Areal Unit Research Articles

America the Beautiful: Meeting “30 × 30” Conservation Goals Through Connected Protected Areas

Protected areas are a primary instrument for biodiversity conservation, and area-based targets have become a hallmark of global efforts with the 2022 Kunming-Montreal Global Biological Framework recommending at least 30 percent of land and water be protected by 2030. In parallel, the United States has implemented “America the Beautiful,” a call for local, state, and regionally led efforts to conserve, connect, and restore 30 percent of U.S. lands and waters by 2030. Achieving these goals is complicated, however, by the multiple policy scales at which conservation decisions are made and governed and the limited guidance provided on how gains to protected and connected areas should be evaluated. We assess the connectedness of U.S. protected areas at multiple scales and find that less than 3 percent of the United States is protected and connected. Connectedness increases when the area under investigation is partitioned into smaller policy units (e.g., counties), a product of the modifiable areal unit problem. Similarly, connectedness values increase by an order of magnitude when assessed relative to the protected area network rather than considering all land area. Both findings support the need for standardized reporting frameworks and highlight the challenges in coordinating conservation goals across administrative units.

Varying size and shape of spatial units

When an analysis over a specific geographic area is performed, the way that area is divided into regions can affect the outcome of the analysis. Results obtained based on different geographic units can be conflicting. This issue is known as the Modifiable Areal Unit Problem (MAUP). The objective of this paper is to understand the extent to which the regional setting influences the results of an analysis with spatially aggregated variables, with a focus on agglomeration effects, in the case of Germany. Relying on a sample of manufacturing firms over 7 years we estimate a fixed effects model to explain the firm-specific total factor productivity in dependence of region-based agglomeration variables. We simulate 1000 regional settings of Germany on three scales and overtake thereby some characteristics of the administrative units, which are used as the baseline. We infer that the spatial scale and shape matter in the case of Germany.

A Sensitivity Test on the Modifiable Areal Unit Problem in the Spatial Aggregation of Fossil Data

In paleobiology and macroevolution research, the spatial aggregation of fossil data can be influenced by the modifiable areal unit problem (MAUP), wherein the selection of different grid-cell sizes for data aggregation can lead to variations in statistical results. This study presents a case analysis focused on the spatial extent of marine bivalves and brachiopods over time across three Areas of Interest (AOIs) to evaluate the potential impact of the MAUP in grid-based fossil data processing. By employing rectangular grid matrices with cell sizes of 50, 100, 200, and 400 km, this research assesses the MAUP-related sensitivity of two commonly used grid-based proxies for species’ spatial distribution. The results reveal that the proxy based on the number of occupied grid cells (OGCs) is particularly sensitive to changes in cell size, whereas the proxy based on minimum-spanning-tree distance (MST distance) demonstrates greater robustness across varying grid scales. This study underscores that when constructing proxies for species’ spatial distribution ranges using grid matrices, the OGC method is more susceptible to MAUP effects than the MST distance method, warranting increased caution in studies employing the OGC approach.

Some critical thinking on the integrative assessment of ecosystem service supply and demand relationships.

In the past decade, research on the relationships between the supply and demand of ecosystem services has been flourishing. To address issues such as the misuse of supply and demand concepts, methods, and results in current research, we proposed five key aspects that need to be considered to enhance the scientific rigor and practical value in assessing relationships between ecosystem service supply and demand. Firstly, it is essential to clarify the distinctions and connections between the concepts related to ecosystem service supply and demand, which are crucial prerequisites and starting points for assessing their relationships. Secondly, it is necessary to integrate relevant environmental standards or policy objectives to develop reliable methods for assessing the demand for ecosystem regulating services. Furthermore, it is important to properly address the modifiable areal unit problem by determining the most appropriate spatial scale and unit for evaluating relationships between ecosystem service supply and demand. Additionally, it is crucial to differentiate between quantitative and qualitative methods for characterizing (im)balances or (mis)matches between ecosystem service supply and demand, particularly avoiding the use of qualitative methods to represent quantitative relationships between supply and demand. Lastly, it is imperative to integrate ecosystem service flows into the assessment of supply and demand relationships, and evaluate the dynamic supply and demand relationships of regional ecosystem services from a coupled "supply-flow-demand" perspective.

Bayesian spatio-temporal modeling of the Brazilian fire spots between 2011 and 2022

Wildfires are among the most common natural disasters in many world regions and actively impact life quality. These events have become frequent due to climate change, other local policies, and human behavior. Fire spots are areas where the temperature is significantly higher than in the surrounding areas and are often used to identify wildfires. This study considers the historical data with the geographical locations of all the “fire spots” detected by the reference satellites covering the Brazilian territory between January 2011 and December 2022, comprising more than 2.2 million fire spots. This data was modeled with a spatio-temporal generalized linear mixed model for areal unit data, whose inferences about its parameters are made in a Bayesian framework and use meteorological variables (precipitation, air temperature, humidity, and wind speed) and a human variable (land-use transition and occupation) as covariates. The meteorological variables humidity and air temperature showed the most significant impact on the number of fire spots for each of the six Brazilian biomes.

The MAUP and the effect of industrial diversity on Brazilian regional economic stability

The correlation between industrial diversity and regional economic stability is theoretically expected to be positive, suggesting that a region with greater industrial diversification will be less affected by exogenous shocks, resulting in less economic instability. Historically, however, empirical studies have produced mixed results, often finding a lack of significance in the correlation. Among the possible reasons that can lead to such divergence, this study focuses on the Modifiable Areal Unit Problem (MAUP), highlighting the importance of changes in geographic scale on the results due to spatial interference of data. To conduct this study, spatial econometrics and data from the RAIS and Demographic Census are used to collect information from Brazilian municipalities, micro-regions, and meso-regions between 2010 and 2019. The results show spatial influence at all geographic levels, as well as variation in the magnitude, significance and direction of the correlation depending on the scale used, confirming the hypothesis of MAUP in the study. Furthermore, the municipal level was the only one that presented results more consistent with the theory in the Brazilian case.

The relationships between Urban Tree Canopy Cover and Crime in São Paulo City, Brazil

Prior research has indicated lower crime rates in areas with greater tree canopy cover predominantly in the Global North. There are few studies from the Global South, and more specifically in Latin America. Given the high prevalence of crime in Latin American cities, the need to address social and environmental inequalities using nature-based solutions is urgent. This study examines crime and tree canopy cover through a series of spatial analyses for São Paulo city, Brazil, while controlling for potential confounders. We tested six levels of data aggregation that were combined with three different crime types and two denominators of crime, to account for spurious findings from Modifiable Areal Unit Problems (MAUP). Of the 36 models, a majority of 27 models (75 %) indicate a negative relationship between crime and tree cover canopy, while 4 models (11 %) show a positive correlation, and 5 models (14 %) suggest no statistically significant relationship. Our best models allow us to infer that 10 % greater tree canopy cover is associated with a 1.20 % fewer property, personal and total reported crimes, with statistical significance at the p < 0.001 level. These findings support our hypothesis that there is a negative relationship between tree canopy cover and crime, with a stronger association observed for property crime than personal or total crime. The negative relationship persisted independently of the level of data aggregation, crime types, crime denominator and spatial models specifications (lag and SARMA), avoiding statistical bias of MAUP. The results follow the literature that have observed tree cover associated with lower crime rates, for different types of crime, while adding a new climatic and cultural context to the evidence base.

Tackling the modifiable areal unit problem: Enhancing urban sustainability through improved land surface temperature and its influencing factors analysis

Exploring the modifiable areal unit problem (MAUP) in land surface temperature (LST) and its influencing factors is crucial for understanding LST variation patterns and quantifying the factors' impact. Neglecting the MAUP could lead to an incomplete understanding of LST changes and their driving mechanisms. This study used optimal parameters-based geographical detector and gradient boosting regressor models to investigate the MAUP in LST and its influencing factors. The analysis covered 87 cities across seven climate zones in China, examining MAUP in 12 spatial scales to discern the scale and zoning effects on LST and its influencing factors. The research findings were as follows: (1) The sensitivity of LST influencing factors to spatial scales exhibited both spatial and temporal heterogeneity. Significant differences in the q-values of LST influencing factors were observed across various climate zones and periods (daytime and nighttime), with human factors, particularly those related to residents' work, buildings, life, and rest, showing higher spatial scale dependency than natural factors. (2) Zoning effects significantly impacted the q-values of LST influencing factors and were closely linked to the discretization methods and quantities used, which could alter the trends of these q-values. (3) Across the 12 spatial scales, more than 67.34 % of LST influencing factor interaction types were classified as bi-variable enhancement types. The q-values for LST influencing factor interactions were higher and more stable than those of single factors. LST influencing factor interactions in transitional climate zones exhibited high sensitivity to spatial scales. This research enhances our understanding of LST variations, providing valuable insights for urban climate adaptability planning and the development of climate-resilient cities.

Investigating the Nonlinear Effect of Land Use and Built Environment on Public Transportation Choice Using a Machine Learning Approach

Understanding the relationship between the demand for public transportation and land use is critical to promoting public-transportation-oriented urban development. Taking Beijing as an example, we took the Public Transportation Index (PTI) during the working day’s early peak hours as the dependent variable. And 15 land use and built environment variables were selected as the independent variables according to the “7D” built environment dimensions. According to the Modifiable Areal Unit Problem (MAUP), the size and shape of the spatial units will affect the aggregation results of the dependent variable and the independent variables. To find the ideal spatial unit division method, we assess how well the nonlinear model fits several spatial units. Extreme Gradient Boosting (XGBoost) was utilized to investigate the nonlinear effects of the built environment on PTI and threshold effects based on the ideal spatial unit. The results show that (1) the best spatial unit division method is based on traffic analysis zones (TAZs); (2) the top four explanatory variables affecting PTI are, in order: mean travel distance, residential density, subway station density, and public services density; (3) there are nonlinear relationships and significant threshold effects between the land use variables and PTI. The priority regeneration TAZs were identified according to the intersection analysis of the low PTI TAZs set and the PTI-sensitive TAZs set based on different land use variables. Prioritized urban regeneration TAZs require targeted strategies, and the results of the study may provide a scientific basis for proposing strategies to renew land use to increase PTI.

Overcoming the MAUP: impact of agglomeration economies on regional performance in Germany

ABSTRACT This study analyses the impact of agglomeration economies on employment growth at the individual firm and regional levels. The analysis is based on a sample of German firms, comprising a total of 134,081. We put forward a Modifiable Areal Unit Problem-free (MAUP-free) approach for the calculation of individual firm-specific agglomeration and local growth measures based on kernel density estimates. This enables us to examine the impact of agglomeration on firm and local growth within a continuous space framework. The econometric analysis demonstrates that the effects of agglomeration economies on firm and local growth are significantly disparate.

The Complexity of Finding and Enumerating Optimal Subgraphs to Represent Spatial Correlation

Understanding spatial correlation is vital in many fields including epidemiology and social science. Lee et al. (Stat Comput 31(4):51, 2021. https://doi.org/10.1007/s11222-021-10025-7) recently demonstrated that improved inference for areal unit count data can be achieved by carrying out modifications to a graph representing spatial correlations; specifically, they delete edges of the planar graph derived from border-sharing between geographic regions in order to maximise a specific objective function. In this paper, we address the computational complexity of the associated graph optimisation problem. We demonstrate that this optimisation problem is NP-hard; we further show intractability for two simpler variants of the problem. We follow these results with two parameterised algorithms that exactly solve the problem. The first is parameterised by both treewidth and maximum degree, while the second is parameterised by the maximum number of edges that can be removed and is also restricted to settings where the input graph has maximum degree three. Both of these algorithms solve not only the decision problem, but also enumerate all solutions with polynomial time precalculation, delay, and postcalculation time in respective restricted settings. For this problem, efficient enumeration allows the uncertainty in the spatial correlation to be utilised in the modelling. The first enumeration algorithm utilises dynamic programming on a tree decomposition of the input graph, and has polynomial time precalculation and linear delay if both the treewidth and maximum degree are bounded. The second algorithm is restricted to problem instances with maximum degree three, as may arise from triangulations of planar surfaces, but can output all solutions with FPT precalculation time and linear delay when the maximum number of edges that can be removed is taken as the parameter.

Disentangling the Modifiable Areal Unit Problem in Housing Density and Price Associations

Urban planning education must address the Modifiable Areal Unit Problem (MAUP) to comprehend the critical impact of urban density on sustainable city development. Quantitative studies using administrative area units face indefinite aggregate level biases. This paper introduces an efficient block-searching method to calculate property densities around residences of various boundary scales and empirically examines their relationship with housing prices in Auckland, New Zealand. Results reveal negative associations between housing prices and densities within neighbourhoods, emphasising the limitations of administrative boundaries. These findings underscore the necessity for planning education to navigate MAUP’s complexities in shaping urban development policies.

Evolution and influencing factors of coastal resilience in the East China Sea

The coastal zone serves as a crucial hub for economic and population concentration. Amid the context of high-intensity development and global climate change, uncertain risks from diverse sources—including extreme weather events (i.e., high temperatures, typhoons, and excessive precipitation), natural disasters (i.e., floods, tsunamis, landslides, and mudslides), and societal disruptions (i.e., economic crises and viral diseases)—are escalating rapidly. Enhancing coastal resilience to minimize these risk impacts is progressively becoming a mandatory requirement for the sustainable development of coastal zones. However, existing research primarily focuses on distinct disasters, the ecological environment, or specific socio-economic aspects, thereby lacking a comprehensive theoretical framework and thorough analysis of the factors influencing coastal resilience. Here, we construct a theoretical framework centered on the unique traits and processes of coastal resilience, analyze the spatiotemporal evolution characteristics of coastal resilience from a grid and administrative division standpoint, and utilize geographic detectors to determine the factors influencing coastal resilience while considering the modifiable areal unit problem (MAUP). Our findings indicate that: (1) Coastal resilience in the East China Sea (ECS) initially declined but then increased, transitioning from a lower to a medium level. Barring the pressure index, other dimensional indices had an upward trend; (2) Continuous improvements were observed in coastal resilience across different land uses. Forests, waters, and oceans demonstrated higher resilience levels than other lands, with construction land resilience developing swiftly. The effect of changes in land use types on coastal resilience showed a rapid initial increase and subsequent decrease; (3) The change pattern of coastal resilience in the ECS is mainly unchanged and slightly increased. Areas with the most drastic changes were concentrated in Shanghai, northern Zhejiang, and central Fujian, with the main change patterns continuously rising; (4) The primary factors influencing coastal resilience in the ECS included gross domestic product and infrastructure construction level. Advanced industrial structure, technological and educational prowess, and effective government management are important determinants of coastal resilience development. The significance of human factors continues to grow. Our findings offer valuable insights for optimizing national spatial planning of coastal zones, responding to internal and external impacts, achieving resilient coastal zones, and implementing a comprehensive sustainable management approach.

Fast Bayesian Functional Regression for Non-Gaussian Spatial Data

Functional generalized linear models (FGLM) have been widely used to study the relations between non-Gaussian response and functional covariates. However, most existing works for FGLM assume independence among observations and therefore they are of limited applicability for correlated data. A particularly important example is spatial functional data, where we observe functions over spatial domains, such as the age population curve or temperature curve at each areal unit. In this paper, we extend FGLM by incorporating spatial random effects. Especially, we study the relationship between the non-Gaussian response variable and functional covariates that are spatially observed. However, such model has computational and inferential challenges. The high-dimensional spatial random effects cause the slow mixing of Markov chain Monte Carlo (MCMC) algorithms. Furthermore, spatial confounding can lead to bias in parameter estimates and inflate their variances. To address these issues, we propose an efficient Bayesian method using a sparse reparameterization of high-dimensional random effects. We also study the average coverage probabilities of the credible intervals of functional parameters. We apply our methods to simulated and real data examples, including malaria incidence data and US COVID-19 data. The proposed method is fast while providing accurate functional estimates.

Beyond hazard-induced migration: Dissecting everyday mobilities in response to air pollution and extreme cold events at multiple spatial and temporal scales

Human mobility can be considered an effective adaptation strategy in response to environmental risks, given that adverse environmental conditions are often temporary and in-situ adaptation may not always be feasible or desirable. Despite its importance, the concept of short-term mobility as a behavioral response to environmental hazards has been understudied in geographies of health and place and behavioral economics. For a comprehensive understanding of how everyday mobilities are used as a risk adaptation strategy, this study avails of a multiscalar approach's ability to examine the influences of air pollution and extreme cold events on origin-destination movements. The modifiable areal unit problem (MAUP) and modifiable temporal unit problem (MTUP) are analyzed. The results suggest that the scale effects of the MAUP and MTUP are evident from the variations in regression coefficients of the differences in air quality and extreme cold events between origin and destination units. It is also found that the prefecture-level units that include both urbanized city proper and rural countryside, are not an ideal spatial analysis scale. Furthermore, this study reveals that the nexus of air quality differences and short-term movements is significantly impacted by changes in temporal scales. Our results offer fresh evidence on the decision-making process underlying mobility as an adaptation strategy to air pollution and cold events.

Data Scaling: Implications for Climate Action and Governance in the UK

Local actors have growing prominence in climate governance but key capacities and powers remain with national policymakers. Coordination between national and local climate action is therefore of increasing importance. Underappreciated in existing academic and policy literature, coordination between actors at different scales can be affected not only by politics and institutional arrangements, but also by methods of data analysis. Exploring two datasets of GHG emissions by local area in England—one of consumption-based emissions and the other of territorial emissions—this paper shows the potential for a data scaling problem known as the modifiable areal unit problem and its possible consequences for the efficacy and equity implications of climate action. While this analysis is conceptual and does not identify specific instances of the modifiable areal unit problem or its consequences, it calls attention to methods of data analysis as possible contributors to climate governance challenges. Among other areas, future analysis is needed to explore how data scaling and other aspects of data processing and analysis may affect our understanding of non-state actors’ contribution to climate action.

Mapping essential surgical care in Mongolia: Do natural barriers and seasonality alter access to essential surgical care?

Measures of access to essential surgery in Mongolia have not accounted for natural barriers to movement, seasonality, and the modifiable areal unit problem scale effects. This physical accessibility analysis indicates natural barriers and seasonality threaten access to surgical care, shifting Mongolia from an attaining to a non-attaining country with estimates below the target population goal of 80%. Remote communities are particularly impacted, with access reduced by up to 6.1%. Spatial resolution of the input data influences the results by up to 14.2%. This highlights the importance of including natural barriers and seasonality in healthcare access scenarios using a fine spatial resolution.

A framework for analyzing the effects of modifiable areal unit problem on ecological security pattern

Ecological security pattern (ESP) provide a solution to balance ecosystems and urban development. The modifiable areal unit problem (MAUP) is a well-known geographical issue that affects the understanding of ecological processes and the results of spatial modeling. However, only a few studies have explicitly clarified the effects of MAUP on ESP. Herein, we propose new methods for identifying ecological sources and mapping the resistance surface, as well as a framework for analyzing the effects of MAUP on ESP. Our results indicate that (1) the datasets used for identifying ecological sources should possess a grain size of smaller than 300 × 300 m2. (2) The resistance surface directly influenced the results of the ecological corridors and nodes. (3) MAUP could generate uncertainties in ESP policymaking. Additionally, this study developed comprehensive network analysis tools based on graph machine learning to analyze the effect of MAUP on ESP policymaking, which can provide important landscape planning. The network analysis approaches may help policymakers gain a comprehensive understanding of the ESP network to improve the credibility of policies.

Does flood risk funding protect the most vulnerable? A case study of England

Not only has the frequency and severity of flooding increased under climate change, but which communities are at-risk and how those risks are distributed within communities has changed too. This realisation points to an important interplay between exposure (risk) and social vulnerability. Who is vulnerable? Answering this question is far from straightforward as different vulnerability indicators identify different groups across different scales. This paper addresses this issue. Using the empirical case of England, the spatial distribution of flood risk at different administrative scales is analysed in relation to the Environment Agency (EA) allocation of flood funding between 2015 and 2021. We find that Upper-tier Local Authority Districts with higher levels of both flood risk and social vulnerability received more funding in the period considered. Yet, that is not the scale at which flood scheme funding decisions are made. Flood schemes are decided at the local level, but funding data for smaller administrative scales is not available. Different understandings of vulnerability, the Modifiable Areal Unit Problem (MAUP), and issues around data transparency and availability in flood risk management, need to be urgently addressed.

On the trade-off between accuracy and spatial resolution when estimating species occupancy from geographically biased samples

Species occupancy is often defined as the proportion of areal units (sites) in a landscape that the focal species occupies, but it is usually estimated from the subset of sites that have been sampled. Assuming no measurement error, we show that three quantities–the degree of sampling bias (in terms of site selection), the proportion of sites that have been sampled and the variability of true occupancy across sites–determine the extent to which a sample-based estimate of occupancy differs from its true value across the wider landscape. That these are the only three quantities (measurement error notwithstanding) to affect the accuracy of estimates of species occupancy is the fundamental insight of the “Meng equation”, an algebraic re-expression of statistical error. We use simulations to show how each of the three quantities vary with the spatial resolution of the analysis and that absolute estimation error is lower at coarser resolutions. Absolute error scales similarly with resolution regardless of the size and clustering of the virtual species’ distribution. Finely resolved estimates of species occupancy have the potential to be more useful than coarse ones, but this potential is only realised if the estimates are at least reasonably accurate. Consequently, wherever there is the potential for sampling bias, there is a trade-off between spatial resolution and accuracy, and the Meng equation provides a theoretical framework in which analysts can consider the balance between the two. An obvious next step is to consider the implications of the Meng equation for estimating a time trend in species occupancy, where it is the confounding of error and true change that is of most interest.