Boundary locations reflect complex underlying physical, biomedical, and/or social processes. Boundary analysis allows investigation of complex and dynamic spatial processes.
Boundary analysis has been used to study genetic hybrid zones in population biology (Endler 1977), where gene frequency boundaries exist at the interface between populations; zones of rapid change in species abundance in ecological communities (Fortin 1992); landscape boundaries in conservation biology (Hansen and di Castri 1992; Fortin 1994; Holland et al. 1991), which represent contact zones between distinct ecosystems; and retroviral molecular data (Bocquet-Appel unpublished manuscript), which may lead to new hypotheses regarding gene expression.
Bocquet-Appel (unpublished manuscript) applied boundary analysis to the geographic distribution of retroviral mutations. He analyzed the env gene of HTLV-1 retroviruses sampled from human populations at 22 African locations. Boundary analysis revealed that zones of rapid change in the env gene overlaid the geographic edge of the tropical rain forest, leading to new hypotheses regarding env gene expression. He concluded that boundary analysis might be used to explore spatial relationships between geographic zones of pathogen (e.g. ribovirus, bacteria) molecular genetic variation and the spatial pattern of pathology in host populations.
Another application is the identification of spatial boundaries demarcating zones of rapid change in cancer mortality. These boundaries define the geographic extent of areas with high mortality. Brown et al. (1995) conducted an etiologic study of bladder cancer that used mortality maps to identify the study population. Other areas of potential application include air pollution and respiratory illness (Bates and Sizto 1983; Buffler 1988; Bates et al. 1990; Dockery et al. 1993), environmental risk factors and cancers (Najem et al. 1985; Carpenter and Beresford 1986; Jacquez and Kheifets 1993), and agricultural and industrial exposures and cancer (Blot and Fraumeni 1977; Matanoski 1981; Stokes and Brace 1988; Linos et al. 1991; Nuckols et al. 1996).
Potential applications of boundary analysis within the relatively new field of spatial epidemiology are numerous and rich. Zones of rapid change in cancer outcomes can be caused by underlying differences in genetic composition, risk behavior and environmental exposures. Thus, boundary analysis provides a basis for formulating and testing spatio-epidemiologic hypotheses. Further, several boundary detection methods are multivariate, and data for multiple diseases, such as cancers at different body sites, can be analyzed simultaneously against exposure data and genetic data from several loci. Boundary analysis has applications for defining zones of rapid change in cancer outcomes (e.g. mortality); for determining whether these zones are statistically unusual; and for testing them against population genetic boundaries in oncogene expression and against edges of areas with high carcinogen concentrations. However, to date applications in the analysis of health data are relatively few. This lack of examples is at least partly attributable to lack of familiarity with boundary analysis techniques.
In ecology, boundary detection is appropriate for finding vegetation zones (Fortin 1994, Fortin et al. 1996, Fortin 1997), which is important in conservation and planning and in other hypothesis-driven research. Boundary analysis is also the ideal tool for investigating 'edge effects', which are differences in ecological processes that occur at or near ecosystem or habitat boundaries. For example, Kupfer et al. (1997) studied factors affecting woody species composition in forest gaps in western Ohio, and found that composition was influenced not only by commonly cited factors such as disturbance patterns and environmental measures, but also by proximity to forest edges.
Recent increases in forest fragmentation and declines in Neotropical migrant bird populations have given rise to much work on edge effects on avian nest success in fragmented landscapes. In a review of the accumulated research on the subject, Paton (1994) found that although some studies report inconclusive results, there is substantial evidence that nest success decreases in edge communities, due to increased brood parasitism by Brown-headed Cowbirds and increased nest predation. Robinson et al. (1995) monitored 5,000 nests in landscapes with varying levels of fragmentation across the U.S. Midwest, and found that nest predation and mortality rates were strongly and negatively correlated with percent forest cover. Donovan et al. (1997) investigated the causes of variation in edge-effect study results, and suggested that landscape context, host abundance, and predator assemblages can influence the strength of such edge effects. Paton (1994) also explained that some research has been compromised by relatively arbitrary edge detection techniques, highlighting the need for more widespread use of appropriate boundary detection methods.
As an analytical tool, boundary analysis is probably best used as a complement to existing spatial techniques, such as clustering and spatial autocorrelation analysis. In many cases boundary overlap analysis (Jacquez 1995) may be a more appropriate measure of spatial association than models such as correlation and regression, which are built on the assumptions of linearity and/or normality. Furthermore, boundary coincidence can be conducted for data sets that do not use the same sampling regime, conferring an additional advantage over other techniques. For many research questions, boundaries and boundary overlap are the logical objects of study.
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