分形模型在生态学研究中的应用

Fractal Models and Their Ecological Applications.

1 前言分形模型(fractal models)是建立在分形几何学(fractal geometry)的基础上而发展起来的一种解释物体的空间形状和结构的研究方法[21,24]。纵观分形几何学的发展也不过20多年的历史,它是由数学家Mandelbrot[19～21]创立,由众多的科学家不断发展和完善,并应用于研究自然界各种传统几何学难以解决的现象[7,9～11,13,17,28,37]。特别是在最近几年,科学界的主流刊物如英国的《自然》和美国的《科学》推波助澜和大批的图书问世,使其与混沌理论(Chaos)和其它一些非线性理论得到广泛的应用[3,41]。分形几何学的核心是描述自然界各种不规则物体,如:云的形状、海岸线的长度。

As an effective tool in describing and explaining the spatial complexity of objects and their patterns in nature, fraetal models recently have received increasing attention. Especially in studies of patchiness and landscape ecology, fractal analysis has shown a considerable potenial. This paper was intended to introduce the concepts and methods of calculation for exact and statistical fractals, as well as the modified fractal dimension analysis, with examples of their applications in ecology. We focused on the methods of changing measurement scales, grid-based counting, perimeter-area relationship, and density-based fractal dimension. In addition, a comparative evaluation was given for these different methods.