## Scale and Ecosystems

Scale has at least two meanings that relate to measurement of objects in ecological systems. One meaning of scale is the unit of measurement in any dimension. Much of ecosystem ecology is measured along dimensions of space and time. As such, meter and foot are different scales of measurement in space, and seconds and years are similar units in time. Ecosystem structures and processes are measured using multiples or fractions of these units. For example, the diameter of a tree is measured using scales of meters, centimeters, and millimeters. The other definition of scale has to do with ratios among measured units and is derived from the Latin word scalaris for ladder. For example, if the scale of a map is 1:250 000, then 1 cm on the map equals 250 000 cm on the ground. Both of these meanings suggest that relationships among units are set, so conversions can be made among units. The second meaning of scale, related to relationships among ecosystem components, is germane to panarchy, but requires defining two more terms.

Two other concepts are useful in understanding scales in ecological systems: grain and extent. Grain is defined as the unit of the smallest resolution of measure for a given system dimension. The resolution of a successional study may be a day or week in the time domain, at an area of a square meter in the spatial domain, depending upon what is being measured (species composition within a meter quadrat). The extent defines the bounds of measurement of a system under study. Continuing the successional study example, some long-term studies of forests may be multiple decades or even a century in extent. For two-dimensional spatial data, such as a map, the extent is also called the window of the map. In temporal data, the grain is usually defined as the minimal time unit, such as minute, day, or year, and the extent is the period ofrecord used in analysis. Therefore, scale ranges can be determined by two components: the grain and extent.

One of the key features of ecological systems is that the components (structures and processes) cover large ranges of scales in both space and time. For example, the Atlantic Ocean ecosystem covers thousands of kilometers from the equator to almost the poles. Biological entities in the ecosystem range from the microbes whose volumes cover fractions of cubic micrometers to masses of Sargassum that cover thousands of cubic kilometers. In the time domain, the processes in the Atlantic Ocean vary from milliseconds to millenia.

One way of examining how ecological systems vary over scales of space is to map key structures and processes along dimensions of space and time. Ecosystem components can be mapped using the grain and extent to define ranges in these two dimensions. Across a range of scales in forested systems, leaves, branches, and trunks make up trees, trees make up stands, stands make up forests, forests make up landscapes, and landscapes comprise biomes (Figure 1a). This can be identified as a vegetation hierarchy. Atmospheric hierarchy is comprised of similar structures (thunderstorms, frontal waves, El Nino Southern Oscillation) that cover ranges of scales.

A cross-scale examination of ecosystems leads to three observations. The first is that as the grain and extent of observation change, different objects (structures and processes) cover distinct scale ranges. For example, aerial photographs of forest stands cannot capture the detail of leaves (at smaller grains), nor spatial biome patterns (at larger extents). The second observation is that scalable processes and structures cover different extents in space and time. Some processes such as forest fires range from scales of a square meter to thousands of square kilometers. Other processes such as changes in carbon dioxide concentration in the atmosphere cover 20 or so orders of magnitude, from the cubic centimeters of cylinders in millions of internal combustion engines, to fossil-fuel-powered plants to regional-scale land clearing. The third observation is that ecological systems are comprised of self-organized processes that are not scale invariant; that is, they are not self-similar across scales (as measured by a constant fractal dimension). While many physical systems are self-similar or scale invariant, ecological ones are not because of the interaction between biotic and abiotic elements. Hence ecological systems are discontinuous in dimensions of space and time. These three observations lead to theories of cross-scale structures, described as hierarchy and panarchy theory.

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