex environments. In this paper I attempt to explore the scaling dependency of in an autecological study on blackberry across a range of scales by applying fractal theory. The fractal dimension of: the blackberry (Rubus hirtus W. K.) distribution within its geographical range is 1.44 ± 0.02; the pattern in the Gorce National Park (5908 ha) is 1.47 ± 0.05; the pattern for Łopuszna Valley (49°34'N, 20°08'E) (185.86 ha) is 1.30 ± 0.09 and 1.32 ± 0.05 for the Ratanica watershed (49°51 'N, 20°02'E) ( 121.76 ha) (Fig. 1 ); the distribution of blackberry within the six plots located within the Ratanica watershed has values: 1.21 ± 0.09 to 1.45 ± 0.06. On the gap plot, located within Ratanica watershade, created in 1987, year the fractal dimension of blackberry distribution increased from 1.21 ± 0.16 to 1.60 ± 0.04 during 5 successive years (Fig. 2). In the same region, on plot located under the dense forest, D of blackberry distribution has not changed and reached value 1.28 ± 0.05. This study demonstrates that the distribution pattern is heavily influenced by scale. There are no possibilities to detect any breakpoint at scale intervals within the range of spatial scales studied, because the study of pattern was carried out on a noncontinuous scale (Fig. 4).

References:

Adamczy k B. 1966 - Gleby leśne w Gorcach (Forest soils in the Gorce Mountains) - Acta Agrar. Silv., s. Silv. 6.
Bradbury R. H., Reichelt R. E., Green D.G 1984 - Fractals in ecology: methods and interpretation - Marine Ecology Progress Series 14: 295-296.
Falconer K. 1985 - The geometry of fractal sets - Cambridge University Press. Cambridge, London, New York, New Rochelle, Melbourne, Sydney.
Gazda A. 1992 - Warunki występowania jeżyny gruczołowatej Rubus hirtus (W. K.) w rezerwacie Ścisłym Dolina Łopusznej, w Gorczańskim Parku Narodowym (Conditions of occurrence of the blackberry (Rubus hirtus W. K.) in the strict area Dolina Łopusznej in the Gorce National Park) - Parki Narodowe i Rezerwaty Przyrody 11: 105-117.
Gazda A. 1996 - Geometria fraktali i niektóre jej zastosowania w ekologii (The fractal geometry and some of its applications in ecology) - Wiad. Ekol. 42: 163-178.
Gutierrez E., Almirall H. 1989 - Temporal properties of some biological systems and their fractal attractors. Bull. Math. Biol. 51 (6): 785-800.
Hastings H. M., Sugihara G. 1993 - Fractals a user's guide for the natural sciences - Oxford University Press.
Hess M. 1965. - Piętra klimatyczne w Polskich Karpatach Zachodnich (Climatic zones of Polish Western Carpathian Mountains) - Zesz. Nauk. Uniw. Jagiell., Pr. Inst. Geogr. 11; 5-267.
Jarosz S. 1935 - Badania geograficzno-leśne w Gorcach (A geographical study on forests of the Gorce Mountains) - Pr. roln.-leśn. PAU 16: 1-125.
Józefiak J. 1993 - Statystyczna analiza występowania wybranych pospolitych gatunków runa leśnego w Gorczańskim Parku Narodowym (The statistical analysis of distribution of chosen plants of forest floor vegetation in the Gorce National Parks) - praca magisterska wykonana w KBLiOP AR, Kraków, msc.
Kolasa J. 1989 - Ecological systems in herarchical perspective: breaks in community structure and other consequences - Ecology, 70 (1): 36-47.
Kornaś J. 1955 - Charakterystyka geobotaniczna Gorców (Geobotanical characteristic of the Gorce Mountains) - Monogr. botan. 3:1-216.
Kornaś J. 1957 - Rośliny naczyniowe Gorców (Vascular Plant of the Gorce National Parks) - Monogr. botan. 5: 1-260
Mandelbrot B. B. 1983 - The Fractal Geometry of Nature - W.H. Freeman & Co., New York.
May R. M. 1989 - Levels of Organization in Ecology (in Ecological Concepts, ed.: Cherrett J. M.). Blackwell Scientific Publications, Oxford, London, Edinburgh, Boston, Melbourne.: 339-363.
Medwecka-Kornaś A. 1955 - Zespoły leśne Gorców (Plant communities of the Gorce Mountains) - Ochr. Przyr. 23:1-111.
Meusel H., Jager E., Weinert E. 1965 - Vergleichende Chorologie der Zentraleuropaischen Flora - VEB Gustav Fischer Verlag, Jena
Palmer M.W. 1988 - Fractal geometry: a tool for describing spatial pattern of plant communities - Vegetatio 75: 91-102.
Pancer-Koteja E. 1991 - Gatunki dynamiczne w runie lasów karpackich warunki występowania Calamagrostis arundinacea (L.) Roth., Chamaenerion angustifolium L., Rubus hirtus W.K., Rubus idaeus L., Senecio nemorensis L. s. l. (incl. S. fuchsii Gmel.) (Dynamic species in the forest floor vegetation of the Carpathian Mountains. Distribution and habitats of: Calamagrostis arundinacea (L.) Roth., Chamaenerion angustifolium L., Rubus hirtus W.K., Rubus idaeus L., Senecio nemorensis L. s. l. (incl. S. fuchsii Gmel.)) - Zesz. Nauk. Akad. Roln. Kraków 254: 133-150.
Pancer-Koteja E., Szwagrzyk J., Bodziarczyk J. 1998 - Small-scale spatial pattern and size structure of Rubus hirtus in a canopy gap - Journal of Vegetation Science 9 (in press).
Peitgen H.-O., Soupe D. 1988 - The Science of Fractal Images. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo.
Rabotnov T. A. 1950 - Life cycles of perennial herbage plants in meadow communities - Proc. Komarov. Bot. Inst. Acad. Sci. USSR ser. 3, 6: 7-240.
Różański W., Pancer-Kotejowa E., Grodzińska K. 1994 - Vegetation of the Ratanica watershed (Carpathian Foothills, Southern Poland) - Ekol. Pol. 41: 347-374.
Sugihara G., May M.M. 1990 - Applications of fractals in Ecology. TREE. 5, 3
Tutin T. G., Heywood V. H., Burges N. A., Valentino D. H. 1968 – Flora europaea.
Wiens J. A. 1989. Spatial scaling in ecology. Functional Ecology. 3: 385-397.