Quantifying Scale in Ecology: Lessons from a Wave-swept Shore

Understanding the role of scale is critical to ecologists’ ability to make appropriate measurements, to ‘‘scale up’’ from local, short-term experiments to larger areas and longer times, to formulate models of community structure, and to address important conservation problems. Although these issues have received increased attention in recent years, empirical measurements of the scales of ecologically important variables are still rare. Here, we measure the spatial and temporal scales of variability of 15 ecologically relevant physical and biological processes in the wave-swept intertidal zone at Mussel Point, near Hopkins Marine Station in California. We analyze temporal variability in wave height, ocean temperature, upwelling intensity, solar irradiance, and body temperature for periods ranging from ten minutes to fifty years. In addition, we measure spatial variation in shoreline topography, wave force, wave-induced disturbance, body temperature, species diversity, recruitment, primary productivity, and the abundances of grazers, predators, and the competitive dominant occupier of space. Each of these spatial variables is measured along three horizontal transects in the upper intertidal zone: a short transect (44 m long with sampling locations spaced at ;0.5-m intervals), a medium transect (175 m long with sampling locations spaced at ;1.7-m intervals), and a long transect (334 m long with sampling locations spaced at ;3.4-m intervals). Six different methods are used to quantify the scale of each variable. Distinct scales are evident in all but one of our temporal variables, demonstrating that our methods for quantifying scale can work effectively with relatively simple, periodic phenomena. However, our spatial results reveal basic problems that arise when attempting to measure the scale of variability for more complex phenomena. For a given variable and length of transect, different methods of calculating scale seldom agree, and in some cases estimates differ by more than an order of magnitude. For a given variable and method of calculating spatial scale, measurements are sensitive to the length of a transect; the longer the transect, the larger the estimate of scale. We propose that the ‘‘1/f noise’’ nature of the data can explain both the variability among methods for calculating scale and the length dependence of spatial scales of variation, and that the 1/f noise character of the data may be driven by the fractal geometry of shoreline topography. We conclude that it may not be possible to define a meaningful spatial scale of variation in this system. As an alternative to the boiled-down concept of ‘‘scale,’’ we suggest that it is more appropriate to examine explicitly the pattern in which variability changes with the extent of measurement (e.g., the spectrum). Knowledge of this pattern can provide useful ecological scaling ‘‘rules’’ even when a well-defined scale (or hierarchy of scales) cannot be discerned.