Indeed, most ecologists are familiar with relationships among life history characteristics such as longevity, generation time, fecundity and body size in animals.
What is the best way to visualize and verify these operations? How are these operations used in solving ecological problems? Ecologists remain vexed by the need to make predictions at broad scales when most measurements have been made at relatively fine scales. How can it be done and what is the current state of knowledge?
The challenges of scaling up lie in 1 correctly defining the spatial and temporal heterogeneity of the fine-scale information and 2 correctly integrating or aggregating this heterogeneity to the broader scale King, The simplest approach to scaling across space is to multiply a measurement made at one scale e. For example, a standing biomass for a 10,ha forest might be predicted by multiplying the amount of biomass measured in a 1-ha stand by the factor of 10, From a modeling perspective see Chapter 3 , this assumption holds only if the equations describing the system are linear.
This approach should only be used with careful consideration of the potential errors and biases that may result. An improvement on the simple multiplicative approach to scaling is an additive approach that accounts for spatial variability within an area of relatively large extent. King identifies two general methods for this type of scaling.
The first, direct extrapolation, uses data or model simulations from a tractable number of discrete elements within a landscape. For example, instead of assuming that biomass is the same throughout the 10,ha forest, we recognize that biomass varies with stand age and composition and that we can account for this spatial variability by mapping or using a remote image. In this case, we use empirical measurements to estimate the biomass in each type defined and then multiply by the area of each type within the 10,ha forested landscape and sum the results.
Within a modeling framework, King notes that this approach is probably the most widely used. The direct extrapolation approach works reasonably well for quantities such as biomass or net primary production, which themselves do not interact spatially and which can be related to attributes that can be measured remotely over large areas e.
The general algorithm for this approach entails 1 a model simulating local behavior of a system, 2 a larger landscape over which the model is to be extrapolated, 3 the frequency distributions of variables that describe landscape heterogeneity, and 4 calculation of expected values of the system behavior as a function of the variables describing the heterogeneity of the landscape.
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The principal source of error in this approach lies in the estimation of the probability or frequency distributions of the landscape variables. However, like direct extrapolation, the more simple approaches to extrapolation by expected value also do not account for spatial interactions or feedbacks. It is important to note that the error, or variance, associated with the original measurements should also be scaled accordingly to estimate confidence in predictions at the broader scale. However, this problem is easier to recognize than to resolve; confidence intervals around a measurement made at one scale may not translate directly to another scale Schneider, This may occur when the extent of observations is increased and greater environmental heterogeneity is encountered.
Thus, as the grain becomes coarser the cell characterized by a single temperature may also have greater variability. Rastetter et al. The multiplicative approach can be implemented as a first approximation with the recognition that it may work in some cases, but be widely off the mark in others. Additional detail can be added as needed, either through improving the computations at the finer scales Wiens et al.
Landscape ecology in theory and practice: pattern and process
Mandelbrot was the first to point out that simple geometric relationships can be used to quantify changes in the measured properties of objects with changes in scale. The range of scales over which this power-law holds defines the range of self-similarity of the object. Unlike smooth geometric objects squares, circles, etc.
Objects with fractional values of D are therefore referred to as fractals also see Chapter 5. Since introduced by Mandelbrot in , fractals have had an immense appeal and impact for addressing problems of scale and hierarchy Sugihara and May, The fractal nature of many objects has been confirmed see Hastings and Sugihara, , and departures from the power-law relationship have been used to identify scales where processes may alter patterns see Krummel et al.
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A fractal dimension may be estimated for almost any object, but this alone does not guarantee a self-similar or scaling relationship the range of the power-law relationship may be uselessly small. The use of fractals for extrapolating across scales requires two things: estimation of the fractal dimension, D, and verification of the range of the power-law relationship. Although our discussion has emphasized the processes associated with scaling up, that is, moving from fine-scale measurements to predictions at broad scales, the inverse process of scaling down is also important.
However, we know that precipitation and temperature vary considerably within areas that are km by km in size and that this variability is important for local ecological processes Lynn et al. Using a rather different example, tabulations of population density or housing units for a census tract do not account for the spatial variability within the census tract, yet this variation may be most important for predicting future patterns of land-use change or the movement of nutrients from land to water.
Recognition of the importance of developing methods for extrapolating information from coarse to fine grains has increased greatly with the wide use of GIS technologies. However, progress in this arena has been slowed by the immense data requirements for verifying these extrapolations. Scale refers to the spatial or temporal dimension of an object or a process, and this is distinct from level of organization, which is used to identify a place within a biotic hierarchy.
Scale is characterized by grain, the finest level of spatial resolution possible within a given data set, and extent, the size of the overall study area. The related concept of cartographic scale refers to the degree of spatial reduction indicating the length used to represent a larger unit of measure.
In practical terms, the scale at which you make any measurement influences the numerical answer obtained. Scale issues are problematic for several reasons. The magnitude of the task of describing and understanding patterns and processes over large areas is enormous. Because observations are influenced by the scales at which they are made, assembling and comparing data from studies conducted at different scales is tedious and time consuming.
Although considerable progress is being made, general methods for extrapolating information across scales have not yet been established. Hierarchy theory is closely related to scale and provides a framework for organizing the complexity of ecological systems. A hierarchy is defined as a system of interconnections wherein the higher levels constrain and control the lower levels to various degrees, depending on the time constraints of the behavior.
The levels within a hierarchy are differentiated by their rates of behavior. When scales change, a shift in the relative importance of variables or the perceived direction of a relationship may also change. Scale issues often arise in attempting to extrapolate ecological studies to larger or smaller scales.
The current understanding has led to a few useful rules of thumb for extrapolation.
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First, scale changes may be ignored in homogeneous space, but not under conditions of spatial heterogeneity. Average dynamics can be applied to a larger area only when the area is homogeneous for the characteristic of interest. If the spatial heterogeneity is present, but is random rather than occurring with a structured pattern, then the average plus the variance can be used to apply local measurements to the broader area. Second, as long as major processes and constraints do not change, the theory of fractals shows that under certain conditions quantities may be extrapolated across scales.
Third, when spatial heterogeneity combines with nonlinear dynamics and the possibility of major changes in constraints, extrapolation becomes a very difficult problem that does not, at present, have any simple solution. There is no right scale for landscape ecological studies. Scales must be selected based on the question or objective of a study. However, identifying the appropriate scale remains challenging, and developing methods for doing so remains a topic of current research.
Indeed, most of the topics covered in this chapter have many unknowns associated with them. Ecologists are still learning how to take the knowledge we have gleaned about patterns and processes at multiple scales into consideration when developing field studies and models and the techniques for extrapolating across scales and landscapes.
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Select a landscape of your choice and list the important ecological processes that occur in the landscape. Next, estimate the temporal and spatial scales over which these processes operate and plot these in a time—space state space see Figure 2. How might such a diagram assist you in selecting appropriate scales for a field study or model? What scales are appropriate for different hypotheses that you might test? Do you think that scale issues will be of passing or enduring interest to ecologists? Provide a rationale for your opinion.
Describe how scale may be considered as a problem as well as an opportunity. Delcourt, and T. Dynamic plant ecology: the spectrum of vegetation change in space and time. Quaternary Science Review 1: — King, A.
Hierarchy theory: a guide to system structure for wildlife biologists. Bissonette, ed. Wildlife and Landscape Ecology. Effects of Pattern and Scale, pp. Levin, S. The problem of pattern and scale in ecology.
Ecology — DeAngelis, J. Waide, and T. A Hierarchical Concept of Ecosystems. Schneider, D. Quantitative Ecology. Spatial and Temporal Scaling. Academic Press, San Diego, California. Wiens, J. Spatial scaling in ecology.
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