Abstract:

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 and 325-570 m), and the fractal dimensions were 1.78 and 1.97, 1.56 and 1.43, and 1.08 and 1.25, respectively. The results indicated that, like trees, species richness of shrubs and herbs were distributed randomly at small scales and changed in a more linear fashion at large scales although variations in herb species richness was less heterogeneous than shrub species richness at large scales. These results also indicated that species richness of shrubs and herbs changed approximately like brown movement at middle scales. The results also suggested that altitudinal variations in species richness of shrubs and herbs were dominated by three ecological processes, short-range ecological processes at small scales, long-rang ecological processes at large scales, and brown fractal processes at middle scales. Interestingly, comparisons of the variations in species richness of shrubs and herbs found that shrubs and herbs presented the same scale ranges in spatial variation in species richness buu displayed contrary trends in species richness along the altitudinal gradient, i.e. shrub species richness decreased with increasing elevation whereas herb species richness peaked at mid-high elevation. These patterns suggest that although the scales at which the main processes affected patterns in species richness were the same, the processes were completely different, or the processes were similar but the responses of shrubs and herbs to the ecological processes were different. Finally, total plant species richness did not show any obvious pattern along the altitude gradient and maintained a constant fractal dimension across all scales, perhaps because the processes defining the patterns of total plant species richness had similar weights and acted over closely related scales.

Key words: Altitudinal patterns, Biodiversity, Ecological processes, Fractal dimension, Scale, Species richness