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Vegetation patterns often resemble the pattern of the geological substratum. In some cases, however, correlations between soils and vegetation in patterned distributions appear to have developed in an initial homogeneous landscape. Here, soil-vegetation feedback processes appear to be responsible for the development of such patterns. In this paper, we discuss various systems and their feedbacks that may lead to formation of patterns. In semiarid systems, soil-water-vegetation feedbacks might lead to Turing-like selforganized pattern formation, as indicated by previously published models. In other cases of patterned soil-vegetation systems, feedback mechanisms may be involved that locally enhance growth of one species and inhibit that of other species. These interactions do not fulfill the criteria of Turing for pattern formation. However, such strong competitive interactions may lead to patterned vegetation as is shown by a study of a competitive model including spreading of the species. This pattern is not due to self-organization but depends on the initial boundary conditions.

The boreal forest covers 14% of the earth's vegetated surface but contains about 27% of the world's vegetation carbon and between 25% and 30% of the world's soil carbon. Unique features of this biome include cold climates, large areas of relatively flat topography, discontinuous permafrost, large and severe fire events, and the accumulation of peat.These characteristics are important in controlling energy and carbon cycling and either influence or are influenced by regional climate and hydrological regimes. Total carbon accumulation within an ecosystem reflects the balance between net primary production (NPP), decomposition, and nonrespiratory losses (dissolved carbon export, fire, and land-use changes). In this chapter, we use soil carbon storage as a long-term estimate of net ecosystem productivity (NEP; the balance between NPP and decomposition) and nonrespiratory losses that integrates annual variability in the ecosystem processes contributing to carbon balance. Our overall hypothesis is that a combination of regional and local physiography creates spatial heterogeneity in hydrology and soil temperatures. Hydrology and thermal regimes, in turn, influence distributions of fire, permafrost, peatlands, and vegetation and ultimately control long-term carbon storage in many boreal climatic zones. Soil carbon storage varies tremendously between boreal stand types or features and is particularly large in poorly drained peatland and permafrost ecosystems. Landscape composition, then, is important for scaling carbon storage in boreal regions. However, whether the configuration of upland and lowland ecosystems influences carbon processes has not been adequately explored but likely is important to variations in carbon emissions during fire. Biological controls such as herbivory and insect outbreaks are important to the distribution of plant species and nitrogen availability in forest ecosystems, but their influence on wetland systems or long-term carbon dynamics is not well understood.

Heterogeneity in urban ecosystems derives from a combination of natural and engineered landscape features, as well as behavior of human individuals and institutions. Modern urban regions in North America and elsewhere are no longer uniformly compact and densely populated but have extended into surrounding regions and include intricate mixes of residential, commercial, and residual agricultural, forest, and other managed and unmanaged vegetated areas. Compared to less developed ecosystems, heterogeneity in water, carbon, nutrient, and energy cycling may be enhanced, specifically over the short distances associated with urban development patterns.We review conceptual approaches to characterizing and representing heterogeneity in urban ecosystems and illustrate some of the main sources of heterogeneity resulting from interactions within and between urban patch networks, with special reference to examples drawn from the Baltimore Ecosystem Study.

Riparian systems epitomize heterogeneity. As transitional semiterrestrial areas influenced by water, they usually extend from the edges of water bodies to the edges of upland terraces. Riparian systems often exhibit strong biophysical gradients, which control energy and elemental fluxes, and are highly variable in time and space.These attributes contribute to substantial biodiversity, elevated biomass and productivity, and an array of habitats and refugia. Focusing on riparian systems of medium-sized floodplain rivers, we describe heterogeneity at multiple space and time scales, illustrate interactions among scales, and propose a conceptual model integrating major system components. We show how climatic and geologic processes shape an array of physical templates, describe how disturbances redistribute materials, and illustrate how soils and subsurface processes form and are sustained. Collectively, these processes strongly influence plant productivity and fluxes of channel-shaping large woody debris (LWD). Ultimately, riparian ecosystem function integrates climate (past and present), geologic materials and processes, soil development and attendant microbial transformations, subsurface characteristics, plant productivity, animal activities, and LWD—and the active, continuous and variable feedbacks between the individual components.

Streams are heterogeneous in both space and time. Hydrologic flowpaths along which biogeochemical processing occurs integrate different patches of the stream. Disturbance events (flood and drying) change these patches, alter connectivity, and reinforce spatial heterogeneity. Heterogeneity within patches (surface stream, hyporheic zone, sand bars, and riparian zone) is generated by the interaction of nitrogen (the limiting nutrient) in transport and organisms such as algae and bacteria.These organisms store nitrogen as they grow, alter N forms and concentrations in transport, and in some cases (e.g., denitrification) export it to the atmosphere. Changes in nitrogen in transport can be large, as are community responses to nitrogen availability, thus reinforcing spatial heterogeneity in successional time. Flowpaths connect patches as well and generate changes in recipient patches as a function of nitrogen delivery rate.This is especially evident at patch boundaries. In streams, flow is markedly linear and inexorably downstream in orientation; however, landscapes are drained by coalescing, dendritic networks that intimately connect stream channels with terrestrial flowpaths over and beneath soils.We propose that a unified theory of landscapes will require a focus on spatial linkage, a consideration of both spatial and temporal heterogeneity, and a blurring of distinctions between terrestrial and aquatic elements.

Lakes, far from being the homogeneous environments we might expect, offer a rich and dynamic heterogeneity at multiple spatial and temporal scales that we are just beginning to understand. At the within-lake scale, a complex set of phenomena such as internal waves and stream intrusions leads to both horizontal and vertical heterogeneity. Developing an understanding of whether and how this heterogeneity affects ecosystem processes is in its early stages, but nutrient movement both horizontally and vertically may be more structured than previously conceptualized and will depend on interactions among nutrient loading, stratification, surface meteorology, and basin morphometry.Within a landscape, lakes often differ from each other both in their average characteristics and in their among-year dynamics. Much of this heterogeneity has been linked to how water flows across the landscape. In landscapes dominated by groundwater flow, there is often more heterogeneity in lake characteristics and response to climatic events than in landscapes where exposed bedrock leads to rapid horizontal transport of water. Humans can affect heterogeneity across lakes by causing changes in land use and cover and within lakes by simplifying the physical structure of the littoral zone.

The occurrence and effects of fire vary greatly over multiple spatial and temporal scales. At a regional scale, variation in synoptic climate and associated vegetation characteristics results in diverse fire regimes, ranging from systems having frequent, low-severity fires (e.g., pine forests of the southwestern and southeastern United States) to systems characterized by infrequent but stand-replacing fires (e.g., subalpine and boreal forests of North America). At a finer scale, spatial variability in fuel mass and structure may influence fire ignition and severity under a middle range of weather conditions, but effects of fuels may be overwhelmed by effects of extreme weather— either extremely wet (no fire) or extremely dry and windy (large, severe fires). Almost all fire events exhibit a heterogeneous pattern of burning and create a mosaic of fire severity within the burned area, resulting in spatially variable changes in plant community structure, soil characteristics, and ecosystem processes of energy and biogeochemistry.We have a pressing need to better incorporate our understanding of spatial heterogeneity into wildland fire policy and management and to address urgent research questions about spatial patterns in fire history, fire effects, and responses of organisms and ecosystems to the spatial variability of fire.

Spatial heterogeneity of ecosystem structure and function is rarely taken into consideration in the management of our planet's freshwater resources. Incorporation of spatial heterogeneity provides a new way to view freshwater resources and leads to potentially useful management strategies. In this chapter, we address the relationship between the management of freshwater resources and spatial heterogeneity by introducing landscape concepts as they apply to water management, developing a conceptual framework, describing how this relationship applies to ecosystem services provided by fresh water, and using a case study that explains the potential relevance of spatial heterogeneity to water management.

In this chapter we ask the question: To what extent does an understanding of landscape spatial heterogeneity inform conservation decisions? We answer this question in the context of two central decision-making fields within conservation biology: systematic conservation planning and population viability analysis.The conservation planning principles of comprehensiveness and representativeness are fundamentally reliant on data and concepts of compositional landscape heterogeneity. The principle of adequacy is not accommodated in conservation planning very well and it relies on an understanding of the configurational heterogeneity of the landscape. A major challenge for conservation planning scientists is to develop theory and decision support tools that incorporate ideas of population viability and spatially explicit ecological processes. Population viability analysis invariably includes spatial population processes, and as a field has largely focused on the importance of the configurational heterogeneity of landscapes. We argue that this focus might only be justified when the scale of planning coincides with either the scale of habitat heterogeneity or the scale at which small populations operate. Integrating population viability analysis into conservation planning, and showing a balanced interest in compositional and configurational heterogeneity, are important future challenges.

Ecological systems usually are heterogeneous, and this heterogeneity has important functional consequences. Nevertheless, it is not always necessary for ecologists to explicitly include this heterogeneity in their studies and models of ecological systems. Heterogeneity may be safely ignored if its grain size is much smaller than the spatial extent over which measurements are integrated or much larger than the spatial extent of the study area. Heterogeneity may be functionally unimportant if the vectors connecting patches are small or slow relative to the time span of the study or if the system is governed by processes with linear dynamics. Further, the heterogeneity expressed by some ecological systems may be amenable to analysis using simplified models. Finally, it may not be efficient to include heterogeneity in study designs or models, even if including heterogeneity would improve the study performance. Despite these considerations, ecologists will need to address heterogeneity explicitly in many cases to achieve a satisfactory understanding of ecosystem functioning, particularly for regional to global scales.