A framework and methods for simplifying complex landscapes to reduce uncertainty in predictions

Abstract

Many of our most pressing ecological problems, such as the conservation of biodiversity, spread of invasive species, patterns in carbon sequestration, and impacts of disturbances (e.g., fire) must be addressed at the landscape scale (see Law et al., Chapter 9, Groffman et al., Chapter 10, Urban et al., Chapter 13). However, much of our information about these problems comes from plot-scale studies that must be extrapolated to the landscape. Because landscapes are complex, this extrapolation is not always straightforward or easy to accomplish (Turner et al. 1989a, Wu and Li, Chapter 2, Braford and Reynolds, Chapter 6). Landscape complexity results from the processes, factors, and their interactions that occur across a range of spatial and temporal scales. The problem is further complicated by the presence of contagious or neighborhood processes that connect different parts of a landscape. Dispersal of seeds by wind or animals, fire, and erosion and deposition of soil and nutrients by wind and water are examples of spatial or contagious processes that influence ecosystem dynamics. Landscape complexity makes it difficult to understand and predict ecosystem dynamics across spatial scales with high levels of confidence or certainty. Our goal is to develop a conceptual framework and operational approach to simplifying complex landscapes in order to minimize both prediction errors and costs associated with measurement, analysis, and prediction. A number of methods are available to extrapolate information that differ in the key processes involved (King 1991, Jarvis 1995). There are three main classes of extrapolation methods: (1) nonspatial, (2) spatially implicit, and (3) spatially explicit (Peters et al. 2004). These methods differ in the amount of spatial information required to carry out the analysis. In most cases, the objective of the extrapolation is to obtain a single estimate for an entire landscape. Nonspatial methods are the simplest and contain the fewest parameters. These methods include linear extrapolation where fine-scale information is extrapolated to broad-scales using weighted averages based on the area covered by each type of landscape unit. The classic example is the extrapolation of net primary production from sampled plots to biomes (Leith and Whittaker 1975). Other extrapolation techniques are possible (King 1991). In each case, it is assumed that spatial location on a map and quantification of contagious processes are not needed for the extrapolation. Spatially implicit methods include the importance of spatial location in both the input and response variables. For example, gap models that simulate grassland or forest successional dynamics (Peters 2002, Keane et al. 2001, Symstad et al. 2003), nutrient cycling models (e.g., Burke et al. 1991, 1997), and most biogeographic models currently used to predict vegetation types at regional to global scales (e.g., Neilson and Running 1996, Melillo et al. 1995) are spatially implicit methods. These models typically simulate grid cells that differ in properties such as soil texture, precipitation, and temperature. Simulations are conducted for each grid cell containing a unique combination of parameters. Spatial location is important to the extrapolation because location is used to determine the value of some parameters, but it is assumed that the important processes occur within a grid cell; thus connections among grid cells are assumed to be negligible. Spatially explicit or interactive methods are the most complex in that they require information on spatial location as well as on neighborhood processes. Familiar examples of spatially explicit models include cellular automata (Hogeweg 1988), dispersal models that compute dispersal likelihood in terms of the distance between the target and source sites (Coffin and Lauenroth 1989, Clark et al. 1998, Rastetter et al. 2003), and models of contagious disturbances such as fire and disease (Turner et al. 1989b, Miller and Urban 1999). In each case, simulations are conducted for grid cells that differ in properties such as soil texture and climate. Furthermore, both processes within and among grid cells are important to ecosystem dynamics. Parameter values of a grid cell may depend upon either the identity of its neighboring cells, or specific exchanges of material or individuals among neighboring cells may be modeled explicitly. Each of the three classes of scaling methods has tradeoffs in errors associated with uncertainty. Studies of model error have shown that simple models are often optimal when information is imprecise (O?Neill 1979, Reynolds and Acock 1985). However, more complicated models may be better when dynamics are complex and extensive data are available; yet these data may be expensive to collect and contain a number of small errors that accumulate to produce disproportionately large uncertainties in predictions (Gardner et al. 1980, Li and Wu, Chapter 3). Thus, there are relative trade-offs between errors of omission (high in simple models, low in complex models) and errors of commission (high in complex models, low in simple models) for each method. In general, one should select the simplest method possible that represents the key processes influencing system dynamics in order to minimize both types of error (Peters et al. 2004). Typically, researchers select one method for an entire landscape that depends on the question being addressed. However, the use of one method likely results in high errors of omission for some parts of a landscape, and high errors of commission for other parts. For example, a nonspatial extrapolation will result in high errors of omission for the areas on the landscape where contagious processes are particularly important, such as topographic lows where water accumulates and production is higher than the landscape average. Similarly, using a spatially explicit method for an entire landscape will result in high errors of commission associated with including unnecessary and poorly estimated parameters for those areas where spatial location and contagious processes are relatively unimportant, such as level uplands where dynamics are best explained by precipitation and soil texture. Because each parameter has an associated uncertainty in its estimate, including unnecessary parameters increases the overall uncertainty of the prediction (Peters et al. 2004). Because landscapes consist of a mosaic of sites differing in spatial heterogeneity and degree of connectedness, we expect that a combination of scaling methods is needed to simplify complex landscapes in order to minimize errors of prediction. This general approach is similar to hierarchical scaling strategies (Wu 1999). Linear extrapolations may be most appropriate for the parts of a landscape that are relatively homogeneous. Spatially implicit or explicit approaches are expected to be necessary for those parts with high spatial heterogeneity or connectedness with neighboring sites (Peters et al. 2004). We focus on the important and timely problem of scaling patterns in carbon sequestration and dynamics across semiarid and arid ecosystems to illustrate our approach of combining these methods to simplify landscapes. Recent estimates suggest that the carbon sink in grasslands and shrublands in the coterminous U.S. from 1980-1990 may be similar to that in forests (Pacala et al. 2001). In particular, shrub-dominated ecosystems are important contributors to carbon sinks due both to their extensive area (44% of the total land area of the U.S.) and to their high potential sequestration rates (Hibbard et al. 2001). The area dominated by shrubs and other woody plants has increased worldwide over the past century because of complex interactions among a number of factors, including effects of large and small animals, drought, fire, climate change, and changes in soil properties (Humphrey 1958, Schlesinger at al. 1990, Allred 1996, Van Auken 2000). Increases in above- and belowground carbon storage as well as increases in emissions of NOx and non-methane hydrocarbons (e.g., terpenes, isoprene, and other aromatics) have resulted from the replacement of grasses by shrubs (Archer et al. 2001, Hartley and Schlesinger 2001, Jackson et al. 2002). Estimates for carbon sinks and losses in areas encroached upon by woody plants have a high degree of uncertainty because of landscape-scale variation in edaphic and topographic factors (Pacala et al. 2001, Hurtt et al. 2002). Furthermore, spatial patterns in carbon and other soil nutrients may be complex because of processes such as wind and water erosion, and animal redistribution of plant material and nutrients (Schlesinger and Pilmanis 1998). Our specific objectives were: (1) to illustrate the use of each of the three scaling methods for extrapolating estimates of carbon dynamics based on aboveground net primary production (ANPP) for arid and semiarid landscapes, (2) to examine the key processes and factors leading to heterogeneity in carbon dynamics at the landscape scale, and (3) to develop a framework to identify the landscape locations where each scaling method is most appropriate. © 2006 Springer.