格局和过程一直是生态学的核心问题，该文应用“非布朗运动随机分形”模型， 在北京东灵山远离人为干扰地区的阴坡设置了两条宽2 m的样带，描述和比较了暖温带落叶阔叶林区乔木、灌木、草本以及总的植物物种丰富度在不同尺度上沿海拔梯度变异特征， 以及相关的生态过程。研究结果表明：1）直接梯度法刻画了植物物种丰富度在海拔梯度上的总体变化趋势，并不能从中获得更多的信息。“非布朗运动随机分形”模型揭示了不同尺度上物种丰富度的空间变化并能和生态过程相联系，研究表明该模型适合对乔木、灌木和草本植物物种丰富度的垂直梯度格局特征进行描述，但对总的植物物种丰富度有一定的局限性 。2）乔木物种丰富度在海拔梯度上的变化主要受两种生态过程的控制，小尺度上分形维数接近于2，主要受独立的不具有长程相关的生态过程控制，呈近随机分布；大尺度上分形维数接近于1，主要受自相关范围大、具有长程关联特性的生态过程控制，随海拔上升呈近似单调下降的趋势。灌木和草本物种丰富度在海拔梯度上的变化主要受3种生态过程的控制，小尺度和大尺度上的特征与乔木相似；但在中等尺度上，分形维数接近于1.5，它们以近似布朗运动的形式变化。虽然乔木和灌木物种丰富度在海拔梯度上变化的尺度范围相似，但决定它们的主要生态过程完全不同，或相同的生态过程以截然不同的方式作用于两种不同的植物类群。总的植物物种丰富度在整个尺度范围内呈现标度不变性，这可能是由于决定其变化的生态过程作用尺度紧密相关，也可能因为该文研究范围的局限性。
Using non_brown fractal model, this study was tailored to quantify and compare the variations of species richness of trees, shrubs, herbs and total plants along altitudinal gradients and characterize the dominating ecological processes that determined the variations. Two transects were sampled far away from any anthropogenic disturbances along the shady slopes of the Dongling Mountains, Beijing, China. Both transects were continuous and 2 m wide, and every individual tree and shrub was recorded in each transect. Discrete quadrats of 1 m×1 m were located along transect A and B for estimation of herb species richness along the altitudinal gradients. The bevel interval between the quadrats was 10 m and 25 m, respectively. In the present study, transect A and B were combined into one transect AB, and 40 m was selected as optimal quadrat length along the altitudinal gradients for measuring plant species richness patterns. Species richness in each quadrat was calculated by a program written in Matlab 6.0. Firstly, direct gradient analysis was used to describe the overall trends in species richness of trees, shrubs, herbs and total plants with changes in altitude, and the non_brown fractal model was used to more accurately detect their variations at various scales along the gradient. The model assumed that each class of ecological processes affecting the distribution of a variable could be represented by an independent spatial random function. Generally, ecological phenomena were determined not by a single ecological process but by multiple ones. These processes acted on ecological patterns at their own spatial scales. In the non_brown fractal model, the spatial random functions were nested within a larger range of spatial scales. The relative contribution of spatial random functions to the spatial variation of a variable was indicated by a weighting parameter that had to be greater than or equal to zero. In this paper, we reached the following results and conclusions. Firstly, the direct gradient method described the general trends of trees, shrubs, herbs and total plants along the altitudinal gradient but was unable to provide more detail about altitudinal variations of species richness. The non_brown fractal model uncovered altitudinal variations in species richness of trees, shrubs and herbs at various scales and related them to ecological processes. The sharp changes in the double_log variograms suggested that the non_brown fractal model was advisable for characterizing the altitudinal patterns in species richness of trees, shrubs and herbs at various scales but not appropriate for explaining the variation of total plant species richness, because there was no obvious sharp change in its double_log variogram. Secondly, for trees, the double_log variogram was divided into two scale ranges (0-245 m and 245-570 m), with a fractal dimension of 1.83 and 1.10, respectively, implying that changes in tree species richness was nearly random at small scales (0-245 m) and nearly linear at large scales (245-570 m) along the altitudinal gradients. This suggested that altitudinal variations in tree species richness were dominated by short_range processes at small scales and by long_range processes at large scales. Thirdly, for shrubs and herbs, the double_log variograms exhibited three sections (0-101 m, 125-298 m a nd 325-570 m), and the fractal dimensions were 1.78 and 1.97, 1.56 and 1.43, a nd 1.08 and 1.25, respectively.