Spatial heterogeneity in a grassland community: Use of power law

Abstract

A new regression analysis was proposed to evaluate the degree of spatial heterogeneity for individual species comprising a plant grassland community. The weighted average of the heterogeneity value of all the species comprising the community provides a measure of community‐level heterogeneity. A field survey was carried out, as an example, in order to analyze the spatial heterogeneity of a pasture with grazing cows, using 100 quadrats 50 cm × 50 cm, each of which was divided into four smaller quadrats 25 cm × 25 cm, on a 50 m long line‐transect. The frequency of occurrence for all the species in each small quadrat was recorded. The regression associated with the ratio of the theoretical and observed variances of occurence counts was used to analyse the frequency distribution of species in a pasture community. A good fit to the regression for the whole community was obtained. These results indicate that (i) each species in the example was distributed more heterogeneously than a random pattern; and (ii) the regression could well describe the spatial heterogeneity of the grassland plant community. In most of the observed species, spatial heterogeneity is often characterized by species‐specific propagation traits and the architecture of plant bodies. Thus, the spatial patterns of a grassland community can be evaluated in detail by this power‐law approach. This measure is suitable for field surveys and comparative studies of grassland communities, and for other plant communities that are generally short in height.

Spatial heterogeneity and diversity of vegetation at the landscape level in Inner Mongolia, China, with special reference to water resources

“…The (adjusted) power law (Madden and Hughes, 1995;Shiyomi et al, 2001) was applied to analyze the communitytype spatial heterogeneity. The sample mean and variance for community type i in a landscape are expressed as m i and v i , respectively.…”

“…Shiyomi et al ( , 2001 and proposed simple methods to measure spatial heterogeneity that have been successfully applied to the analysis of grassland vegetation Wang et al, 2002;Yasuda et al, 2003;Shiyomi et al, 2004;Chen et al, 2005;Tsuiki et al, 2005;Chen et al, 2006) and landscape-scale analyses using vegetation and land-use maps (Huang et al, 2004;Hori et al, 2005;Song et al, 2005). Here, we used the power law (Madden and Hughes, 1995;Shiyomi et al, 2001) as a statistical model to determine the macro-scale spatial heterogeneity of vegetation within and among landscapes with special reference to water resources.…”

Analysis of Grassland Vegetation of the Southwest Heilongjiang Steppe (China) Using the Power Law

“…The power law was extended by Shiyomi et al (2001) to deal simultaneously with many plant species from a vegetation survey. Herein, we let the sample mean and sample variance for species i be expressed as m i and v i , respectively.…”

Is the patch size distribution of vegetation a suitable indicator of desertification processes?

“…Recent modeling studies have shown that the patch size distribution of arid and semiarid vegetation can be described using power law distributions (Ke´fi et al 2007a, Scanlon et al 2007) and that deviations from such patterns (e.g., from a power law to a truncated power law) could be used as an early-warning signal to monitor desertification processes (Ke´fi et al 2007a). These findings are appealing because power laws occur in other ecosystems (Shiyomi et al 2001, Sole´and Bascompte 2006, Bridges et al 2007) and because their use could represent a significant step toward the development of a sound and widely applicable desertification monitoring system. Despite their potential implications, the suggestions of these studies have not been widely validated, and it is largely unknown how variations in power laws are connected to ecosystem functioning and desertification processes under field conditions (Sole´2007).…”