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In this chapter, Arthur Getis discusses Waldo Rudolph Tobler, one of the world’s leading cartographers, who specialized in mathematical representations of the Earth’s surface. Tobler was among the first to use computers in cartographic and geographic research. He was the inventor of novel and unusual map projections, including a hyper-elliptical, equal area projection that became popular for its ease of use. In one of his publications he made a casual statement about observable earth characteristics: Everything is related to everything else, but near things are more related than distant things. This became known as Tobler’s First Law of Geography. Its profundity comes from his awakening in many scholars the importance of a spatial or distance-related perspective of the world around them.

Large numbers of people are currently migrating from the poor, inland areas of West Coast Africa to the major cities of Lagos, Accra, Abidjan, and other budding metropolises (Figures 1 and 2). The infrastructure of the Sub-Saharan African cities is inadequate to service their burgeoning populations. An argument is presented for using scientifically derived neighborhoods as the building blocks for current African urban understanding and planning. In this paper, I will explore the neighborhood concept and use available data and new heterogeneity statistics to derive homogeneous neighborhoods. The statistics are explained and maps of Accra neighborhoods are given.

This Manifesto provides a joint proposal to create a Regional Science Academy as a think-tank support platform for a strategic development of the spatial sciences. The Regional Science Academy is a strategic spatial knowledge catalyst: it acts as a global intellectual powerhouse for new knowledge network initiatives and scholarly views on regions and cities as vital centrepieces of interconnected spatial systems. This contribution highlights its role and presents various activity plans.

West Africa has a rapidly growing population, an increasing fraction of which lives in urban informal settlements characterized by inadequate infrastructure and relatively high health risks. Little is known, however, about the spatial or health characteristics of cities in this region or about the spatial inequalities in health within them. In this article we show how we have been creating a data-rich field laboratory in Accra, Ghana, to connect the dots between health, poverty, and place in a large city in West Africa. Our overarching goal is to test the hypothesis that satellite imagery, in combination with census and limited survey data, such as that found in demographic and health surveys (DHSs), can provide clues to the spatial distribution of health inequalities in cities where fewer data exist than those we have collected for Accra. To this end, we have created the first digital boundary file of the city, obtained high spatial resolution satellite imagery for two dates, collected data from a longitudinal panel of 3,200 women spatially distributed throughout Accra, and obtained microlevel data from the census. We have also acquired water, sewerage, and elevation layers and then coupled all of these data with extensive field research on the neighborhood structure of Accra. We show that the proportional abundance of vegetation in a neighborhood serves as a key indicator of local levels of health and well-being and that local perceptions of health risk are not always consistent with objective measures.

In keeping with the Annals of Regional Science 50-year tradition of emphasizing spatial analytic contributions, a new statistic, H i , is introduced as an extension of the recent work on map pattern analysis using local spatial criteria. In conjunction with local statistics for the mean level of a spatial process, H i tests for local spatial heteroscedasticity. The statistic measures spatial variability while attempting to avoid the pitfalls of using the non-spatial F test in georeferenced situations. H i is defined and suitably scaled, and an inferential procedure is given. Three artificial cases are explored: a random pattern, a cluster pattern of high values, and a binary-based cluster. The statistic may be used to identify boundaries of clusters and to describe the nature of heteroscedasticity within clusters.

The statistics Gi(d) and Gi*(d), introduced in Getis and Ord (1992) for the study of local pattern in spatial data, are extended and their properties further explored. In particular, nonbinary weights are allowed and the statistics are related to Moran's autocorrelation statistic, I. The correlations between nearby values of the statistics are derived and verified by simulation. A Bonferroni criterion is used to approximate significance levels when testing extreme values from the set of statistics. An example of the use of the statistics is given using spatial-temporal data on the AIDS epidemic centering on San Francisco. Results indicate that in recent years the disease is intensifying in the counties surrounding the city.

Introduced in this paper is a family of statistics, G, that can be used as a measure of spatial association in a number of circumstances. The basic statistic is derived, its properties are identified, and its advantages explained. Several of the G statistics make it possible to evaluate the spatial association of a variable within a specified distance of a single point. A comparison is made between a general G statistic and Moran’s I for similar hypothetical and empirical conditions. The empirical work includes studies of sudden infant death syndrome by county in North Carolina and dwelling unit prices in metropolitan San Diego by zip-code districts. Results indicate that G statistics should be used in conjunction with I in order to identify characteristics of patterns not revealed by the I statistic alone and, specifically, the G i and G i ∗ statistics enable us to detect local “pockets” of dependence that may not show up when using global statistics.

The impetus for Cliff and Ord's landmark article, “The Problem of Spatial Autocorrelation,” was to avoid the problem of topological invariance in the spatial weights matrix. The problem and three points of view on it – theoretical, topological, and empirical – are discussed.

Irrigated urban agriculture (UA), which has helped alleviate poverty and increase food security in rapidly urbanizing sub-Saharan Africa, may inadvertently support malaria vectors. Previous studies have not identified a variable distance effect on malaria prevalence from UA. This study examines the relationships between self-reported malaria information for 3,164 women surveyed in Accra, Ghana, in 2003, and both household characteristics and proximity to sites of UA. Malaria self-reports are associated with age, education, overall health, socioeconomic status, and solid waste disposal method. The odds of self-reported malaria are significantly higher for women living within 1 km of UA compared with all women living near an irrigation source, the association disappearing beyond this critical distance. Malaria prevalence is often elevated in communities within 1 km of UA despite more favorable socio-economic characteristics than communities beyond 1 km. Neighborhoods within 1 km of UA should be reconsidered as a priority for malaria-related care.

We investigated how temporal and spatial effects confound the functional relationship between pupal and adult populations of Aedes aegypti and thus the value of pupal numbers as predictors of dengue transmission risk in Kamphaeng Phet, Thailand. We found considerable seasonal shifts in productivity of key containers. Tires contained much less pupae in the dry season than in the wet season. Earthenware jars and cement tanks for washing purposes were consistent producers over the entire study period. Houses in the two villages, with approximately twice as many houses per unit area, were significantly more likely to have adults and pupae. No significant annual, seasonal, or spatial effects on the strength of correlations between pupal and adult populations were found. Except for 2 (of 16) occasions, pupal, and adult populations were correlated strongly in time and space. Our results are consistent with application of the pupal survey technique for assessing dengue transmission risk.

The concept, spatial autocorrelation, is central to many concerns expressed in Regional Science and Urban Economics. The term, first used in 1967, had precursors embodied in such ideas as distance-decay and spatial interaction. Today, spatial autocorrelation is the mainstay of the burgeoning field of spatial econometrics. Its study has many advantages such as providing tests on model misspecification. The Moran's I statistic is one of many ways spatial autocorrelation can be represented. Interestingly, the concept has yet to make a significant appearance in the mainstream econometrics literature.

Spatial association means connectedness or relationship between and among variables over space (the Earth's surface). A single variable may be spatially autocorrelated ; that is, values of the variable are somehow connected or related spatially. Many variables may be associated with one another at one or more sites. If there is spatial interaction, there is also spatial association. Maps can depict spatial association. A mathematical shorthand technique can be used to represent, in general, measures of spatial association. Scientists test or theorize about variables to determine whether spatial association, either observed or expected, actually can be confirmed. Statistical procedures that have been developed for identifying and measuring the existence of spatial association are outlined.

The creation of a spatial weights matrix by a procedure called AMOEBA, A Multidirectional Optimum Ecotope-Based Algorithm, is dependent on the use of a local spatial autocorrelation statistic. The result is (1) a vector that identifies those spatial units that are related and unrelated to contiguous spatial units and (2) a matrix of weights whose values are a function of the relationship of the ith spatial unit with all other nearby spatial units for which there is a spatial association. In addition, the AMOEBA procedure aids in the demarcation of clusters, called ecotopes, of related spatial units. Experimentation reveals that AMOEBA is an effective tool for the identification of clusters. A comparison with a scan statistic procedure (SaTScan) gives evidence of the value of AMOEBA. Total fertility rates in enumeration districts in Amman, Jordan, are used to show a real-world example of the use of AMOEBA for the construction of a spatial weights matrix and for the identification of clusters. Again, comparisons reveal the effectiveness of the AMOEBA procedure.

As cities of developing nations absorb an increasing fraction of the world's population increase, questions have arisen about the potential for emerging inequalities in health within places that are already suffering from inadequate infrastructure. In this paper we explore the pattern of child mortality inequalities (as a proxy for overall health levels) within a large sub-Saharan African city—Accra, Ghana—and then we examine the extent to which existing residential patterns by ethnicity may be predictive of any observed intra-urban inequalities in child mortality. We find that the spatial variability in child mortality in Accra is especially associated with the pattern of residential separation of the Ga from other ethnic groups, with the Ga having higher levels of mortality than other ethnic groups. Being of Ga ethnicity exposes a woman and her children to characteristics of the places in Accra where the Ga live, in which one-room dwellings and poor infrastructure predominate. At the individual level, w...

A technique of analysis is presented that is designed to circumvent the problem of finding wasy to estimate parameters of spatially stochastic independent variables. It is based on 1) a type of second-order analysis that describes the spatial association among weighted observations, and 2) a screening procedure that removes most of the spatial dependence in the dependent variable. The approach is illustrated by a study of the incidence of certain crimes in 49 districts of Columbus, Ohio. It is concluded that spatial justaposition of observations plays a large role in regression analyses that are based on spatial series.

Large-scale longitudinal cohort studies are necessary to characterize temporal and geographic variation in Aedes aegypti (L.) (Diptera: Culicidae) production patterns and to develop targeted dengue control strategies that will reduce disease. We carried out pupal/demographic surveys in a circuit of ≈6,000 houses, 10 separate times, between January 1999 and August 2002 in the Amazonian city of Iquitos, Peru. We quantified the number of containers positive for Ae. aegypti larvae and/or pupae, containers holding pupae, and the absolute number of pupae by 4-mo sampling circuits and spatially by geographic area by using a geographic information system developed for the city. A total of 289,941 water-holding containers were characterized, of which 7.3% were positive for Ae. aegypti. Temporal and geographic variations were detected for all variables examined, and the relative importance of different container types for production of Ae. aegypti was calculated. Ae. aegypti larvae and pupae were detected in 64 types of containers. Consistent production patterns were observed for the lid status (lids: 32% wet containers, 2% pupal production), container location (outdoor: 43% wet containers, 85% pupal production), and method by which the container was filled with water (rain filled: 15% wet containers, 88.3% pupal production); these patterns were consistent temporally and geographically. We describe a new container category (nontraditional) that includes transient puddles, which were rare but capable of producing large numbers of pupae. Because of high variable pupal counts, four container categories (large tank, medium storage, miscellaneous, and nontraditional) should be targeted in addition to outdoor rain-filled containers that are not covered by a lid. The utility of targeted Ae. aegypti control is discussed, as well as the ability to achieve control objectives based on published but untested threshold values.

RESUME.—La description des morphologies geographiques a depuis toujours retenu l’attention des spatialistes, economistes aussi bien que geographes ; la presente etude reprend ce probleme mais d’une facon purement abstraite. Sur une aire de reference de type fractal, l’on definit successivement des mesures de concentration (ou de dispersion), d’excentricite, du caractere aleatoire, de regroupement (clustering) ; une visualisation des resultats d’ensemble peut etre obtenue a l’aide d’un geophenogramme. Finalement deux exemples concrets sont presentes, l’un pour cinq Etats americains, l’autre pour les douze provinces neerlandaises ; ils montrent que le cadre abstrait developpe peut en fait etre adapte de facon tres souple aux situations concretes rencontrees.

Fertility transitions are historically thought to have started in cities and then spread to the rest of the country. This would suggest that in Egypt we would find that Cairo was well ahead of the rest of the nation in its fertility transition. The data suggest otherwise and highlight the fact that many parts of Cairo are still experiencing high levels of fertility. Population geographers have generally examined differences only between urban and nonurban areas, but incorporating census tract level data from the 1996 and 1986 censuses of Egypt into a geographic information system, we are able to show that there are substantial intraurban geographic variations in fertility within the greater Cairo area. These spatial patterns are indicative of underlying clusters of differences in human reproduction that have important implications for understanding the decline of fertility within Cairo and the spread of that decline throughout the remainder of Egypt.

Geographers increasingly use the Internet as an instructional tool in higher education. The effect of Internet-based instruction on learning, however, is essentially unknown. This research involves a matched-pairs experiment that assesses the differences in student performance between a group of students taking an Internet-based lesson in introductory physical geography, and another group learning the same material via traditional classroom methods. Both groups were subject to the same knowledge assessment post-test, and scores were statistically analysed to determine whether one instructional method led to better student performance over the other. Results show that the Internet can be a viable alternative instructional tool compared with traditional classroom methods.

A fundamental concern of spatial analysts is to find patterns in spatial data that lead to the identification of spatial autocorrelation or association. Further, they seek to identify peculiarities in the data set that signify that something out of the ordinary has occurred in one or more regions. In this paper we provide a statistic that tests for local spatial autocorrelation in the presence of the global autocorrelation that is characteristic of heterogeneous spatial data. After identifying the structure of global autocorrelation, we introduce a new measure that may be used to test for local structure. This new statistic Oi is asymptotically normally distributed and allows for straightforward tests of hypothe- ses. We provide several numerical examples that illustrate the performance of this statistic and compare it with another measure that does not account for global structure.

The rapid advances in computer technology give regional scientists the opportunity to employ data sets that are much larger than those currently in use. Increasingly, metadata are being created in order to give researchers a better understanding of the qualities of data sets. Nonetheless, a number of problems associated with large data sets, outlined in this paper, stand in the way of proper scientific use of the data. Regional scientists should not only take advantage of the new data but they should be prepared to handle the problems associated with them.

The arrangement of trees within a stand by location and age (stand structure) is in part determined by the life history strategy of the species and the disturbance history of the stand. In western North America such disturbances are often the product of wildfires and human management activities. The current study uses spatial analysis to characterize three stands of Pinus torreyana with known disturbance histories. Two stands are located at Torrey Pines State Reserve (TPSR). Of these, one stand has burned twice since 1972. Fire has been successfully excluded from the other stand since the early part of this century. A third stand, on Santa Rosa Island, Channel Islands National Park (SRI), has been grazed heavily since the mid-19th century and has not experienced fire since that time. One-hectare study plots were established in the interior of each stand. Considering the known life history attributes of P. torreyana, and the disturbance histories of the stands, predictions are made concerning the spatial characteristics of the respective stands. All trees within each study plot were sized by diameter breast height (DBH) and mapped. Three techniques of spatial analysis are applied to the resulting unweighted point pattern distributions and the distributions weighted by the square root of DBH as a surrogate for age. The results are consistent with predictions and confirm the following generalizations concerning patterns of aggregation in Torrey pine stands. Young trees tend to be more aggregated than old trees within the same stands. Young stands tend to be more aggregated than old stands on otherwise ecologically similar sites. On a periodically disturbed site there are clusters of trees that represent cohorts of post-disturbance recruitment.

In this paper we estimate the amount by which firms' labor costs are increased by compliance with affirmative action regulations imposed on federal contractors for 160 SMSAs in 1980. The paper focuses on determining the cause(s) for variation in these “compliance costs” across SMSAs and in identifying areas of high and low compliance cost. We find that compliance costs are lower in larger SMSAs, more rapidly growing SMSAs, and SMSAs that have relatively large proportions of minorities and females in the labor market.

Flexibility is what people seek when striving to increase or expand economic and social choices, equity, and technological innovations. Flexibility provides the robustness needed to adjust to changes such as those arising from a warmer/colder world, and the actions required when managing threats from and results of social strife, economic downturns, environmental catastrophes, infrastructure disruptions, and war. Flexibility is easy to praise at the level of principle, if allowed that a bit of stability and resistance to change does have merit. At the level of practice or operations the concept is most elusive, and explaining what flexibility means, why it is thwarted, and how it might be obtained is a challenging task. This paper begins by contrasting views of systems and their behaviors. Alternative explanations for behaviors thwarting flexibility are identified. Consequences of inflexible, locked-in development paths are illustrated using examples from transportation and similar systems. Suggestions for increasing flexibility are made after examining system behaviors in dynamic contexts. Academic, government, and industry experiences inform and color interpretations.

Background Based on spatiotemporal clustering of human dengue virus (DENV) infections, transmission is thought to occur at fine spatiotemporal scales by horizontal transfer of virus between humans and mosquito vectors. To define the dimensions of local transmission and quantify the factors that support it, we examined relationships between infected humans and Aedes aegypti in Thai villages. Methodology/Principal Findings Geographic cluster investigations of 100-meter radius were conducted around DENV-positive and DENV-negative febrile “index” cases (positive and negative clusters, respectively) from a longitudinal cohort study in rural Thailand. Child contacts and Ae. aegypti from cluster houses were assessed for DENV infection. Spatiotemporal, demographic, and entomological parameters were evaluated. In positive clusters, the DENV infection rate among child contacts was 35.3% in index houses, 29.9% in houses within 20 meters, and decreased with distance from the index house to 6.2% in houses 80–100 meters away (p, Author Summary Dengue is the leading cause of mosquito-borne viral infections globally. An improved understanding of the spatial and temporal distribution of dengue virus (DENV) transmission between humans and the principal vector, Aedes aegypti, can enhance prevention programs. Human DENV infection is known to occur at very fine spatiotemporal scales. We sought to link and quantify human DENV infections with infectious mosquitoes at these fine scales by conducting geographic cluster investigations around febrile children with and without DENV infection. We found that DENV infection in children was positively associated with houses in which infectious mosquitoes were captured. These houses also had more Ae. aegypti pupae and adult female mosquitoes than neighboring houses. However, the neighboring houses still had elevated rates of human DENV infection. Our results indicate that certain houses with high risk of DENV transmission contribute disproportionately to DENV amplification and spread to surrounding houses. At a given point in time, people and mosquitoes from a small portion of houses are responsible for the majority of DENV transmission.

Dengue virus (DENV) causes more human morbidity and mortality than any other arboviral disease. Each year, an estimated 3.6 billion people are at risk, 36 million develop dengue fever (DF), 2.1 million develop severe dengue hemorrhagic fever (DHF)/dengue shock syndrome, and 21 000 die [1]. Much of the available epidemiologic and clinical data on dengue are based on passive reporting. An improved understanding of both the patterns of DENV transmission and clinical spectrum of infection would improve public health surveillance and inform mitigation strategies. Prospective cohort studies in Thailand [2–6], Indonesia [7, 8], Nicaragua [9], Vietnam [10], and Peru [11, 12] are addressing knowledge gaps by providing a more comprehensive picture of the spectrum of DENV infection from clinically inapparent infection to severe disease. These increasingly detailed datasets have revealed marked spatial and temporal heterogeneity in the intensity of DENV transmission and the ratio of inapparent-to-symptomatic infections [13]. To further explore the range of DENV infection outcomes, especially with regard to inapparent infections that may contribute to transmission dynamics, we and others have initiated studies incorporating geographic cluster designs [6, 14, 15] in which symptomatic DENV infections trigger sampling of people who live in close proximity to an individual with a documented DENV infection. Geographic cluster studies can elucidate transmission dynamics on a finer spatial and temporal scale than is possible with longitudinal cohort studies, thus allowing increasingly detailed analysis of the factors that affect transmission dynamics. We previously published the findings from the first 2 years of a 4-year combined longitudinal cohort and geographic cluster study in Kamphaeng Phet, Thailand [6]. Those data indicated that DENV transmission in rural locations occurs in a remarkably focal manner and suggested that environmental factors may influence transmission risk. In the current report, we present a more detailed analysis of the full 4-year prospective study, which includes a transition in the predominant circulating DENV serotype. Our results indicate that many DENV infections that were considered clinically inapparent in the longitudinal cohort were, in fact, viremic and therefore potentially contributed to DENV transmission.

Fertility levels remain high in most of sub-Saharan Africa, despite recent declines, and even in a large capital city such as Accra, Ghana, women are having children at a pace that is well above replacement level and this will contribute to significant levels of future population growth in the city. Our purpose in this paper is to evaluate the way in which neighborhood context may shape reproductive behavior in Accra. In the process, we introduce several important innovations to the understanding of intra-urban fertility levels in a sub-Saharan African city: (1) despite the near explosion of work on neighborhoods as a spatial unit of analysis, very little of this research has been conducted outside of the richer countries; (2) we characterize neighborhoods on the basis of local knowledge of what we call "vernacular neighborhoods"; (3) we then define what we call "organic neighborhoods" using a new clustering tool-the AMOEBA algorithm-to create these neighborhoods; and then (4) we evaluate and explain which of the neighborhood concepts has the largest measurable contextual effect on an individual woman's reproductive behavior. Multi-level regression analysis suggests that vernacular neighborhoods are more influential on a woman's decision to delay marriage, whereas the organic neighborhoods based on socioeconomic status better capture the factors that shape fertility decisions after marriage.

This paper explores the supposition that quantitative geography, broadly defined, is the key to the survival of geography as a discipline. Thirteen events of the last 40 years are identified that have laid the groundwork for the success of a number of strong geography departments. These include some of the activities that occurred at the University of Washington, Northwestern University, Bristol University, The University of Iowa, The Ohio State University, the National Science Foundation, and the University of California, Santa Barbara. The elements found in this paper to be crucial for the development of successful departments of geography are: scholars who can mix easily with colleagues in such disciplines as economics, computer science, statistics, and geology; department chairs who commit themselves to high quality quantitative research; and leaders willing to use their energy to recruit high-quality faculty.