Comparison of fractal characteristics of species richness patterns among different plant taxonomic groups along an altitudinal gradient

Abstract

This study was done using the non brown fractal model to quantify and compare the variations in the species richness of trees, shrubs, herbs and all plants along an altitudinal gradient and to characterize the dominating ecological processes that determine the variations. Two transects were sampled far away from any anthropogenic disturbances along the shady slopes of the Dongling mountains in Beijing, China. Both transects were continuous and 2 m wide, and every individual tree and shrub was recorded in each of them. Discrete quadrats of 1 m?1 m were located along the transects A and B for estimation of the herb species richness along the altitudinal gradients. The level interval between the quadrats was 10 m and 25 m respectively. In this study, transects A and B were combined into one transect AB, and 40 m was selected as the optimal quadrat length along the altitudinal gradients for measuring the plant species richness patterns. Species richness in each quadrat was calculated using a program written in Matlab 6.0. Direct gradient analysis was used to describe the overall trends in the species richness of trees, shrubs, herbs and other plants with change in altitude, while the non-brown fractal model was used to detect more accurately 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 are determined not by a single ecological process but by multiple ones. These processes act on ecological patterns within their own spatial scales. In the non-brown fractal model, the spatial random functions are nested within a larger range of spatial scales. The relative contribution of the spatial random functions to the spatial variation of a variable is indicated by a weighting parameter that has to be greater than or equal to zero. In this paper, we reached the following results and conclusions. Firstly, the direct gradient method describes the general trends of trees, shrubs, herbs and all plants along the altitudinal gradient but is unable to provide further details on the altitudinal variations in the species richness. The non-brown fractal model brought out the altitudinal variations in the species richness of trees, shrubs and herbs at various scales and related them to the ecological processes. The sharp changes in the double-log variograms suggest that the non-brown fractal model is suitable for characterizing the altitudinal patterns in the species richness of trees, shrubs and herbs at various scales but is not appropriate for explaining the variations in the plant species richness, since no significant changes were found in the double-log variograms in this case. Secondly, for the 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 the tree species richness were random at small scales (0 245 m) and almost linear at large scales (245 570 m) along the altitudinal gradients. This suggests that altitudinal variations in the tree species richness are 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 ranges (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 indicate that, as in the case of trees, species richness of shrubs and herbs are distributed randomly at small scales and change in a linear manner at large scales although variations in the herb species richness is less heterogeneous than shrub species richness at large scales. Theses results also indicate that species richness of shrubs and herbs change approximately like brown movement at middle scales. The results also suggest that altitudinal variations in the specie richness of shrubs and herbs are dominated by three ecological processes, short-range ecological processes at small scales, long-range ecological processes at large scales, and brown fractal processes at middle scales. Interestingly, comparisons of the variations in the species richness of shrubs and herbs reveal that shrubs and herbs present the same scale range in spatial variation in species richness but display different trends in species richness along the altitudinal gradient, i.e. the shrub species richness decreased with increasing elevation whereas the herb species richness peaked at the mid-high elevation. These patterns suggest that although the scales at which the main processes affect patterns in species richness are the same, the processes are completely different, or the processes are similar but the responses of the shrubs and herbs to the ecological processes are different. Finally, the plant species richness did not show any obvious pattern along the altitude gradient and maintained a constant fractal dimension across all scales, this is perhaps because the processes defining the patterns of plant species richness had similar weights and acted over closely related scales.