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The ecosystem concept has been a powerful tool in ecology, as it allows the use of the quantitative and rigorous laws of conservation of mass and energy in the analysis of entire ecological systems.These laws require delimiting an ecosystem by specifying its boundaries; however, we know that these boundaries are porous and that all ecosystems are open systems that exchange matter, energy, information, and organisms with their surroundings. This openness means that ecosystems defined as spatially separate are in fact interconnected parts of a larger landscape. Once we begin to ask about the source of the inputs or the fate of the outputs, we need to consider the ecosystem in its landscape context.

Understanding the causes and consequences of spatial heterogeneity in ecosystem function represents a frontier in both ecosystem and landscape ecology. Ecology lacks a theory of ecosystem function that is spatially explicit, and there are few empirical studies from which to infer general conclusions. We present an organizing framework that clarifies consideration of ecosystem processes in heterogeneous landscapes; consider when spatial heterogeneity is important; discuss methods for incorporating spatial heterogeneity in ecosystem function; and identify challenges and opportunities for progress. Two general classes of ecosystem processes are distinguished. represent rates measured at a particular location; are assumed to be small relative to the measured response and are ignored. Spatial heterogeneity is important for point processes when (1) the average rate must be determined over an area that is spatially heterogeneous or (2) understanding or predicting the spatial pattern of process rates is an objective, for example, to identify areas of high or low rates, or to quantify the spatial pattern or scale of variability in rates. Lateral transfers are flows of materials, energy, or information from one location to another represented in a two-dimensional space. Spatial heterogeneity may be important for understanding lateral transfers when (1) the pattern of heterogeneity influences net lateral transfer and potentially the behavior of the whole system, (2) the spatial heterogeneity itself produces lateral transfers, or (3) the lateral transfers produce or alter patterns of spatial heterogeneity. We discuss homogeneous, mosaic, and interacting element approaches for dealing with space and identify both challenges and opportunities. Embracing spatial heterogeneity in ecosystem ecology will enhance understanding of pools, fluxes, and regulating factors in ecosystems; produce a more complete understanding of landscape function; and improve the ability to scale up or down.

Ecosystem processes are inherently variable in space and time, in part because they occur on a spatially heterogeneous template or landscape. For many purposes, the patterns of heterogeneity can be characterized as gradients, patchworks, or networks—or some combination of these fundamental patterns. Each class of landscape pattern implies that it has been generated by certain kinds of abiotic or biotic mechanisms, which can be described by particular mathematical formulations.We illustrate these points with a few selected, ecologically relevant examples. Quantitatively characterizing the patterns of variation in the template and understanding their causes, correlates, and consequences are important steps in investigating the influence of spatial heterogeneity on the structure and function of ecological systems at all scales from molecular to global.

Landscapes are spatially dynamic because materials and energy spread over them and change the distribution of ecosystem properties.This heterogeneity of the distribution of ecosystem properties can either be random or patterned. The landscape becomes patterned when the spread of materials and energy correlates an ecosystem property in one local neighborhood with that at another.When the spread of materials and energy does not correlate properties of different neighborhoods, then the landscape can still be heterogeneous but random.Various processes that result in spatial heterogeneity include physical disturbances (e.g., fire, erosion, etc.) that spread across neighborhoods and remove materials but whose spread is partly determined by previous disturbances; directional gradients in the flow of materials, energy, or information; and different diffusion rates of coupled ecosystem components combined with positive feedbacks, otherwise known as diffusive instability. Examples of these processes will be given from other papers in this conference and elsewhere.

The objective of this paper is to explore the relationships between environmental heterogeneities and the flows and movements that suffuse through all environments. Flows and movements are treated as propagations of ecological influence through environmental space. Propagations are composed of four elements: (1) initiating events or conditions, (2) transport vectors, (3) transported entities, and (4) deposition or impact processes. All four elements have multiple dimensions in type and scale, but vectors are the most convenient means of discussing these phenomena. At a medial level of causation, 10 major vectors are convenient descriptors. These vectors are molecular diffusion; transport by fluvial, colluvial, or glacial modes, gravitational sedimentation, currents (tidal and extratidal), wind (with fire as a special case) agencies; and by electromagnetic radiation, sound, and animal locomotion. Obviously, each of these vector types has different behavior. Propagations can be initiated, or modified by, environmental heterogeneities. But also, propagations can create, maintain, and destroy heterogeneities. Thus, reciprocal cause and effect relationships exist between propagations and environmental heterogeneities. Analysis and understanding of these reciprocal interactions between propagations and heterogeneities requires some understanding of the mechanics of propagations, whether they involve wind, waves, or wallabies. In the same sense, analysis and understanding of how environmental heterogeneities alter propagations requires an appreciation for the global range of heterogeneity types, whether they are ripples, runnels, or run-on patches. Spatially explicit two- and three-dimensional models of propagations in heterogeneous environments are useful ways to develop understanding and, with caveats, to predict how processes and patterns interact. Some of the representational issues of building such models are reviewed in this paper, and three model examples are described.

Historically, population ecologists have equated environmental spatial heterogeneity with habitat spatial structure. Early models represented habitat spatial structure simply as population subdivision into habitat patches. Later models included at first partially and then fully explicit representation of the spatial relationships among habitat patches. More recently, landscape population ecologists have broadened the view of spatial heterogeneity to include the composition and configuration of the whole landscape. A change in landscape composition refers to a change in the cover types in the landscape, the proportions of each, or both. A change in landscape configuration refers to a change in the spatial pattern of cover types, independent of any change in landscape composition. We hypothesize that changes in landscape composition generally have much larger effects on population persistence than changes in landscape configuration. Landscape configuration should have a large effect on population persistence when both (i) configuration has a large effect on among-patch movement of the organism and (ii) among-patch movement has a large effect on population persistence. The first condition should hold for species whose movement direction is constrained, and the second condition should hold either (i) when colonization of empty habitat is important for persistence or (ii) for species that require more than one type of habitat.We discuss extensions of these ideas to the effects of landscape configuration on ecosystem processes.

Heterogeneity of land surface and atmospheric processes contributes to all aspects of the hydrologic cycle. Understanding the types and sources of this heterogeneity is a fundamental component of both theoretical and applied hydrology. Observations of heterogeneity occur at multiple scales ranging from within-canopy variation in water-holding capacity of a single leaf to spatial variation in precipitation at continental to global scales. Consequently, strategies for addressing heterogeneity in hydrologic modeling depend on the scale and type of process being modeled. Further, hydrologic models must address heterogeneity in both inputs and parameters as well as the representation of underlying physical processes. This paper provides an overview of heterogeneity and its implications for hydrologic modeling. Crucial examples of heterogeneity in inputs, parameters, and underlying physical processes are described, and approaches used to deal with heterogeneity within hydrologic modeling are discussed. In particular, the use of effective parameters, probabilistic approaches, and landscape tessellation are described as strategies to address heterogeneity in parameters and inputs. Explicit consideration of process heterogeneity is also considered from the perspective of physically based hydrologic modeling, and the implications for the coupling between hydrologic and ecological process models is discussed.

Infectious disease epidemics in populations are inherently spatial—infectious agents are spread by contact from an infectious host to a susceptible host nearby.Among-host differences can determine which hosts suffer disease and the population dynamics of infectious disease epidemics.From the perspective of the infectious agent, a host is a habitat patch; among-host differences that are epidemiologically important are related to the concepts of compositional and configurational heterogeneity in landscape ecology. Heterogeneous mixing in epidemiology encompasses factors that determine who comes into contact with whom; it is analogous to configurational heterogeneity in landscape ecology. Other sorts of heterogeneity are analogous to compositional heterogeneity, including among-host differences in the duration of an infection, susceptibility to infection, or the amount of an infectious agent that is dispersed from an infected host. In real epidemics, compositional heterogeneity and configurational heterogeneity can introduce an overwhelming amount of complexity. Mathematical modeling provides a method for understanding epidemic processes and for taming the complexity. The idea of epidemic distance is introduced as a way of comparing and contrasting two different epidemic processes, and it is used to compare and contrast some of the mathematical models used to understand the role of space and spatial heterogeneity in epidemiology. In understanding real epidemics, the notion of parsimony is a guiding principle—heterogeneity should be weighed and ignored whenever possible. Several case studies are presented in which compositional and configurational heterogeneity are shown to be important.

In the ocean, the spatial distribution of biogeochemical tracers is affected by their physical transport in the fluid medium. Many tracer distributions such as sea surface chlorophyll and temperature are highly correlated at length scales of 1–100 km on account of a commonality in the transport processes that affect them. We characterize and differentiate between the spatial heterogeneity of the tracers by using a variance-based measure for “patchiness.” When we analyze the satellite-derived fields of surface chlorophyll and temperature, we find that chlorophyll is more patchy than temperature (i.e., a greater proportion of its variance occurs at small scales). We explain such differences in heterogeneity by taking the approach that the observed spatial heterogeneity of a tracer results from a balance between processes that generate variance and those that shift the variance from one length scale to another. The longevity of the tracer determines the extent to which the variance can be shifted to another scale. In the surface ocean, variance introduced at large scales due to geographic variations can be driven to smaller scales by the horizontal stirring and stretching of fluid filaments. On the other hand, small-scale vertical motion associated with fronts introduces small-scale variance that spreads to larger scales if the tracer anomalies are long lasting. For the latter case, we derive a quantitative relationship between a tracer's patchiness and the timescales of processes that modify its concentration in the upper ocean. This relationship links the observed spatial heterogeneity in the system to the processes that contribute to its generation. It lends hope to our being able to use quantitative measures of spatial heterogeneity, like the patchiness parameter defined here, to gain information about processes or, , to predict how the spatial heterogeneity might be modified as a result of a change in processes.

Spatial heterogeneity is a hallmark of vegetation patterns in arid and semiarid landscapes. First observed in terms of the spatial array of vegetation patches, spatial heterogeneity is now more broadly interpreted as the cumulative outcome of the processes affecting the spatial and temporal distribution of vital resources such as water, topsoil organic matter, and propagules individually and collectively. Spatial resource redistribution is shown to be important at a variety of scales varying from millimetres to hundreds of metres and beyond and can be conveniently studied as a nested spatial hierarchy. The processes by which heterogeneous resource distribution arises are a mixture of physical and biological and can be represented by an information-structuring conceptual framework, which is described. Heterogeneity is crucial to the functioning of arid and semiarid lands, and changes in the scale of heterogeneity can be used to study and understand the processes underlying desertification and rehabilitation. Models of heterogeneous landscapes in semiarid landscapes have had two broad themes: a pragmatic approach, describing ecosystem function in landscapes under management, and a curiosity-driven approach, speculating about the development of landscape heterogeneity.