Scaling effects of grazing in a semi-arid grassland
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Previous studies have demonstrated relationships between spatial scale and spatial pattern and developed general hypotheses of scaling effects. Few studies, however, have examined the interactive relationship between scale and pattern-driving processes such as grazing. The goal of this study is to evaluate scale-dependent patterns across three spatial scales for three grazing intensities over 45 yr and to identify some mechanisms that may be associated with scale related differences. Correlation analysis and analysis of the coefficients of variation indicate that the relationships between units are dependent upon spatial scale and treatment. Across all grazing treatments, the relationship between units of the same scale becomes stronger as the spatial scale is increased. However, the rate of increase in the correlation coefficient is different for each treatment. The coefficient of variation responded inversely across scales with the greatest variation between small-scale units and little difference between the intermediate- and large scales. In addition to different relationships between units at each scale, differences in heterogeneity within treatments over time is illustrated by the relationship between small-scale units within each treatment and their associated larger scale units. The strongest relationship occurred in the heavily grazed treatments where correlation coefficients of small-scale units with intermediate- and large-scale units were ca. 0.60, indicating similar dynamics across scales. For the moderately grazed and ungrazed treatments this relationship varied from 0.40 to 0.47. Results from this study suggest that grazing alters scaling effects. Variability between small-scale units was greatest in the ungrazed treatment which had greater heterogeneity and less predictability than grazed treatments because of the influence of grazing on plant morphology, demography and composition. At the intermediate scale, relationships between units were fairly similar with the least variation occurring in the moderately grazed treatment. Alternatively, variation between large-scale units was greatest in the moderately grazed treatment because of the relationship between rest cycles, weather patterns, and patch grazing. Therefore, grazing can have a positive, a negative, or no influence on heterogeneity between units depending upon the scale of observation. Evaluation of long-term dynamics across these treatments at the same small spatial scale results in different variances within each treatment which may violate assumptions of some statistical and experimental designs. Therefore, evaluations of temporal dynamics should consider scale relative to the relationship between plant size, density and longevity (relative scale).
