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This chapter lays out the concept and framework for a “patch dynamics” approach and briefly reviews its contributions to describing and quantifying patterns and changes in spatial heterogeneity of bioecological systems. Patch dynamics emerged in ecology as an approach to understanding spatial heterogeneity. Though ecology is its original disciplinary home, patch dynamics resonates with contemporary urban social theory. Consequently, a patch dynamics approach can serve as a critical node of synthesis between contemporary social and ecological approaches for an ecology of cities. Thus, the chapter applies patch dynamics to urban systems and demonstrates how it addresses the drivers of urban systems identified in earlier chapters.

This chapter discusses the historical connections between biophysical ecology and sociological approaches to urban ecology. This historical narrative lays the foundation for linking the study of spatial heterogeneity in the social and economic sciences with the contemporary understanding of spatial heterogeneity in biophysical ecology that is discussed in the next chapter. To provide context to these historical connections, the chapter first gives an overview of contemporary ecology and its subdisciplines. It then describes the Chicago School of urban ecology and some of its critiques. It locates the Chicago School in the context of four dominant biological perspectives that social scientists have used for the study of cities, before concluding this historical narrative in terms of spatial and organizational complexity issues for the study of urban ecological systems.

Heterogeneity is a defining characteristic of landscapes and therefore central to the study of landscape ecology. Landscape ecology investigates what factors give rise to heterogeneity, how that heterogeneity is maintained or altered by natural and anthropogenic disturbances, and how heterogeneity ultimately influences ecological processes and flows across the landscape. Because heterogeneity is expressed across a wide range of spatial scales, the landscape perspective can be applied to address these sorts of questions at any level of ecological organization, and in aquatic and marine systems as well as terrestrial ones. Disturbances—both natural and anthropogenic—are a ubiquitous feature of any landscape, contributing to its structure and dynamics. Although the focus in landscape ecology is typically on spatial heterogeneity, disturbance dynamics produce changes in landscape structure over time as well as in space. Heterogeneity and disturbance dynamics are thus inextricably linked and are therefore covered together in this chapter.

Disturbances contribute to the number and variety of spatial patterns at many scales and disturbance effects are best considered at a particular scale and for specific types of heterogeneity. Hierarchical analyses of scales allow a broader and more realistic integration across spatial scales than measurements of disturbance effects at only a single spatial scale. This chapter examines how spatial dynamics are compared across spatial scales; how disturbances contribute to spatial heterogeneity; the role of dispersal in creating patches; spatial heterogeneity in two very heterogeneous environments (soils and shorelines); the dynamics of habitat patches; and the contrasting spatial patterns derived from natural and anthropogenic disturbances.

Invasive species are one of the most significant threats to native species diversity, and identifying the factors that make places more or less invasible has been one of the most important issues in the study of invasions. Serpentine systems have provided significant insight into the reasons some communities are more invasible than others, because the environment within these systems is often extreme. Spatial heterogeneity, spatial scale, and productivity have all proven to be critical elements in understanding the invasibility of communities. This chapter takes the following elements—spatial heterogeneity, scale, and productivity—and contrasts the contributions of studies in serpentine systems with studies in systems that are not serpentine.

Most studies evaluating relationships between neighborhood characteristics and health neglect to examine and account for the spatial dependency across neighborhoods, that is, how neighboring areas are related to each other, although the possible presence of spatial effects (e.g., spatial dependency, spatial heterogeneity) can potentially influence the results in substantial ways. This chapter first discusses the concept of spatial autocorrelation and then provides an overview of different spatial clustering methods, including Moran’s I and spatial scan statistics as well as different models to map spatial data, for example, spatial Bayesian mapping. Next, this chapter discusses various spatial regression methods used in spatial epidemiology for accounting spatial dependency and/or spatial heterogeneity in modeling the relationships between neighborhood characteristics and health outcomes, including spatial econometric models, Bayesian spatial models, and multilevel spatial models.

This chapter gives some quantitative information about the rates of genetic and environmental deterioration. The first section in this chapter is about history, chance, and necessity, and includes subsections on Lamarckian evolution; the selection of undirected variation; descent; and delection. The second section is about drift and includes subsections concerning the rate of genetic deterioration; two scaled mutation rates; the rate of deleterious mutation; decay of isolate lines in the absence of selection; mutation rate in other replicators; mutation rate in stressful environments; the genomic mutation rate; the effect of mutations; beneficial mutations; the effect of gene deletion on growth; the rate of accumulation of genetic variance in fitness; the replication limit; the size spectrum; the distribution of species abundance; and finally genetic variation and species abundance. The final section is on the rate of environmental deterioration. Subsections in this section concern aggregation; the ecological population concept; dispersal; and the genetic population concept. Five theories of the environment are offered and environmental variation in space; environmental variation over time; and the biotic environment are also detailed.

Prediction of spatial heterogeneity in disease incidence based on measurable spatial factors is a major goal of spatial epidemiology. There are a number of applied goals of these predictions, including appropriately targeting resources for surveillance and intervention and accurately quantifying disease burden. Although spatial heterogeneity is evident in the epidemiology of many diseases, several aspects of the biology of vector-borne diseases amplify this form of heterogeneity. Here, we review several aspects of this biology, highlighting seven distinct ways in which the biology of vector-borne diseases impacts understanding spatial heterogeneity in disease incidence. Whereas traditional methods place emphasis on spatial regression and other forms of statistical analysis of empirical data, the goal here is to offer a perspective on potential pitfalls of analyses that take data at face value and do not acknowledge the complex, nonlinear, and dynamic relationships between spatial patterns of disease incidence and spatial heterogeneity in transmission.

Animal movement is a general strategy for dealing with environmental variability, but takes on a variety of forms according to life history constraints and environmental covariates. This chapter contrasts migration with less regular nomadic movements, and invokes the niche concept for linking the diversity of movement patterns to the resource environment and the mechanisms of movement ecology. The statistical properties of the resource environment are key to understanding the merits of movement strategies in different environments, and particular emphasis is put on dimensions and scales of resource variability and predictability in space and time. While migration is frequently seen as an adaptation to avoiding severe conditions and exploiting predictable spatiotemporal variation in resource abundance, nomadism can be seen as an adaptation to variability and unpredictability rather than severity. An exploratory exposition illustrates how analysis of space-time data on resources can be helpful for explaining diversity of movement patterns.

This chapter focuses on mechanistic theoretical approaches to explain the emergence of ratio dependence at a global scale from various behavioral models of species interaction. It explains how refuges and spatial heterogeneity as well as forms of temporal and biological heterogeneities can lead to a ratio-dependent functional response. It provides a two-patch model that shows by what method donor control can emerge from being a prey refuge and being subject to intense predation. It also discusses how ratio dependence emerges in realistic models of predator-prey interactions where spatial distribution of both the predator and prey is explicitly followed. It highlights application of these models to the explanation of successful biological control of insect pests.

Approaches for tidal-marsh restoration in San Francisco Bay and Delta continue to evolve, with a focus on promoting the natural development of restored marshes. Allowing for natural marsh development enhances the physical and biological heterogeneity of restored marshes, including tidal-channel formation. The scope of restoration efforts within the bay and delta has increased substantially over the last few decades, with large-scale, regional efforts replacing smaller-scale, mitigation-based restoration. There has also been a growing focus on the restoration of brackish and freshwater tidal marshes, rather than just salt-marsh restoration. Finally, climate change has become a major consideration for current and future bay and delta restoration; major restoration concerns for climate change include evaluating its impact on marsh migration and connectivity, carbon sequestration, and invasive species.

Globally, for troglobionts, southern Europe, especially the Dinaric karst, and the Canary Islands are regions of high richness. For stygobionts, southern Europe, especially the Dinaric karst, is a hotspot. Other sites are typically chemoautotrophic and/or phreatic. In Europe and North America, there appears to be a ridge of high troglobiotic and stygobiotic diversity in southern Europe and the southeast United States that corresponds to an area of long-term high surface productivity. In Europe, local diversity is a small component of regional stygobiotic diversity and the importance of spatial heterogeneity, historical climate stability, and productivity are both scale and spatially dependent. Habitat availability seems especially important at smaller scales. The analogy with islands in ecological time is most appropriate at scales smaller than caves, such as seeps or epikarst drips, and the analogy with caves in evolutionary time is more appropriate at larger scales, such as karst basins or contiguous karst areas.

The size of annual outbreaks in seasonally forced host-pathogen systems is poorly understood. We studied contributing factors to the six-fold observed variation in the number of human cases of West Nile virus in New York City in the years 2000–2008. Sampling error and intrinsic noise (demographic stochasticity) explain roughly half of the observed variation. To investigate the remaining sources of variation, we estimated the monthly force of infection from data on the distribution and abundance of mosquitoes, virus prevalence, vector competence, and mammal biting rate at two spatial scales. At both scales, the West Nile virus force of infection was remarkably consistent from year to year. We propose that fine scale spatial heterogeneity is the key to understanding the epidemiology of West Nile virus in New York City.