Fractal dimension of vegetation and the distribution of arthropod body lengths

Morse, David; Lawton, John H.; Dodson, M. M.; Williamson, Mark

doi:10.1038/314731a0

Cited by 491 publications

(328 citation statements)

References 14 publications

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“…In cases where a scaling relationship is not accounted for by a single D or other scaling exponent, the observed complexity might result from fundamentally different processes operating between different scales (Burrough, 1981;Krummel et al, 1987;Sugihara & May, 1990). This observation has been applied in ecology as evidence of differing processes acting on different scales in the formation of landscapes (Krummel et al 1987) and complex spatial structuring of vegetation allowing for diverse assemblages of habitats for invertebrates (Morse et al, 1985;Gunnarsson, 1992). Fitter (1986Fitter ( , 1987 has suggested that the PL ordering system is valuable for describing plant root Rose's (1983) numerical model of root growth (Berntson 1995 Refer to text for a more detailed description of model.…”

Section: Complex (Non-linear) Topological Scalingmentioning

confidence: 99%

Topological scaling and plant root system architecture: developmental and functional hierarchies

Berntson

1997

New Phytologist

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SUMMARYTopology is an important component of tbe arcbitecture of wbole root systems. Unfortunately, most commonly applied indices used for characterizing topology are poorly correlated witb one anotber and thus reflect different aspects of topology. In order to understand better bow different methods of cbaracterizing topology vary, tbis paper presents an exploration of several different methods for assigning order witbin branched root systems on tbe basis of (a) developmental (centrifugal) vs. functional (centripetal) ordering sequences and (b) wbetber orders are assigned to individual links or groups of adjacent links (segments). For eacb ordering system, patterns of scaling in relation to various aspects of link and segment size are explored using regression analyses. Segment-based ordering systems resulted in better fits for simple scaling relationships with size, but these patterns varied between developmental vs. functional ordering as well as tbe different size metrics examined. Tbe functional (centripetal), link-based ordering system sbowed complex, non-linear scaling in relation to numbers of links per order. Using a simple simulation model of root growth, it is demonstrated tbat this metbod of cbaracterizing root topology in relation to root size migbt be a more powerful tool for cbaracterizing root system arcbitecture tban in the use of simple, single-index cbaracterizations of topology.

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Section: Complex (Non-linear) Topological Scalingmentioning

confidence: 99%

Topological scaling and plant root system architecture: developmental and functional hierarchies

Berntson

1997

New Phytologist

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“…Applications of fractals are used to distinguish malignant and benign tumor cells (Nonnenmacher et al 1994;Losa et al 1997Losa et al , 2002, to study geometry of auditory nerve-spike trains (Teich and Lowen 1994), and the neural network (Jelinek and Fernandez 1998). Fractals have also been used in microbiology (Smith et al 1989;Sedlák et al 2002;Veselá et al 2002), and to characterize biological objects like leaf shape (Morse et al 1985;Vlcek and Cheung 1986;Prusinkiewicz 1993;Slice 1993;Mancuso 2001). However, the origins of fractal structures are diYcult to understand.…”

Section: Introductionmentioning

confidence: 99%

Use of fractal dimensions to quantify coral shape

et al. 2007

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A morphometrical method to quantify and characterize coral corallites using Richardson Plots and Kaye's notion of fractal dimensions is presented. A Jurassic coral species (Aplosmilia spinosa) and Wve Recent coral species were compared using the Box-Counting Method. This method enables the characterization of their morphologies at calicular and septal levels by their fractal dimensions (structural and textural). Moreover, it is possible to determine diVerences between species of Montastraea and to tackle the high phenotypic plasticity of Montastraea annularis. The use of fractal dimensions versus conventional methods (e.g., measurements of linear dimensions with a calliper, landmarks, Fourier analyses) to explore a rugged boundary object is discussed. It appears that fractal methods have the potential to considerably simplify the morphometrical and statistical approaches, and be a valuable addition to methods based on Euclidian geometry.

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“…This is somewhat surprising for several reasons. First, observations of scale dependence are not new (Burrough 1981(Burrough , 1983 are found in almost all of the many applications (Morse et al (1985) and references therein), and Sugihara & May (1990) suggest using this information to detect hierarchies in ecological systems. For example, Meltzer & Hastings (1992) noted a strong ¢rst-order autocorrelation among residuals from a linear regression of a log-log plot representing a hyperbolic distribution of the cumulative probability that grass patches have a certain size versus the area of the patches.…”

Section: Discussionmentioning

confidence: 99%

“…It is likely that this di¤culty is largely driven by variations in D within real-world structures. For example, fracture and fault lines in the Earth's crustal plates (Hatton et al 1994), spatial and temporal variability in zooplankton biomass (Pascual et al 1995), borders between disturbed and non-disturbed habitats (Krummel et al 1987), and the above- (Morse et al 1985) and belowground (Berntson 1997) branching structures of plants, can all exhibit either discrete or continuous scaledependent variations in D. This scale-dependent variation in real-world structures has been acknowledged since the beginning of work with fractal geometry. Early work in soil science, for example, referred to this phenomenon as`partial self-similarity' (Burrough 1981(Burrough , 1983.…”

Section: Introductionmentioning

confidence: 99%

“…Typically, the fractal dimension of a real-world object is calculated using the box-counting method (and related techniques, reviewed in Hastings & Sugihara 1993;Sugihara & May 1990;Vicsek 1992). The technique has been applied to such varied structures as plant shoot systems (Corbit & Garbary 1995;Morse et al 1985) and root systems (Berntson 1996), nerve ganglia (Morigiwa et al 1989), and blood vessels (Masters 1994). The wide array of applications suggest that this method can provide a powerful tool for quantifying the space-¢lling properties of complex structures.…”

Section: Introductionmentioning

confidence: 99%

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Correcting for finite spatial scales of self–similarity when calculating fractal dimensions of real–world structures

Berntson

Stoll²

1997

Proc. R. Soc. Lond. B

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Fractal geometry is a potentially valuable tool for quantitatively characterizing complex structures. The fractal dimension (D) can be used as a simple, single index for summarizing properties of real and abstract structures in space and time. Applications in the ¢elds of biology and ecology range from neurobiology to plant architecture, landscape structure, taxonomy and species diversity. However, methods to estimate the D have often been applied in an uncritical manner, violating assumptions about the nature of fractal structures. The most common error involves ignoring the fact that ideal, i.e. in¢nitely nested, fractal structures exhibit self-similarity over any range of scales. Unlike ideal fractals, real-world structures exhibit self-similarity only over a ¢nite range of scales.Here we present a new technique for quantitatively determining the scales over which real-world structures show statistical self-similarity. The new technique uses a combination of curve-¢tting and tests of curvilinearity of residuals to identify the largest range of contiguous scales that exhibit statistical self-similarity. Consequently, we estimate D only over the statistically identi¢ed region of self-similarity and introduce the ¢nite scale-corrected dimension (FSCD). We demonstrate the use of this method in two steps. First, using mathematical fractal curves with known but variable spatial scales of self-similarity (achieved by varying the iteration level used for creating the curves), we demonstrate that our method can reliably quantify the spatial scales of self-similarity. This technique therefore allows accurate empirical quanti¢cation of theoretical Ds. Secondly, we apply the technique to digital images of the rhizome systems of golden rod (Solidago altissima). The technique signi¢cantly reduced variations in estimated fractal dimensions arising from variations in the method of preparing digital images. Overall, the revised method has the potential to signi¢cantly improve repeatability and reliability for deriving fractal dimensions of realworld branching structures.

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Fractal dimension of vegetation and the distribution of arthropod body lengths

Cited by 491 publications

References 14 publications

Topological scaling and plant root system architecture: developmental and functional hierarchies

Topological scaling and plant root system architecture: developmental and functional hierarchies

Use of fractal dimensions to quantify coral shape

Correcting for finite spatial scales of self–similarity when calculating fractal dimensions of real–world structures

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