%0 Journal Article %1 bez2011duality %A Bez, Nicolas %A Bertrand, Sophie %D 2011 %J Theoretical Ecology %K fish fishery fractals scale stochastic-process theoretical-ecology %N 3 %P 371--383 %R 10.1007/s12080-010-0084-y %T The duality of fractals: roughness and self-similarity %U http://dx.doi.org/10.1007/s12080-010-0084-y %V 4 %X The fractal dimension (DHB) is an interesting metrics because it is supposed to quantify by a single value, scale independence and roughness of ecological objects. However, we show here that those two properties may be quantified by a single dimension only in some specific cases. In general, a non-integer DHB quantifies only the roughness, and self-similarity needs to be evidenced or postulated by other means. Second, we revisit some aspects of the practical estimation of DHB. We recommend the use of madogram instead of variogram for estimations based on geostatistics. We propose a simplification of its estimation for 2D fields and discuss its possible relationship with self-similarity. We finally underline the problem of scale and resolution. Field data recorded during a scientific acoustic survey on the North Sea herring are used for illustrations. The paper concludes on a synthesis of practical recommendations to ecologists when using fractal dimension.

@article{bez2011duality, abstract = {The fractal dimension (DHB) is an interesting metrics because it is supposed to quantify by a single value, scale independence and roughness of ecological objects. However, we show here that those two properties may be quantified by a single dimension only in some specific cases. In general, a non-integer DHB quantifies only the roughness, and self-similarity needs to be evidenced or postulated by other means. Second, we revisit some aspects of the practical estimation of DHB. We recommend the use of madogram instead of variogram for estimations based on geostatistics. We propose a simplification of its estimation for 2D fields and discuss its possible relationship with self-similarity. We finally underline the problem of scale and resolution. Field data recorded during a scientific acoustic survey on the North Sea herring are used for illustrations. The paper concludes on a synthesis of practical recommendations to ecologists when using fractal dimension.}, added-at = {2016-09-04T12:46:14.000+0200}, author = {Bez, Nicolas and Bertrand, Sophie}, biburl = {https://www.bibsonomy.org/bibtex/221a0ab74f1cdb2634cfd2d84c3e9d2c4/hyphen}, doi = {10.1007/s12080-010-0084-y}, interhash = {78ceb1a5d122b4cd94fc87526a73c39a}, intrahash = {21a0ab74f1cdb2634cfd2d84c3e9d2c4}, journal = {Theoretical Ecology}, keywords = {fish fishery fractals scale stochastic-process theoretical-ecology}, number = 3, pages = {371--383}, timestamp = {2016-09-04T14:15:39.000+0200}, title = {The duality of fractals: roughness and self-similarity}, url = {http://dx.doi.org/10.1007/s12080-010-0084-y}, volume = 4, year = 2011 }