Spatially Explicit Analysis of Landscape Structures, Urban Growth, and Economic Dynamics in Metropolitan Regions

Abstract

Assuming that settlement morphologies and landscape structures are the result of economic transformations, the present study illustrates a statistical framework investigating metropolitan growth due to the inherent changes in landscape configurations vis à vis socio-demographic functions. Focusing on the evolution of their spatial drivers over time, metropolitan development was studied by adopting land parcels (or ‘patches’, as they are referred to in the ecological literature) as the elementary analysis unit—with the individual surface area and a specific shape indicator as the dependent variables and background socioeconomic attributes as predictors of landscape change over time. We specifically ran a Multiscale Geographically Weighted Regression (MGWR) testing the spatial dependence of the size and shape of landscape parcels on a vast ensemble of socioeconomic factors in a dense region (metropolitan Athens, Greece) with natural landscapes exposed to increasing human pressure. To investigate the spatial direction and intensity of the settlement expansion and landscape change, local regressions using the parcel area and fractal index (perimeter-to-area ratio) as the dependent variables and the elevation, distance from selected economic nodes, transport infrastructures, and natural amenities as the predictors were run separately for 1990 and 2018, representative of, respectively, a mono-centric configuration and a moderately polycentric organization of economic spaces. In a strictly mono-centric setting (1990), the parcel size showed a linear dependence on the distance from business districts, elevation, and wealth. Changes in the relationship between the parcel size and spatial (economic and non-economic) drivers may suggest a latent process of settlement de-concentration, and a possible shift toward polycentric development (2018), as documented in earlier studies. By integrating socioeconomic and ecological dimensions of landscape analysis and land evaluation, the empirical results of this study outline the increased complexity of dispersed landscape structures within dense metropolitan regions and along urban–rural gradients in Europe.

1. Introduction

Metropolitan expansion is a dynamic process resulting from vastly differentiated land-use equilibrium conditions [1,2,3]. These usually reflect the interplay between economic agents shaping the intrinsic structure of regions and countries [4,5,6]. Various dimensions of growth coexist in metropolitan landscapes, producing distinctive relationships between socioeconomic functions, settlement forms, and the differential (economic and non-economic) uses of land [7,8,9]. Metropolitan expansion and landscape change thus depend on cooperative forces that include a growing population, rising incomes, and falling commuting costs [10,11,12]. Economic theory highlights the latent trade-off between the optimal and equilibrium city size involving dynamic externalities (e.g., of human capital), in addition to congestion externalities [13,14,15]. Agglomeration factors reflect the ‘differential rent’ theory predicting higher prices for land with high accessibility [16,17,18]. Differential levels of accessibility have extensively shaped density hierarchies from inner cities to peripheral locations [19,20,21]. The latent crisis of industrial regions and the emergence of a new kind of economic dynamics have been increasingly dependent upon the expansion of production systems centered on advanced services [22]. This leads to rapid changes in metropolitan spaces that may result in diversified landscapes and particularly complex spatial distributions of land uses [23,24,25].

The post-Fordist growth of metropolitan regions featured settlement dispersion and polycentric development [26], exerting a variable impact on natural landscapes around cities [27,28,29]. In this perspective, inner cities have created a series of multi-directional linkages with the surrounding (rural) locations, involving trade, commuting, and information exchange [30,31,32]. These relationships have been demonstrated to impact the structure of geographical gradients responding to population concentration [33], accessibility [34], land/house prices [35,36], natural/cultural amenities [37,38], planning restrictions [39], and policy constraints [40,41,42]. Based on these premises, this study assumes morphological and territorial metrics as dynamic attributes of landscape systems at different time points. The hypothesis suggests that landscape structures, particularly the spatial organization of land use both in natural contexts and in districts heavily impacted by human pressure and ecological disturbances, are governed by a complex set of underlying drivers of both territorial and economic origin. However, the recent literature, while dedicating a huge effort to delineating land-use change and the main forces at the base of such continuous transformations over time, has been only occasionally devoted to a spatially explicit analysis of the factors regulating the intrinsic organization of different land-use classes within the same landscape scene at two or more points in time [43,44,45,46,47,48,49,50]. Building on this perspective, an exploratory–interpretative model was developed, likely marking one of the first instances in the recent literature to delineate the primary socioeconomic and territorial forces underpinning both historical and current landscape structures. This model encompasses a sufficiently large area that has experienced varying degrees of human pressure and ecological disturbance over time, while simultaneously considering diverse land uses with significantly different economic values, ranging from built-up areas to forestry. Based on quantitative data and techniques elaborating on the basic predictors of the spatial structure characteristic of a given landscape, a comparative analysis of the results of a local regression with a simplified econometric specification contributed to identifying the most relevant drivers of the spatial organization of the land use around a city, giving relevant information from both positive (science) and normative (policy-planning) perspectives.

In line with the previous assumption, a sufficiently long time window, encompassing different demographic phases and social dynamics [51], a relatively large landscape scene, encompassing multiple classes of land use with different economic values and ecological roles [52], and a vastly differentiated region in terms of both the environmental and socioeconomic conditions [53] are the basic elements in the selection of the relevant area in such kinds of studies. Selected as a representative study area for its Mediterranean ecological and socioeconomic conditions, metropolitan Athens in central Greece offers a representative example of socio-demographic diversification and territorial complexity under sequential waves of economic expansion and decline [54]. Despite some local-scale deviations because of contextual factors (e.g., the topography, the soil quality, the land protection regime, the socio-demographic attributes of rural communities, second-home expansion, etc.), Athens has expanded in a mostly radio-centric fashion, realizing, since the late 1980s, a spatial structure compatible with concentric land-use zoning [55]. Local regressions were adopted for analyzing the spatial relationship between the parcel size (or shape) and indicators, assessing multiple aspects of metropolitan growth and landscape change at the end of, respectively, the urbanization (1990) and suburbanization (2018) stages of Athens’s life cycle (sensu [56,57]). The empirical results of this study provide the knowledge base necessary for designing socio-demographic policies and planning measures that promote metropolitan sustainability and regional competitiveness throughout different phases of the economic cycle.

2. Methodology

2.1. Study Area

The present study investigates the landscape dynamics in metropolitan Athens, Greece, a region extending nearly 3000 km² and administered by 115 municipalities (Figure 1) and 8 prefectures [29]. The region includes flat areas, basically occupied by human settlements, uplands dominated by a mixed agricultural–forest landscape, and mountainous districts, especially within the mountains of Parnitha, Pendeli, Pateras, and Imitos, preserving natural habitats thanks to the relatively low accessibility and modest (while increasing) anthropogenic pressure [58]. As a result of a long-lasting settlement history, the most intense transformations of Athens’s spatial structure have been recorded since World War II [59]. The population density increased from nearly 650 inhabitants per km² in 1951 to 890 inhabitants per km² in 1981 to 1240 inhabitants per km² in 2021. Sequential expansion waves included (i) mono-centric, dense growth around downtown Athens between the late 1940s and the late 1970s, and (ii) a dispersed expansion of fringe settlements from the beginning of the 1980s to nowadays [60].

Regional planning in the last decades has prioritized development via the property market [61], frequently at the expense of high-quality land, with an insufficient level of policy enforcement for environmental quality [62,63,64,65]. Town master plans define land-use zoning for a (more or less restricted) fraction of their administered areas [25]. Settlement development has been generally permitted on the remaining land, unless otherwise stated, such as in protected areas or locations with physical limits to urban growth [66]. The partial lack of land-use plans covering the entire municipal area is seen as a latent factor of sprawl via clearcutting, wildfires, and informal settlement expansion into cropland [67]. This indicates that forests and the agricultural landscape matrix are particularly sensitive to urbanization and, together, are a serious obstacle to local development when providing economically viable production [68,69].

2.2. Data Source and Variables

This study made use of two Corine Land Cover maps dated 1990 and 2018 and released by the European Environment Agency (www.eea.europa.eu/en (accessed on 20 September 2024)) at a 1:100,000 scale. Land parcels (corresponding with the ‘patch’ notion commonly used in the ecological literature) were considered the elementary analysis unit forming the entire investigated landscape scene. These parcels are categorized by land use, distinguishing built-up (code 1) from agricultural (code 2) and natural (code 3) land uses [70]. The term land ‘parcel’ is typically used in land-use science and indicates a portion of space with homogeneous anthropogenic (i.e., economic) use. The notion of a land ‘patch’ (physically corresponding with a land ‘plot’) is associated with the ecological role of a given, homogeneous portion of landscape [71], having the same structural and functional characteristics of a habitat or ecosystem (e.g., a conifer forest). In this perspective, the term ‘parcel’ is generalized to all the homogeneous and spatially continuous landscape portions (or fragments) identified in this study, whether anthropogenic or natural. This generalization is based on the assumption that the landscape is composed of multiple land uses with diversified economic values, ranging along a gradient from ‘built-up’ parcels, which form urban conurbations and have the highest economic value, to ‘forest’ parcels mainly constituting natural habitats and having the lowest economic value [58,72,73].

Landscape parcels were derived from the procedure of spatially merging polygons classified with the ‘1.xx’, ‘2.xx’, and ‘3.xx’ codes extracted from the first hierarchical level of the Corine nomenclature system, as described above, with the aim of obtaining a homogeneous representation of the whole landscape scene that is fully coherent with the ground conditions at various time points (namely, 1990 and 2018). The operational definition of parcels (e.g., boundaries, use, type, neighbors) follows the one delineated by the original data source adopted in this study, namely, Corine Land Cover maps and the associated geo-database. While any definition of a land parcel and the associated landscape introduces some subjective aspects and ad hoc interpretations of the structure and functions of land use, the adoption of the Corine Land Cover land system classification of landscapes assures statistical reliability, spatial coherency, semantic homogeneity, temporal comparability, an unsurpassed geographical coverage (i.e., the whole of Europe), and stable (and widely accepted) definitions for the multiple uses of land organized into 44 micro-classes and 3 basic classes (built-up, agricultural, forest) with decreasing economic value. These characteristics fit well with the aims and scope of the present study and allow for a full reproducibility of the methodological procedure illustrated here to many other socioeconomic and territorial contexts all over Europe and—with some adaptations/generalizations—to several other conditions all over the world.

Based on these premises, land parcels with homogeneous use—classified as built-up, agricultural, or forest—are assumed to be individual (homogeneously defined) elements of any landscape with different economic values [74,75]. It is also hypothesized that the physical structure of these land parcels may reflect—at least indirectly—the overall economic functioning of the landscape [76,77], considering its overall configuration over space, which intrinsically depends on the spatial organization of the land use (e.g., along the metropolitan gradient [78,79]), as investigated in this study. The intrinsic structure of a given landscape scene is deduced by identifying the main (candidate) factors underlying the structural characteristics of its individual units with homogeneous (economic) use (i.e., land parcels). Underlying factors are defined as some specific socioeconomic and territorial forces known to influence (directly or indirectly) anthropogenic decisions on land use [80]. Comparing the empirical results of the analysis at two (sufficiently distanced) dates (1990 and 2018) may provide important insights into the socioeconomic dynamics at the base of landscape change [81].

Selected as the dependent variables in this study, the parcel metrics included (i) the total area (ha) and (ii) a fractal index—a well-known proxy of landscape shape computed as the ‘perimeter-to-area ratio’ and indicating patch fragmentation and convolution [82,83,84]. The size and shape represent two basic dimensions of any individual land parcel forming a given landscape [85,86], being intrinsically influenced by a number of territorial constraints and socioeconomic factors [87,88]. Their analysis may additionally delineate the differential roles of economic and non-economic factors of change when investigating landscape transformations [89,90]. All in all, 8 candidate predictors of land parcel structure were selected, and their significance (role and importance) in influencing both the size and shape of individual parcels across the study area was tested using econometric models [91]. These models compare the spatially implicit and spatially explicit results of any regression analysis in order to comprehensively define the role of space in the landscape structure and the related economic functioning (land use). The predictors of the land parcel’s structure tested in the present study included three measures of distance from relevant economic nodes in the study area; elevation intended as a territorial constraint when promoting a given (economic) use of land (e.g., for tourism [92], agriculture [93], or forestry [94], e.g., based on accessibility [95], climate conditions [68], planning constraints [52]: all these factors were, directly or indirectly, well represented along the elevation gradient in the study area); a standard, proxy measure of the socioeconomic (wealth) conditions of local communities in the area; and three proxies for the specific use (built-up, agriculture, forest) of each land parcel.

A multivariate analysis of distances from relevant economic nodes at the local scale (e.g., business districts, infrastructures, amenities) allows for characterizing latent relationships between the size and spatial configuration of built-up parcels in metropolitan regions. Under this assumption, three metrics of accessibility from key economic nodes were tested in the study area, including the linear distances from the following:

(a)

The neighbor land infrastructure (i.e., road or railway), intended as a gross (indirect) metric (hereafter ‘Infr’) of the parcel accessibility, and computed from the parcel’s centroid and the closest point in the road axis or the closest railway station [96];

(b)

Downtown Athens (namely, Syntagma Square in the central settlement of Athens’s municipality); such an indicator (hereafter ‘DisA’, km) allows for evaluating the contribution of traditional (e.g., ‘centralized’) or more complex (e.g., ‘decentralized’) morphological structures to metropolitan growth, since settlements at moderate–low distances from Athens reflect the possible persistence of a traditional mono-centric model [97];

(c)

The Olympic Stadium of Athens, “Spyros Louis”, corresponding with Attica’s business district in Maroussi, northern Athens (hereafter ‘DisS’, km); low distances from the Olympic Stadium indicate the predominance of a settlement growth model centered on the economic expansion of the new Attica’s business district northeast of Athens, leveraging a dual metropolitan structure prodromal of polycentric development [98,99].

The other predictors are as follows:

(d)

A proxy measure of local communities’ wealth (‘Poor’) implementing a dichotomous variable (0–1) derived from previous studies on the same area [100], and classifying the municipalities of metropolitan Athens as affluent (or economically disadvantaged) depending on the per capita income (below or above average) of the resident population estimated from official elaborations of tax declarations. Data for each municipality of the study area (n = 115) were assigned to each land parcel geographically belonging to that administrative unit;

(e)

The average elevation (meters at sea level) of each land parcel (‘Elev’) as an indirect indicator of natural amenities is more frequent at higher altitudes in the area, on average, because of the reduced human pressure. The variable was derived from a Digital Elevation Model (100 m spatial resolution) available for download and elaboration in raster format from the European Environment Agency and covering the study area homogeneously;

Finally, three dichotomous variables (f–h) were used to define the basic (aggregate) use (urban (‘Urb’), agricultural (‘Agr’), and forestry (‘For’)) of each landscape parcel, following the original Corine Land Cover classification. Distances were calculated for each land parcel using the spatial calculator tools available in ArcGIS software (ESRI Inc., Redwoods, CA, USA: release 10.8.2) and were computed on official shapefiles provided by the Hellenic Statistical Authority (www.statistics.gr/en/home (accessed on 20 September 2024)) and freely downloadable from the institutional website. Distances were specifically measured using the ‘centroid’ command computing the linear distance from the center of gravity of each land parcel and the reference places mentioned above (e.g., Syntagma Square, the Olympic Stadium of Athens, “Spyros Louis”, the nearest railway station or neighboring road). The parcel size, elevation, and distance metrics were log-transformed and, after this transformation, all input variables were standardized prior to analysis. The precision of the collected data and variables depended on the basic characteristics of the adopted maps, assumed to be particularly low and fully comparable across time and space since they were derived from strictly public (national and international) data sources and providers.

2.3. Local Regressions

Based on empirical evidence from earlier studies [91], the parcel size (or shape) was hypothesized as a structural characteristic of metropolitan landscapes depending on five dimensions of growth and change [101], as follows:

Parcel size (or shape) = f (A, E, N, W, L)

(1)

where A is the accessibility to transport infrastructure; E is a measure of the economic agglomeration and scale processes; N means natural amenities; W indicates wealth accumulation; and L reflects the current use of land [3]. These dimensions were operationally estimated with the predictors illustrated above in Section 2.2 [44]. More specifically, dimension A was assessed via indicators (a) and (c); dimension E via indicator (b); dimension N via indicator (d); dimension W via indicator (e); and dimension L via indicators (f–h) [100].

The spatial distribution of and variability in landscape parcels were estimated separately for each study year (1990 or 2018) according to Equation (1) using spatially implicit Ordinary-Least-Square (OLS) regressions [102] and spatially explicit Multiscale Geographically Weighted Regression (MGWR) models [103] with 8 predictors (see above) and the parcel size (or shape) as the dependent variable [104]. Considering the number of metrics used to assess each dimension of metropolitan growth, the Variance Inflation Factor (VIF) was calculated to estimate the redundancy among the predictors [105]. For both 1990 and 2018, the predictors were only slightly redundant, having a VIF systematically below 5 in all cases, and allowing for the computation of regression models under appropriate statistical assumptions [106]. Used as a benchmark reference for spatially explicit models, the OLS regression outcomes include slope coefficient estimates and the associated significance level (testing for the null hypothesis of the insignificant regression coefficient) based on Student t statistics at p < 0.05. The goodness of fit of each model was assessed using the adjusted R² and was tested for significance (against the null hypothesis of the insignificant model) through a Fisher–Snedecor F test with p < 0.001 [107].

A spatially explicit (local estimation) strategy adopting the same specification presented above and implementing MGWRs was run with the aim of allowing for a full exploration of the contribution of the spatial location in determining a given landscape structure [108]. MGWRs are usually adopted in the statistical exploration (and, often, confirmation) of geographically varying relationships between dependent variables and predictors (i.e., independent/explanatory variables). Starting from the standard approach to modeling the process of spatial heterogeneity initially developed in Geographically Weighted Regressions (GWRs), MGWR relaxes the GWR assumption that all of the processes being modeled operate at the same spatial scale, allowing for the comprehensive scrutiny of the importance of the spatial location and the (geographical) observation scale together [109]. MGWRs estimate regression parameters at each location using weighted least squares, implying that each coefficient in the model is a function of space (s), and thus giving rise to a distribution of local estimated parameters [17]. Unlike GWR—which assumes that the local relationship within each model varies at the same spatial scale—MGWR allows the conditional relationship between the response variable and the different predictor variables to vary at different spatial scales [103].

The weights for the estimation of the local regression models were derived from an adaptive bi-square nearest-neighbor kernel function, a common specification placing more weight on the observations closer to the locations [110]. An adaptive kernel was adopted with the aim of controlling for an optimal number of k neighbors to be included in the model fitting [101]. The bandwidth Golden Section searching option was used, finding the optimal value for the bandwidth by successively narrowing the range of values within which the optimal value exists—and comparing the optimization score of the model for each—returning the value that has the lowest score [103]. Standardized variables allow for the interpretation and comparison of the individual bandwidths since, in this case, the bandwidths serve as indicators of the spatial scale at which the conditional relationship between the dependent variable and (local) predictors varies. The model’s goodness of fit was assessed using (global and local) R² coefficients and Akaike Information Criterion (AIC) values [111]. Considering the inherent (local) variability in any landscape configuration, it is hypothesized that local models are possibly able to intercept and explain a higher proportion of the variance in the estimated model than global models [108]. However, based on the relatively high sample size, possibly low (or intermediate) adjusted R² values, while displaying considerable statistical significance, may depend on the large sample heterogeneity, considering both the size and shape of the land parcels [109].

As an indirect validation of MGWR against the OLS estimation strategy, adjusted R² coefficients and AIC values were finally compared between the models’ outcomes in order to estimate the econometric improvement when adopting local approaches instead of global procedures. Addressing the specific objective of this study, such comparisons, in turn, provide an indication of the role of the spatial location in the geographical variability in the parcel size and shape, taken as elementary components of landscape structures [112]. Maps with the spatial distribution of local parameters were provided for the intercept, predictors’ slope coefficients, R² value, and standardized residuals of each model [113]. Regression estimation was carried out through the software called ‘MGWR’ (Multiscale Geographically Weighted Regression) (version 2.0.1), a new release of an open source Microsoft Windows- and MacOS-based application software calibrating local regression models that imply geographically varying parameters [103]. Compared with other spatially explicit econometric models (mainly based on global approaches), local regressions have been demonstrated to be more flexible tools for modeling territorial heterogeneity under less rigid statistical assumptions on both dependent and independent variables [108], as the dataset collected in this study may require.

3. Results

3.1. Parcel Size and Landscape Dynamics

Considering the whole landscape scene along the urban–rural gradient in metropolitan Athens, the parcel size (mixing together built-up, cropland, and natural land uses) was demonstrated to be moderately (or slightly) correlated with the economic predictors, as clearly outlined in the outcomes of the spatially implicit regressions (

Table 1. Results of spatially implicit (OLS) and spatially explicit (MGWR) regression models for land parcel size by year; predictors’ acronyms as in the main text (* statistical significance at p < 0.05); n indicates the regression sample size in terms of the parcel number; M/A indicates the ratio of the median to average MGWR local estimation of the slope coefficients; AIC represents Akaike Information Criterion.

Predictor	OLS			MGWR
	Estim.	St.Err	p	Avg.	St.Dev	I (m)	Min	Med.	Max	M/A
1990
Infr	0.042	0.032		0.083	0.490	0.2	−1.419	0.030	2.286	0.36
Poor	0.059	0.030	*	0.034	0.014	2.4	0.010	0.039	0.052	1.15
DisA	0.026	0.034		0.055	0.011	5.0	0.028	0.060	0.067	1.09
DisS	0.372	0.049	*	0.477	0.065	7.3	0.361	0.491	0.604	1.03
Elev	−0.153	0.051	*	−0.219	0.031	−7.1	−0.264	−0.213	−0.181	0.97
Urb	0.105	0.180		0.306	0.010	30.6	0.286	0.305	0.327	1.00
Agr	0.248	0.198		0.472	0.004	118.0	0.465	0.472	0.479	1.00
For	0.256	0.225		0.547	0.045	12.2	0.468	0.549	0.617	1.00
Adj-R2	0.083			0.178
AIC	3097			3027
n	1123
2018
Infr	0.067	0.030	*	0.276	0.675	0.4	−1.133	0.104	3.057	0.38
Poor	−0.012	0.028		−0.017	0.043	−0.4	−0.069	−0.019	0.052	1.12
DisA	0.015	0.032		0.063	0.011	5.7	0.04	0.066	0.077	1.05
DisS	0.230	0.045	*	0.284	0.032	8.9	0.225	0.28	0.361	0.99
Elev	0.119	0.047	*	0.157	0.258	0.6	−0.435	0.143	1.212	0.91
Urb	−0.214	0.146		−0.374	0.054	−6.9	−0.493	−0.364	−0.262	0.97
Agr	−0.148	0.150		−0.348	0.043	−8.1	−0.431	−0.331	−0.281	0.95
For	−0.206	0.164		−0.383	0.009	−42.6	−0.402	−0.381	−0.372	0.99
Adj-R2	0.095			0.300
AIC	3348			3131
n	1220

). Displaying a moderately low goodness of fit in the global OLS model based on 1123 observation units (adjusted R² equal to 0.08 and 0.10, respectively, for 1990 and 2018), the parcel size increased in affluent municipalities and at locations placed at greater distances from the Attica business district (Olympic Stadium of Athens, “Spyros Louis”), while decreasing with the elevation, especially in the first observation year, 1990. Based on a slightly larger sample of land plots (n = 1220), the parcel size increased in 2018 with the elevation and the distances from (i) transport infrastructures and (ii) the Attica business district. These results indicate a substantial differentiation in the structure of the Attica landscape between 1990 and 2018, which, in turn, evidences a latent (cross-sectional) heterogeneity possibly associated with the different land uses (built-up, cropland, natural). The use of spatially explicit techniques substantially improved the goodness of fit of the econometric estimation of the parcel size (adjusted R² equal to 0.1 and 0.3, respectively, for 1990 and 2018). At the beginning of the study period, the parcel size increased with the municipal affluence and distances from downtown Athens and the Attica business district, in turn decreasing with the elevation. Natural land had larger parcels than those of agriculture and urban uses. At the end of the study period, the distances from downtown Athens and the Attica business district, as well as the elevation, positively influenced the size of the land parcels. The role of the land use was, in this case, more homogeneous, with both urban and natural uses exerting comparable impacts on the parcel size.

3.2. Parcel Shape and Landscape Dynamics

The landscape-level parcel shape (perimeter-to-area ratio) was correlated with both the economic and non-economic predictors in a rather similar pattern to that of the parcel size, as clearly outlined in both the spatially implicit (OLS) and spatially explicit (MGWR) models’ results (

Table 2. Results of spatially implicit (OLS) and spatially explicit (MGWR) regression models for land parcel shape (perimeter-to-area ratio) by year; predictors’ acronyms as in the main text (* statistical significance at p < 0.05); n indicates the regression sample size in terms of the parcel number; M/A indicates the ratio of the median to average MGWR local estimation of the slope coefficients; AIC represents Akaike Information Criterion.

Predictor	OLS			MGWR
	Estim.	St.Err	p	Mean	St.Dev	I (m)	Min	Med.	Max	M/A
1990
Infr	−0.110	0.033	*	−0.090	0.064	−1.4	−0.165	−0.116	0.015	1.29
Poor	−0.037	0.030		0.073	0.115	0.6	−0.077	0.047	0.223	0.64
DisA	−0.061	0.034	*	0.013	0.052	0.3	−0.067	−0.012	0.115	−0.92
DisS	−0.407	0.049	*	−0.376	0.360	−1.0	−2.181	−0.309	0.899	0.82
Elev	0.200	0.051	*	0.252	0.065	3.9	0.127	0.260	0.373	1.03
Urb	0.002	0.182		−0.139	0.005	−27.8	−0.147	−0.140	−0.127	1.01
Agr	−0.028	0.199		−0.139	0.006	−23.2	−0.148	−0.140	−0.121	1.01
For	−0.059	0.227		−0.207	0.005	−41.4	−0.218	−0.206	−0.199	1.00
Adj-R2	0.067			0.336
AIC	3117			2806
n	1123
2018
Infr	−0.087	0.031	*	−0.014	0.199	−0.1	−0.679	−0.018	0.689	1.29
Poor	0.018	0.029		−0.001	0.007	−0.1	−0.009	−0.003	0.012	3.00
DisA	0.063	0.033	*	−0.043	0.167	−0.3	−0.544	−0.013	0.255	0.30
DisS	0.169	0.046	*	0.006	0.137	0.0	−0.358	−0.010	0.384	−1.67
Elev	−0.397	0.048	*	−0.225	0.710	−0.3	−6.039	−0.065	0.244	0.29
Urb	0.327	0.149	*	0.241	0.002	120.5	0.235	0.240	0.245	1.00
Agr	0.253	0.153	*	0.234	0.047	5.0	0.024	0.242	0.341	1.03
For	0.404	0.167	*	0.293	0.007	41.9	0.281	0.294	0.303	1.00
Adj-R2	0.067			0.753
AIC	3386			1859
n	1220

). Showing a moderate goodness of fit in the global OLS model based on 1123 observation units (adjusted R² equal to 0.07 for 1990), the parcel fractal index decreased with the distances from downtown Athens and the Attica business district, as well as with the linear distance from transport infrastructure, increasing moderately with the elevation. Based on a slightly larger sample (n = 1220), the parcel fractal index increased in 2018 (adjusted R² equal to 0.07) with the distances from downtown Athens and the Attica business district, being significantly higher for the forest and built-up parcels and less significant for cropland. Conversely, the parcel fractal index decreased with the distance from transport infrastructure and with the elevation. These results indicate a substantial differentiation in the landscape configuration between 1990 and 2018, which, in turn, evidences a cross-sectional heterogeneity possibly associated with the different uses of land (built-up, cropland, natural), especially for 2018. The use of spatially explicit techniques improved the goodness of fit of the econometric estimation of the parcel fractal index, as the increase in the adjusted R² from 0.34 (1990) to 0.75 (2018) may outline.

3.3. Comparative Analysis of Model Diagnostics

Together with the adjusted R², the estimated values of the AIC confirmed the improvement in the econometric estimation moving from the spatially implicit OLS model to the spatially explicit GWR model (

Table 3. Model diagnostics by dependent variable and year; improvement rate in both adjusted R² and Akaike Information Criterion (AIC) when moving from spatially implicit (OLS) to spatially explicit (MGWR) econometrics.

Variable	Land Parcel
	Size (Area)	Shape (Fractal Index)
1990
R2 (MGWR vs. OLS)	2.14	5.01
AIC (MGWR vs. OLS)	0.98	0.90
No. of significant predictors (OLS)	3	4
No. of significant predictors (MGWR)	3	4
2018
R2 (MGWR vs. OLS)	3.16	11.24
AIC (MGWR vs. OLS)	0.94	0.55
No. of significant predictors (OLS)	3	7
No. of significant predictors (MGWR)	3	7

) for all the specifications and dependent variables used in this study.

Table 4. Optimal bandwidth estimation of MGWR model by dependent variable, predictor, and year; bandwidths are estimated as index numbers from 0 (minimum bandwidth; local influence) to 1 (maximum bandwidth; global influence); predictors’ acronyms as in the main text; * significance at p < 0.05.

Predictor	Area		Fractal Index
	1990	2018	1990	2018
Infr	0.05	0.04 *	0.68 *	0.09 *
Poor	0.99 *	0.81	0.63	0.98
DisA	1.00	1.00	0.58 *	0.25 *
DisS	0.42 *	0.57 *	0.04 *	0.17 *
Elev	0.90 *	0.07 *	0.57 *	0.04 *
Urb	1.00	0.32	1.00	1.00 *
Agr	1.00	0.58	1.00	0.26 *
For	0.61	1.00	1.00	1.00 *

illustrates the results of the optimal bandwidth estimation, considering an index number from 0 to 1 (the unity represents the maximum bandwidth extent reflecting the entire study area). Predictors with an optimal bandwidth close to 0 indicate a topical (local) impact on the respective dependent variable (i.e., exerting a rather heterogeneous influence over the landscape scene). Conversely, predictors with an optimal bandwidth estimated as close to 1 have a regional impact (i.e., exerting a homogeneous influence over the whole landscape scene). Considering only significant predictors (see Table 1 and Table 2), transport infrastructures exerted a topical impact on the parcel size (0.04) for 2018, contrary to municipal affluence, which was estimated with an optimal bandwidth indicating a strictly global effect (1.0 for 1990). The distance from the Attica business district had an intermediate bandwidth, indicating mixed-scale effects, in between the global and local scales. The elevation was demonstrated to have a mostly global (0.9) impact in 1990, turning to a mostly local impact (0.07) in 2018. Transport infrastructures exerted an intermediate-scale impact on the parcel shape (fractal index) in 1990 (0.68) and a more topical impact in 2018 (0.09); a similar pattern was observed for the distance from downtown Athens and the elevation. Local impacts were also characteristic of the distance from the Attica business district in most of the econometric models. Built-up and forest parcels had optimal bandwidths indicating a global-scale influence (1.0) on the parcel fractal index for 2018, contrary to cropland (0.26), having a mostly topical impact.

3.4. Local Regressions

Focusing only on the significant regressions’ predictors, Figure 2 and Figure 3 report the main (local) results and estimates of an MGWR for the parcel size as the dependent variable for 1990 and 2018, respectively. The distances from transport infrastructure and the Attica business district, as well as the elevation, were the only significant predictors of the parcel size for both years, and, for this reason, the estimation of the regression slope coefficient was illustrated for these three variables only using maps. For 1990, the distance from transport infrastructures was found to positively influence (slope > 1) the parcel size in a restricted area north of Athens within the national park of Mount Parnitha (Figure 2). The same predictor positively impacted (0 < slope < 1) the parcel size in the southern part of Athens’s conurbation. By contrast, the same predictor negatively influenced the size of the landscape parcels in the agricultural districts of Megara (western Attica) and Marathon (northeastern Attica). The distance from the Attica business district and the elevation were both significant predictors of the parcel size across the study area. The distance from the Attica business district impacted the parcel size positively (slope > 0.5) in Athens’s conurbation, in the coastal district of western Attica (Megara-Kinetta) along the motorway to Corinth, as well as in a restricted district (Oropos) along the A1 motorway to Thessaloniki in northern Attica. The elevation more negatively influenced the parcel size in western Attica than in eastern Attica, possibly because of the presence of extended mountain reliefs (Parnitha–Pateras). The local adjusted R² was systematically higher in western Attica, decreasing slightly in central Attica (in locations coinciding with Athens’s conurbation) and, more markedly, in eastern Attica (Figure 4).

For 2018, the distance from transport infrastructure positively influenced (slope > 1) the parcel size in a broad area encompassing rural districts and natural parks in western and northern Attica (i.e., the Pateras–Parnitha mountain reliefs). The same predictor was moderately associated with the parcel size (0 < slope < 1) in the southwestern part of Athens’s conurbation (Figure 3). Compared with 1990, the distance from transport infrastructure negatively influenced the size of the landscape parcels in a smaller area belonging to the agricultural districts of Megara (western Attica), Marathon (northeastern Attica), and Messoghia (eastern Attica). The distance from the Attica business district (Olympic Stadium of Athens, “Spyros Louis”) was revealed to be the only predictor exerting a significant impact homogeneously across the whole study area. A careful inspection of the MGWR map estimating the (local) slope coefficient for this variable may suggest how the distance from the Attica business district is positively associated with the parcel size (slope > 1) in specific locations of the study area, namely, central Athens, Salamina island, and the coastal district of western Attica (Megara-Kinetta) along the motorway to Corinth. The elevation positively influenced the parcel size in three districts: (i) Parnitha national park in northern Attica, (ii) the Pateras–Vilia rural district in western Attica, and (iii) central Athens in between the Egaleo and Imitos mountain reliefs. The locally adjusted R² was systematically higher in western Attica, decreasing slightly in Athens’s conurbation and in eastern Attica (Figure 4).

4. Discussion

Socioeconomic policies and regional planning have resulted in specific form–function relationships in European metropolitan landscapes that can be considered representative of more general patterns of urban–rural change [30,47,48]. In this vein, changes in the relationship between the parcel size (or shape) and a number of (economic and non-economic) predictors are reflective of joint territorial and demographic transitions [22,114,115]. Although relevant for policy design and evaluation, relating metropolitan expansion to landscape structures has been infrequently studied, since deriving a joint classification of the structural and functional characteristics of different landscape models is a challenging task [6,43,116]. However, identifying form–function relationships at the base of different metropolitan spatial structures is crucial when developing scenarios of metropolitan growth and landscape change based on realistic assumptions that reflect specific local contexts [57,117,118].

With this perspective in mind, the present study determined the empirical relationship between the size (or shape) of the land parcels forming a complete landscape scene along an urban–rural gradient and a number of economic (and non-economic) territorial predictors [119,120]. Complementing the traditional change detection analysis, these results provide an honest, and possibly more complete, description of the landscape transformations over time, analyzing the land characteristics in 1990 and 2018 in metropolitan Athens [100,114]. Despite the considerable interest in this issue, as clearly demonstrated in the consolidated and more recent literature, the argument remains highly relevant from different academic perspectives since it has been proven that the operational approach proposed here is able to identify a number of factors that influence urbanization and suburbanization processes [69,85]. While a possible problem with such measurements is the complexity and scale of estimating predictors, our study serves as a practical example of a comprehensive analysis of the form–function relationship characteristic of a complete landscape along the urban–rural gradient [121]. Based on regression diagnostics, the results obtained from the multiple regression analysis and examined in a cross section of predictors allow us to draw reasonable conclusions about the shift from a mono-centric and compact settlement model (1990) to more heterogeneous and spatially discontinuous landscape patterns (2018) [97,122]. In doing so, key factors influencing urbanization were identified, confirming, and sometimes enriching, the empirical literature on this topic for Mediterranean cities [110,118,123].

The empirical results of this study confirm the importance of spatial configuration in metropolitan landscapes as an intrinsic factor at the base of parcel size and shape [79,85]. Spatially explicit econometric models (namely, MGWRs) have proven to be more appropriate than spatially implicit regression in the investigation of such latent factors and dynamics [124]. Local regressions indicate how the economic agglomeration or scale (e.g., distance from the business district) and wealth accumulation negatively affect the parcel size, confirming the dominance of a strictly mono-centric model of metropolitan expansion at the end of the ‘urbanization’ stage of the city life cycle of Athens (see the regression results for 1990). Seconding the expansion of scattered settlements with diversified functions, the parcel size has started disempowering economic growth in a spatially unbalanced network of sub-centers, as the regression results for 2018 latently reveal. The elevation, associated with natural amenities, displays a reverse relationship, consolidating urban–rural divides along the gradient from coastal to internal land. In this perspective, spatial heterogeneity is considered an additional explanation of (vastly differentiated) local-area growth processes [17], possibly justifying the fragmented expansion of residential settlements into fringe land in Athens, as well as in other Mediterranean cities, and confirming the appropriateness of the methodological choice of MGWR as an econometric strategy [103].

With suburbanization (2018), the parcel size is dependent on factors possibly less related to economic performances and more associated with transport accessibility and the presence of natural amenities [44,79]. Accessibility and elevation exerted local-scale impacts on the parcel size; conversely, the distance from the Attica business district continues to exert, like in the early 1990s, a global impact on the parcel size [78]. Such changes may impact the structure of metropolitan regions, lowering socioeconomic divides and propelling a latent shift into land-saving and more sustainable morphologies [29]. If this interesting trend is to be consolidated in the near future, it should be intensively investigated in further empirical studies, addressing, in turn, the economic base of such processes in theory [113]. The results of the current research are finally supportive of the assumption that the spatial configurations of complex metropolitan systems are an outcome of historical evolutionary processes [121]. From a policy perspective, the econometric outcomes of this study may also be supportive of new perspectives on land management and shed further light on the operational planning of natural conservation areas, green infrastructures, wildfire buffer zones [80], and other habitat measures, improving the overall sustainability of the whole landscape transformation path [125].

5. Conclusions

Territorial development has been increasingly regarded as a complex systems’ path under the tight regulation of non-equilibrium forces [126], reflecting the mutual interplay of landscape structures and the associated (socioeconomic) functions, and shaping the final configuration of regions [127]. Assuming this perspective, this study identifies changes in the relationship between the parcel size (or shape) and selected socioeconomic attributes at two stages of metropolitan expansion (1990, namely, the end of the compact ‘urbanization’ stage, and 2018, reflecting socioeconomic dynamics typical of late suburbanization). Local regressions run separately on the parcel size or shape have delineated the intrinsic shift from a mono-centric and compact model to more heterogeneous and spatially discontinuous landscape structures representative of the entropic form–function relationships typical of contemporary metropolitan regions on the old continent [128]. Following the empirical evidence of previous studies and the findings of the econometric estimate performed in this work, long-term metropolitan growth in Athens—and the consequent evolution of urban and non-urban landscapes in Attica—have been demonstrated to be the result of the latent interaction of regional forces (e.g., agglomeration and scale economies [129], transport infrastructure [130], and spatial distribution and the availability of natural amenities [32,53]) with local processes (uses of land [28]) and social dynamics (wealth accumulation in municipalities [131] possibly at the base of territorial disparities into ‘rich’ and ‘poor’ local communities [132]).

Based on the empirical scrutiny of the role of spatial location, economic forces, and non-economic (additional) factors of social change, the logical framework introduced in this study allows for a joint interpretation of functional and structural transformations in metropolitan regions assuming the landscape configuration as the ultimate result of urban–rural dynamics. In this perspective, a refined interpretation of the intrinsic linkage of urban expansion and rural development with political, social, and economic power relations—and the emergence of new forms of local governance—is particularly welcome as a future research line. In the context of increasing metropolitan complexity and the unpredictability of future growth paths, it may specifically inform policies and planning, driving metropolitan transformations in the direction of, together, environmental resilience, social equity, and economic competitiveness, achieving the truly sustainable development of urban and rural lands in districts exposed to high human pressure and ecological disturbance.