Scale dependency and the expression of hierarchical structure in Delphinium patches

Abstract

Hierarchy theory has provided a valuable conceptual framework for studies of heterogeneity. However, there have been few empirical studies of hierarchical structure and little is known about how hierarchical structure originates or varies among systems. Here, I explore how scale dependency can influence the detection of hierarchical structure. Specifically, I compared how heterogeneity changed with scale in patches of larkspur (Delphinium spp). The distribution of Delphinium nelsonii inflorescences was quite uniform over the range of measured scales (1 m2-2500 m 2) and only a single level of patchiness was observed. Aggregations ofD. barbeyi inflorescences were much more pronounced and this patchiness was evident at many scales. The number of hierarchical levels and the scales at which patchiness occurred varied both within and between plots ofD. barbeyi. Because patchiness was not strongly scale-dependent for either species, discrete patch boundaries and well-defined hierarchical levels were not usually apparent even when multiple scales of patchiness were present. In several cases, the scales of detected patchiness depended on the difference in scale between grain (resolution) and extent. I predict that because of the lack of dominant and strongly scale-dependent processes, microlandscapes such as Delphinium meadows, may be less likely to exhibit well-defined hierarchical structure than larger-scale landscapes, especially those heavily altered by human activities.

Variation in timing and abundance of flowering by Delphinium barbeyi Huth (Ranunculaceae): the roles of snowpack, frost, and La Niña, in the context of climate change

“…Plants produce multiple stems each year, about 1 m tall. Stems bearing inflorescences are about 1.5 m tall with dense racemes of dark purple flowers visited by bumblebees and hummingbirds (Inouye 1978;Wright 1988;Kotliar 1996). Mean date of flowering (first flower) is about 15 July in our study site, about 1 month after its congener D. nuttallianum.…”

Scale of Disturbance and the Structure of a Temperate Fish Guild

“…3 bance, over a wide range of spatial scales (Chaneton and Facelli 1991, Clark 1991, Hiura 1995. While descriptive studies have frequently examined patterns in relation to changes in the spatial extent of sampling (e.g., Fowler et al 1992, Morrisey et al 1992, Migné and Davoult 1995, the effects of changes in the spatial scale (the grain) of sampling on the perception of patterns have been less frequently investigated (but see Schneider and Duffy 1985, Schneider and Piatt 1986, Moody and Woodcock 1995, Kotliar 1996, Qi and Wu 1996, Obeysekera and Rutchey 1997, Riitters et al 1997. While descriptive studies have frequently examined patterns in relation to changes in the spatial extent of sampling (e.g., Fowler et al 1992, Morrisey et al 1992, Migné and Davoult 1995, the effects of changes in the spatial scale (the grain) of sampling on the perception of patterns have been less frequently investigated (but see Schneider and Duffy 1985, Schneider and Piatt 1986, Moody and Woodcock 1995, Kotliar 1996, Qi and Wu 1996, Obeysekera and Rutchey 1997, Riitters et al 1997.…”

Implications of a Hierarchical Relationship Among Channel Form, Instream Habitat, and Stream Communities for Restoration of Channelized Streams

“…Future research needs to examine if the relationship among these components changes as the scale of observation is altered because of the hypothesized scale-dependency of hierarchical relationships (Kotliar, 1996;O'Neill & King, 1998). Regardless of the potential influence of scale, our study suggests the assumption implicit within the design of many restoration projects in channelized streams of the southeastern United States may not be appropriate.…”

“…However, only a few studies have used hierarchy theory to develop research hypotheses and predictions (Kolasa, 1989;Taylor et al, 1993;Vaughn & Taylor, 2000). Therefore, there is a limited amount of information on the presence of hierarchical structure in streams and other ecosystems (Kotliar, 1996).…”