1 Introduction

Social science research indicates that demographic divides in Europe have persisted over recent decades (Hank 2001; Arapoglou and Sayas 2009; Haase et al. 2010), being more intense in regions with a traditional economic base, social segregaton, and urban shrinkage (Boyle 2003; Potter et al. 2010; De Rosa and Salvati 2016). In this context, knowledge of spatio-temporal fertility patterns and trends has been recently improved (Sobotka 2004; Butler 2004; Mills 2010; Kulu 2013; Vitali and Billari 2017). Since the late 1980s, an increasing number of European countries exhibited a particularly low level of fertility (Caldwell and Schindlmayr 2003), associated with a progressive transformation of family structures, marriage and childbearing postponement, and lower propensity to have more than one child (Kohler et al. 2002). These transformations reflected population dynamics typical of the last stages of the first demographic transition (Kirk 1996) and the beginning of the second demographic transition (Hank 2002; Billari and Kohler 2004; Goldstein et al. 2013).

A (more or less intense) reverse of fertility decline attracted the attention of demographers in several European countries since the early 2000s (Goldstein et al. 2009; Kulu and Boyle 2009; Myrskyla et al. 2009). At the same time, fertility varied largely over time and space, responding positively to economic expansions, and declining (more or less rapidly) with recessions (Kulu and Vikat 2007; Mills and Begall 2010; Sobotka et al. 2011; Kreyenfeld et al. 2012). For instance, the 2007 recession was demonstrated to influence spatio-temporal demographic dynamics, e.g. depressing fertility rates (Lerch 2013; Gavalas et al. 2014; Cazzola et al. 2016). The average age of women at marriage and childbearing exceeded 30 years in most of European countries (Rontos 2007, 2010; Kreyenfeld 2010, Lee and Painter 2013). Fertility trends were negatively influenced by youth unemployment (Adserà 2004; Vignoli et al. 2012; Tragaki and Bagavos 2014), economic uncertainty (Hofmann and Hohmeyer 2013), and other social forces shaping propensity to marriage and childbearing (Waldorf and Franklin 2002; Voss 2007; Goldstein and Klüsener 2014).

While a vast ensemble of socioeconomic forces may shape regional population trends (Cherlin et al. 2013), a comprehensive analysis of the spatial structure of basic demographic indicators—including fertility rates—contributes to reconnect local-scale population dynamics to more general patterns of urban growth (Bocquier and Costa 2015), evidencing the inherent complexity of metropolitan systems (Isik and Pinarcioglu 2006; Kroll and Kabisch 2012; Salvati et al. 2016). Assuming that demographic dynamics were (more or less intensively) associated with long-term urban cycles (Lerch 2016), fertility trends in Europe were increasingly studied at more disaggregated spatial scales, especially in metropolitan contexts (Bocquier 2015). High fertility rates were considered an important factor of growth in early urbanization stages (Kulu et al. 2009; Muniz 2009; Kabisch and Haase 2011; Munafò et al. 2013). Internal migration and small-range residential mobility fueled late urbanization and the subsequent suburbanization (Ogden and Hall 2000; Liu 2005; Lerch 2014; Rees et al. 2017), with a subordinate role of fertility (Bocquier and Bree 2018). International migration was finally driving the recent expansion of cities in a context of low fertility and high mortality (Serra et al. 2014; Gkartzios and Scott 2015; Lerch 2016; Carlucci et al. 2017)—with spatially heterogeneous fertility dynamics reflecting latent changes in family structures, marriage postponement and aging (Pinnelli and Di Cesare 2005; Haase et al. 2010; Salvati and Carlucci 2017).

While urban–rural fertility divides have been investigated extensively in advanced countries (e.g. Hank 2001; Thygesen et al. 2005; Kulu and Vikat 2007), fertility in recent times was demonstrated to diverge more at smaller spatial scales, e.g. between small towns and central cities (Weeks et al. 2000; Hank 2001, 2002; Caltabiano 2008). Suburban communities were frequently found to have higher fertility than communities living in central cities (Kulu et al. 2009), with single-family households often related to a particularly high fertility (Kulu and Vikat 2007). These differentials persist when controlling for the underlying socioeconomic context (De Beer and Deerenberg 2007; Chi and Zhu 2008; Kulu and Boyle 2009), suggesting that background conditions may outline specific and spatially-homogeneous fertility choices (Kulu 2013).

Based on these premises, we assumed that distinctive fertility dynamics—more or less aligned with urban transformations—took place in inner cities, suburbs and the surrounding rural areas, often producing heterogeneous and unpredictable social landscapes (Michielin 2004; Garcia 2010; Lee and Painter 2013; Wang and Chi 2017; Panori et al. 2018; Salvati 2018). In these regards, the present study investigates the spatial structure of a gross fertility rate in a Southern European metropolitan region (Athens, Greece) over a relatively long time period (1956–2016), with the aim to identify and quantify the impact of long- and short-term socioeconomic changes on local fertility patterns. Earlier studies indicate Athens (and, more generally, Greece) as a paradigmatic example of heterogeneous demographic dynamics with a strong linkage with the underlying socioeconomic context (e.g. Arapoglou and Sayas 2009; Di Feliciantonio and Salvati 2015; Zitti et al. 2015). Analysis of long-term fertility dynamics in the study area provides a unique opportunity to study apparent and latent linkages between the stage of urban growth and the spatial structure of local fertility rates along a complete city life cycle (Salvati and Carlucci 2017).

The traditional ‘city life cycle’ model originally proposed by Berry (1976) and subsequently adopted in seminal works by Klaassen et al. (1981) and van den Berg et al. (1982), identified four stages of growth (urbanization, suburbanization, counter-urbanization and re-urbanization). Although sometimes criticized for the simplified approach to the intrinsic complexity of urban dynamics (Salvati et al. 2016), this framework is still regarded as representative of basic socioeconomic transitions in metropolitan regions—especially in Southern Europe (Carlucci et al. 2017; Cuadrado-Ciuraneta et al. 2017; Duvernoy et al. 2018)—and for this reason it was adopted in the present study. Following specific studies dealing with the recent Athens’ development (Morelli et al. 2014; Rontos et al. 2016; Pili et al. 2017), the city life cycle was characterized by sequential waves of urbanization (between World War II and the late 1970s) and suburbanization (approximately between the 1970s and the late 1990s), with a subsequent trend towards counter-urbanization (Gkartzios and Scott 2015; Di Feliciantonio et al. 2018; Panori et al. 2018). More recent evidences suggest the emergence of re-urbanization processes (Pili et al. 2017).

Fuelled by population dynamics, real estate speculation, volatile land prices, class segregation and planning deregulation, post-war compact urbanization in Athens was increasingly dependent on the accelerated demographic dynamics typical of the 1950s and the 1960s (Colantoni et al. 2016; Rontos et al. 2016; Zambon et al. 2017). On the contrary, suburbanization was associated with demographic decline of the historical center and higher fertility in fringe districts (Arapoglou and Sayas 2009). Up to the late 1990s, counter-urbanization determined a progressive abandonment of central settlements, making residential mobility a key driver of urban growth—in a context of population ageing and low fertility (Michielin 2004; Haase et al. 2010; Munafò et al. 2013; Lerch 2014). Finally, re-urbanization manifested more recently in a relatively puzzled way, as a result of gentrification, international migration, social segregation and filtering (Di Feliciantonio and Salvati 2015; Di Feliciantonio et al. 2018; Carlucci et al. 2017; Panori et al. 2018). In this regard, the impact of recent economic dynamics was indirectly evaluated through the analysis of changes in the spatial regime of fertility during expansion (2000–2008) and recession (2009–2016).

A statistical approach integrating spatial analysis (Moran’s global and local indexes of spatial autocorrelation), parametric and non-parametric inference and exploratory multivariate statistics was adopted here with the aim to assess the influence of (1) individual stages of a long-term urban cycle from the early 1950s to nowadays (urbanization, suburbanization, counter-urbanization, and re-urbanization) and (2) short-term economic downturns (the most recent phases of expansion and recession from the late 1990s to nowadays) on fertility trends (Salvati and Carlucci 2017). In particular, this work hypothesized that the spatial structure of local fertility responds to social transformations coinciding with individual stages of a complete urban cycle, and controls for the impact of short-term economic downturns (Muniz 2009). In other words, this study aims at verifying if the spatial structure of local fertility is a relatively stable feature of urban systems, being influenced by socioeconomic transformations across medium-long time scales. At the same time, our work tries to demonstrate how changes over time in the spatial structure of a basic indicator of fertility are a slow but irreversible process—contributing either to reduce or to consolidate urban–rural divides that impact the spatial structure of cities.

The paper is organized as follows: Sect. 2 describes the methodology adopted in this study and the statistical data analyzed through descriptive, inferential and multivariate approaches. Section 3 reports the most relevant results of the quantitative analysis. Section 4 provides a long discussion of these results, offering a comparative view of local demographic dynamics in similar socioeconomic contexts in Southern Europe and, finally, Sect. 5 gives some concluding remarks focusing on the originality and novelty of this work and providing suggestions for future investigations of the complex relationship between demographic dynamics and urban cycles.

2 Methodology

2.1 Study area

The present study investigates demographic dynamics in a large urban region (nearly 3000 km2) of Southern Europe (Athens, Greece). Boundaries of the study area were identified according with the Urban Atlas (UA) classification of metropolitan regions in Europe (Salvati and Serra 2016) and mostly coincide with the administrative region of Attica (Pili et al. 2017). Municipalities were regarded as the elementary analysis’ domain of this work (Fig. 1), in line with earlier studies investigating urban growth and population trends in Greece (Colantoni et al. 2016; Rontos et al. 2016; Zambon et al. 2017).

Fig. 1
figure 1

A map illustrating the Athens’ metropolitan region, the main districts and locations in the area

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A partition in 114 statutory municipalities (and local communities) was adopted here: 58 municipalities formed the conurbation of Athens-Piraeus (430 km2), hereafter called the ‘Greater Athens’ area’, characterized by high settlement density and purely compact urban development (Morelli et al. 2014). The remaining 56 municipalities have mostly peri-urban or rural characteristics (Zitti et al. 2015). Population residing in the study area amounted to nearly 1.5 million inhabitants in 1951 (501 inhabitants/km2) and increased to 3.8 million inhabitants in 2011 (1248 inhabitants/km2). The Athens’ case is representative of Mediterranean contexts experiencing changes in the socioeconomic relationship among relevant territorial actors because of intense and spatially complex metropolitan transformations (e.g. Duvernoy et al. 2018).

2.2 Demographic data

The present study provides a comprehensive analysis of the spatial distribution of a basic indicator of fertility across the study area over a sufficiently long time interval between 1956 and 2016. Total fertility rate, i.e. the number of children in the total number of women in fertile age, was adopted here as a generalized indicator of fertility (Lerch 2014). This indicator has been used extensively to describe regional demographic patterns and trends (e.g. Muniz 2009; Bocquier 2015; Salvati and Carlucci 2017), sometimes controlling for the underlying territorial and socioeconomic structure (Vitali and Billari 2017). More specifically, period fertility rates were derived from computation on the total number of births observed at a given time point (e.g. year) and the contingent of women at fertile age (15–49 years) at the same location and time. Official statistics of births and population age structure at a given time (year) and location (municipalities) have been obtained from the Hellenic Statistical Authority (ELSTAT) for 8 years (1956, 1960, 1970, 1980, 1990, 2000, 2008 and 2016). Birth data were derived from vital statistics released annually by the ELSTAT for the whole of Greece and for specific territorial partitions of the country using one of these two approaches: (1) extraction from digital data collected from the ELSTAT web site or made available after an ad-hoc request, or (2) manual digitalization of statistical data reported in official publications of the ELSTAT and made available in a specific digital library (www.statistics.gr). Information on population structure by sex and age class were derived at the same spatial scale from the national Census of Population and Households held every 10 years in Greece.

The use of relatively long time series of local fertility rates brings some problems that should be faced before elementary data or the related indicators are considered in further analysis (Muniz 2009). While the selected territorial disaggregation of municipalities (and local communities) in the study area was representative of the metropolitan hierarchy since the early 1950s—when the majority of urban centers and rural villages were already populated and forming autonomous administrative units (Pili et al. 2017), demographic rates for a few spatial domains were estimated for the first 2 years of investigation (1956 and 1960) considering additional information derived from ELSTAT (when available) or calculated from the related demographic figures and rates as the average of the five nearest spatial units (e.g. Colantoni et al. 2016; Rontos et al. 2016; Salvati et al. 2016). At the same time, the use of such indicators could bring to a partial overview of local fertility (e.g. Bongaarts and Feeney 1998), since fertility estimates for small areas can be more vulnerable to the influence of external factors, e.g. in- and out-migration, than estimates for larger areas (Toulemon 2004).

However, when finding the most appropriate approach and indicators delineating the relationship between fertility and development shifts through time and space, we assumed that “the importance of each variable depends on its spatial distribution” (Muniz 2009). Considering the level of fertility of neighboring municipalities as a predictor for local fertility rates (Salvati and Carlucci 2017), the present study implemented a descriptive analysis of local fertility under the hypothesis that past fertility is a significant determinant of how quickly fertility declines (Muniz 2009). Based on these premises, the use of a basic indicator of fertility from official statistics supplemented with the results of spatial clustering techniques—as we did in this study—was considered detailed enough to assure a comprehensive investigation of past and present fertility trends, taking account of spatial heterogeneity and socioeconomic changes.

2.3 Contextual variables

Demographic data were supplemented with 8 variables assessing basic (territorial and socioeconomic) characteristics of each municipality in the study area. These variables include: (1–4) the linear distance from 4 important urban nodes in the Athens’ metropolitan region (downtown Athens, Piraeus harbor, Maroussi-Olympic Stadium, Markopoulo Messoghias-Airport), (5) average municipal elevation (m at the sea level), (6) proximity to the sea coast (a dummy variable classifying municipalities as coastal: ‘0’ or internal: ‘1’), (7) soil quality index, and (8) per-capita income (a dummy variable distinguishing affluent (‘0’) from economically disadvantaged (‘1’) municipalities). These variables were extensively used in earlier studies profiling socioeconomic characteristics of the study area; technical details can be found in Colantoni et al. (2016), Salvati and Serra (2016) and Pili et al. (2017).

More specifically, these variables describe the territorial structure of the Athens’ metropolitan region (elevation) focusing on accessibility (distance from downtown Athens), urban–rural divides (distance from Piraeus), and land capability for agriculture or forestry (soil quality index) taken as an indicator of dynamic (agriculture) or marginal (forest) contexts in peri-urban and rural Attica (e.g. Colantoni et al. 2015). The (potential) role of sub-centers (distance from Maroussi-Olympic Stadium and Markopoulo Messoghias-Airport) and natural amenities (proximity to the sea coast) shaping past and present urban growth was also evaluated (Pili et al. 2017). Finally, socioeconomic conditions were assessed using a simplified variable that reflects the East–West gradient in Athens. This approach takes account of the well-known polarization in wealthier urban districts (situated in Eastern Athens) and economically disadvantaged districts of Western Athens (Di Feliciantonio et al. 2018). This spatial pattern was observed since the late 1950s and is still evident nowadays (Arapoglou and Sayas 2009; Di Feliciantonio and Salvati 2015; Rontos et al. 2016). Taken together, these variables provide a detailed overview of the evolution of settlements in the study area along the different stages of the Athens’ life cycle. A shapefile of municipal boundaries produced and disseminated by ELSTAT was used to create maps and to perform spatial analysis of demographic and contextual indicators using the ArcGIS ‘Spatial Analyst’ tool (ESRI, Inc., Redwoods, USA).

2.4 Data analysis

An integrated statistical approach was developed in this study with the aim of identifying possible changes in the distribution of fertility rates at different stages of the city life cycle. This approach integrates descriptive statistics, spatial autocorrelation analysis, parametric and non-parametric inference (using pair-wise Pearson and Spearman coefficients), and exploratory multivariate data analysis (hierarchical clustering, Principal Component Analysis). Similarities or differences over time in fertility rates were studied at different geographical scales—from urban (local) to metropolitan (regional). A diachronic analysis of spatial autocorrelation coefficients (global Moran’s z-score) applied to local fertility rates has been proposed with the aim of verifying homogeneity (or diversification) in the spatial structure of fertility over time. Moran’s indexes are measures of spatial autocorrelation, i.e. a correlation in a given variable among nearby locations in space, that can be computed at global scale (producing an overall coefficient of spatial autocorrelation for the entire study area) or at local scale (producing coefficients of spatial autocorrelation for each elementary spatial unit in the study area). Spatial autocorrelation is more complex than one-dimensional autocorrelation because spatial correlation is multi-dimensional (i.e. 2 or 3 dimensions of space) and multi-directional (Salvati and Serra 2016).

A hierarchical clustering has been developed on a data matrix constituted of Moran’s global coefficients by year and bandwidth in order to identify (apparent and latent) changes in the spatial distribution of fertility rates over the city life cycle. Local Moran’s spatial autocorrelation coefficients were calculated with the aim at discriminating spatial clustering or heterogeneity in local fertility rates. Having a long historical series of demographic data, this allows identification of high (and low) fertility areas, and their persistence over time. Assuming that temporal persistence of spatial clusters with different fertility levels is associated with a specific stage of the urban cycle (Salvati and Carlucci 2017), transformations in their territorial structure may indicate transition to a new stage of the cycle (Morelli et al. 2014). For each observation year, a correlation analysis was also performed to test the significance of the relationship between the local fertility structure (local Moran’s index) and the distance from downtown Athens. Assuming a mono-centric model (Salvati and Serra 2016), results of this analysis contribute to characterize spatial clustering along the urban gradient, one of the most effective factors influencing regional fertility in the Mediterranean region (Serra et al. 2014). A diachronic analysis of the influence of the background (territorial and socioeconomic) context on the spatial regime of fertility was finally carried out through a Principal Component Analysis. This technique was adopted to demonstrate how the Athens’ life cycle (Morelli et al. 2014) was associated with specific changes in the spatial structure of local fertility.

2.4.1 Descriptive statistics

A descriptive analysis of regional and local fertility rates was carried out in the study area through the use of simple statistics (e.g. average, median, absolute range, percentiles, coefficient of variation). These statistics were calculated with the aim to provide insights in the statistical distribution of fertility rates in the study area at the 8 study years.

2.4.2 A global Moran’s analysis of spatial autocorrelation in total fertility rates in Athens

Using municipal-level data, a global Moran’s index of spatial autocorrelation in fertility rates (z-score and the related p value) was calculated for 8 time intervals, considering separately 10 bandwidths (2.5, 5, 7.5, 10, 15, 20, 25, 30, 35 and 40 km) representative of different spatial scales from strictly urban (2.5 km) to metropolitan at large (40 km). Coefficients were tested for significance at p < 0.001 under the null hypothesis of no spatial relationship in fertility levels. Taking account of changes in the global Moran’s index (z-score) at different bandwidths allows a comparative estimation of intensity and extent of spatial interactions between the selected analysis’ domains, i.e. municipalities (Salvati and Carlucci 2017).

2.4.3 Hierarchical clustering

A hierarchical clustering based on Ward’s agglomeration rule computed on a matrix of Euclidean distances (Di Feliciantonio et al. 2018) was run on a data matrix composed of the global Moran’s auto-correlation coefficients by year and bandwidth (see Sect. 2.4.2). Separate dendrograms were prepared for years and bandwidths with the aim to illustrate similarities in the spatial structure of fertility rates across geographical scales and along the investigated time horizon.

2.4.4 A local Moran’s analysis of spatial autocorrelation in fertility levels

Fertility divides reflecting a (more or less steep) gradient in the studied variable reveal specific spatial regimes changing (more or less rapidly) over time (Salvati et al. 2016). A diachronic investigation of high (or low) fertility clusters was carried out using local Moran’s coefficients of spatial autocorrelation (z-scores) calculated at each year and municipality of the study area and illustrated through maps. Based on the local Moran’s coefficient at each location, municipalities were classified as (1) high fertility hotspots (high rates with similar neighbors) when z-score > 2 and (2) low fertility cold spots (low rates with similar neighbors) when z-score < − 2.

2.4.5 Exploring correlation between local Moran’s coefficients and distance from downtown Athens

The spatial relationship between local Moran’s coefficients of spatial autocorrelation (z-scores) and the distance of each municipality from downtown Athens was tested for significance (p < 0.05 after Bonferroni’s correction for multiple comparisons) using pair-wise parametric (Pearson) and non-parametric (Spearman, Kendall) correlation coefficients. The use of both parametric and non-parametric inference contributes to discriminate linear from non-linear correlations in the studied variables (Pili et al. 2017), assuming to find both types of relationship between them.

2.4.6 Principal component analysis

A Principal Component Analysis (PCA) was finally run on the (municipal-scale) data matrix composed of 16 variables (8 annual series of local Moran’s coefficients and 8 contextual variables, see Sect. 2.3) with the aim to assess the multivariate relationship between the (evolving) spatial structure of local fertility and the background (territorial and socioeconomic) context. PCA is a multivariate exploratory analysis aimed at evaluating the (latent) correlation structure in a complex dataset, after reducing redundancy and multi-collinearity among variables (Duvernoy et al. 2018). More specifically, changes over time in the (multivariate) correlation between background variables and the spatial structure of fertility in Athens were considered indicative of the latent impact of urban stages on demographic patterns and processes (Salvati and Carlucci 2017). Components with eigenvalues > 1 were retained and analyzed. Component loadings > |0.5| were considered significant when identifying multivariate relationships among variables (Colantoni et al. 2016).

3 Results

3.1 Descriptive statistics

Fertility levels in the study area were relatively high up to the late 1970s (Table 1), decreasing since the late 1980s; the lowest value was recorded for 2000. With economic expansion, a moderate recovery in fertility was observed in the late 2000s. With crisis, fertility levels decreased again. Spatial variability of fertility rates across municipalities decreased slowly between 1956 and 2000, increasing moderately in 2008 and 2016. The lowest spatial variability in fertility rates was recorded for 2000. The normalized range of fertility rates followed a comparable trend over time: spatially-heterogeneous rates were recorded for 1956 and 2008. Trends over time in both 25th and 75th percentiles highlight an overall reduction of fertility since the early 1990s. Median and mean rates converged since the early 1960s, indicating a quasi-normal statistical distribution of fertility rates in the study area: the median-to-mean ratio was 1 in 1960 and 1970 and deviated slightly from 1 in 2008 and 2016.

Table 1 Descriptive statistics of the distribution of fertility rates in the municipalities of the Athens’ metropolitan region (n = 114)
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3.2 A global Moran’s index of spatial autocorrelation in total fertility rates in Athens

The global Moran’s index of spatial auto-correlation in local fertility rates was calculated for 10 bandwidths and showed a comparable trend over time (Fig. 2). The global Moran’s index was low and statistically insignificant for two bandwidths (2.5 km and 5 km). The highest values of the index were observed for bandwidths ranging between 15 and 20 km, decreasing moderately at larger bandwidths—between 25 and 40 km—and maintaining relatively stable over time. The 2  years with the highest indexes at all the investigated bandwidths were 1956 and 1980. Conversely, 2008 and 2016 were the years with the lowest coefficients of spatial auto-correlation for all bandwidths.

Fig. 2
figure 2

Distribution of the global Moran’s index of spatial autocorrelation in total fertility by year and bandwidth

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3.3 Hierarchical clustering

A cluster analysis (Euclidean distances, Ward’s agglomeration rule) was run on the data matrix composed of global Moran’s auto-correlation coefficients, grouping separately years and bandwidths (Fig. 3). Hierarchical clustering showed differences in the spatial regime of fertility between smaller neighborhoods (< 5 km) and intermediate-large neighborhoods (> 5 km)—although the greatest similarity was observed for neighborhoods between 15 and 25 km. These results reveal a spatial regime with the highest similarity at the urban scale (15–25 km) and the lowest similarity at the local (neighboring) scale (< 7.5 km). An intermediate level of similarity was observed at larger scales (30–40 km). Time periods (i.e. years) with accelerated urban growth and concentration of resident population in central districts were classified together (1956 and 1980). A high similarity in the spatial regime of local fertility was also observed for specific years (1960, 1970, 2000) reflecting a transition between subsequent urban stages (respectively from urbanization to suburbanization and from suburbanization to counter-urbanization). The spatial regime observed for the last 2 years (2008 and 2016) showed greater similarity with that recorded for 1990. These periods were characterized by a particularly low level of fertility at the regional (and country) scale.

Fig. 3
figure 3

A dendrogram (hierarchical clustering with Euclidean distances and Ward’s agglomeration rule as amalgamation parameters) illustrating similarities in global Moran’s indexes of spatial autocorrelation by bandwidth, km (left) and year (right)

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3.4 A local Moran’s analysis of spatial autocorrelation in fertility levels

The statistical analysis of local Moran’s coefficients outlines changes over time in the spatial regime of fertility (Fig. 4). Highly positive auto-correlation coefficients (indicating spatial clustering) were found (1) in rural municipalities north of Athens for 1956 and (2) in peri-urban municipalities surrounding the Greater Athens’ area since the early 1960s. The highest (positive) local Moran’s coefficients were observed for 1980 in urban locations. In the subsequent decades, the highest positive auto-correlation coefficients were recorded in some peripheral municipalities West of Athens (1990), in suburban municipalities East and West of Athens (2000) and, more specifically, in Western Attica locations (2008 and 2016). Conversely, municipalities characterized by local Moran’s negative coefficients (< 2) were scattered all over the study area, concentrating preferentially in rural, marginal locations West, North-east and South of Athens.

Fig. 4
figure 4

Spatial distribution of the Moran’s local index of spatial autocorrelation in total fertility rate by year

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3.5 Exploring correlation between local Moran’s coefficients and distance from downtown Athens

The relationship between the local Moran’s indexes of spatial autocorrelation and the distance from downtown Athens was studied graphically (Fig. 5) and through hypothesis testing (Table 2). The results of both parametric (Pearson) and non-parametric (Spearman and Kendall) inference indicate a significant and negative correlation between the two variables for the years 1980, 1990, and 2000. Correlation coefficients declined sharply in both 2008 and 2016. By contrast, the statistical correlation between the two variables was negative and non-significant at the beginning of the study period.

Fig. 5
figure 5

Empirical relationship between the local Moran’s index of spatial autocorrelation in total fertility rate (z-score) and the distance from downtown Athens (dAth, km) by year

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Table 2 Parametric (Pearson) and non-parametric (Spearman and Kendall) pair-wise correlation coefficients between local Moran’s index of spatial autocorrelation in total fertility rate and distance from downtown Athens (km) by year (bold indicates significance at p < 0.05 after Bonferroni’s correction for multiple comparisons)
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3.6 Principal component analysis

The results of a principal component analysis investigating changes over time in the spatial regime of local fertility together with (municipal-scale) background variables were presented in Table 3. Three components were extracted explaining together 59% of total variance of the data matrix. Component 1 (30%) was found negatively associated with the local Moran’s coefficients of spatial autocorrelation during most of the study years (decreasing between 1956 and 2000) and positively associated with the distance from three urban centers (Athens, Piraeus and Maroussi). Component 2 (17%) was negatively associated with the local Moran’s coefficients for 1960 and 1970, and with the distance from all urban centers considered in this study. Finally, component 3 (12%) was negatively correlated with local Moran’s and the average elevation of each municipality at the last three years of investigation (2000, 2008, 2016). Taken together, these findings suggest that, with urbanization, the spatial structure of fertility was associated with the urban gradient (which is partly coinciding with the elevation gradient in the study area). The intensity of this relationship decreased with suburbanization and, much more, with counter-urbanization.

Table 3 Principal component analysis identifying latent spatial structures in the local Moran’s index of spatial autocorrelation of fertility levels and background (territorial and socioeconomic) variables in the Athens’ metropolitan region (only component’s loadings > |0.4| were shown)
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4 Discussion

Assuming the influence of territorial structures, culture, institutions and policy strategies on local fertility (Bongaarts and Watkins 1996; Dijkstra et al. 2015; Carbonaro et al. 2018), a comprehensive explanation of current fertility declines in advanced economies requires a contextual understanding of local socio-demographic patterns and the related economic forces (Wang and Chi 2017). Although relatively few works dealt with long-term changes in the spatial regime of population variables (Işik and Pinarcioglu 2006; Muniz 2009; Potter et al. 2010; Goldstein and Klüsener 2014), earlier studies have identified specific spatial patterns and structures for different demographic dimensions, including fertility (e.g. Weeks et al. 2000; Waldorf and Franklin 2002; Goodchild and Janelle 2004). Although spatial contiguity normally implies dependence in demographic behaviors, the concept of spatial auto-correlation was more recently considered in regional demography (Castro 2007), assuming spatial heterogeneity as a trait of recent fertility trends (Vitali and Billari 2017). In these regards, spatial analysis is appropriate to represent how fertility varies over space, providing an original interpretation of the long-term evolution of demographic divides among urban and rural areas (Kulu and Boyle 2009; Haase et al. 2010; Di Feliciantonio et al. 2018).

Although spatial dependence in fertility rates has been continuously observed along the study period, our work highlights how polarization in high and low fertility clusters is not a common phenomenon to all phases of the Athens’ growth. A polarized spatial structure was observed with the ‘urbanization’ stage, basically from 1956 to 1980. Spatial analysis also indicates that similar fertility patterns were clustered in areas with a specific territorial and socioeconomic profile. A closely polarized structure associated with rapid population growth in central districts was observed in the mid-1950s. At this stage, a high fertility cluster was observed in a rural area North of Athens, declining progressively in the subsequent decades. Clustered structures were also observed in the 1960s and the 1970s, outlining a divide between the Greater Athens’ area (with the highest fertility) and rural municipalities (with the lowest fertility). In the same years, the highest population concentration (92% of Attica inhabitants) and the highest rate of population growth (2% per year) were observed in the Greater Athens’ area (Salvati 2018). Natural balance and internal migration from rural areas both contributed to population growth in central Athens (Rontos et al. 2016). At a larger scale, the 1970s coincided—in Greece and in other Mediterranean countries—with an impressive demographic boom, followed by a rapid and continuous decline in fertility (Rontos 2010; Gavalas et al. 2014; Kotzamanis and Kostaki 2015; Kotzamanis et al. 2017).

The most polarized structure was observed for 1980, a period coinciding with the highest urban concentration in the Greater Athens’ area and with the end of the ‘urbanization’ stage. At that time, the largest high-fertility cluster (z-score > 2) coincided with the Greater Athens’ area. Low-fertility clusters were observed in marginal, rural areas West, North-east, and South of Athens, emphasizing the importance of the urban gradient. Results of Pearson and Spearman correlation analysis went in the same direction: the highest and significant correlation coefficients between local Moran’s z-scores ​​and the distance from downtown Athens were observed for 1980, and progressively decreased in the following period, becoming non-significant since 2008.

With ‘suburbanization’, a shift from a clustered spatial regime to a more heterogeneous structure of fertility took place over a relatively long time period (Morelli et al. 2014). In this regard, the 1980s were a turning point in the spatial regime of fertility in Athens: spatial polarization in high- and low-fertility districts decreased and a new, smaller cluster located in a suburban area west of the city emerged and persisted in the following decades. In other words, the spatial distribution of high-fertility districts in the 1980s and 1990s reflected a progressive suburbanization—with the rapid development of peri-urban districts physically independent from the Greater Athens’ area. Since the 1990s, territorial disparities in fertility levels have been further reduced and the spatial structure of fertility rates became progressively less clustered (Salvati and Carlucci 2017). With counter-urbanization, the increased heterogeneity in fertility levels has been fairly evident in the study area. These results seem to be in line with empirical evidence of previous studies carried out in other socioeconomic contexts (e.g. Muniz 2009). This structure has changed little during the 2000s, when a moderate recovery of fertility was observed (from 1.2 to 1.5 children per woman between 2000 and 2008). While a new reduction in fertility rates was observed in the subsequent years coinciding with the great recession, the spatial structure of local fertility remained (more or less) comparable to what was observed in the time period before the economic crisis (2008).

Spatial heterogeneity in local fertility is presumably the result of individual attitudes towards family formation and childbearing; these became increasingly diversified and less influenced by the local context (Vitali and Billari 2017). Compared with the past, the background (territorial and socioeconomic) context was becoming a less important factor in the discrimination between high and low fertility areas, as demonstrated by the results of the correlation analysis. At the same time, spatial heterogeneity characterizing fertility patterns in recent years may reflect a transition towards more dispersed and chaotic urban models typical of the late phase of counter-urbanization (Carlucci et al. 2017), likely anticipating a new phase of re-urbanization (Salvati 2018). The increased unpredictability of spatio-temporal changes in small-scale fertility rates makes it also more difficult to estimate the contribution of different spatial trends to fertility levels at regional or national scale (Rontos 2007, 2010).

The present study finally suggests that spatial fertility structures in Athens are more associated with long-term urban transformations than with short-term economic dynamics. As a matter of fact, changes in the spatial structure of fertility during the most recent economic downturns (expansion between 2000 and 2008; recession between 2009 and 2016) were relatively weak. While regional fertility patterns were sometimes demonstrated to be associated with short-term economic dynamics (e.g. Tragaki and Bagavos 2019 for Greece), local spatial structures demonstrated to be less sensitive to such trends (Salvati 2018). Although the most recent economic crisis has sometimes exacerbated the divide between rich and poor districts (Di Feliciantonio et al. 2018), the impact on the spatial structure of fertility rates was relatively modest in Athens (Rontos et al. 2016). As fertility levels generally respond slowly to the effects of an economic crisis, further investigations could provide more refined results considering longer demographic time series that include a greater number of economic events.

Based on these results, changes in the spatial structure of local fertility is considered a demographic indicator reflecting different stages of a complete urban cycle in Athens. More specifically, our work outlines how the relationship between the spatial structure of fertility and urban configuration (e.g. the distance from downtown Athens) changes with the different stages of the city life cycle. Assuming that demographic dynamics are a key component of cities’ attractiveness (Dijkstra et al. 2015), a spatially explicit analysis of metropolitan population trends covering enough long time intervals has demonstrated to provide appropriate insights in urban theory and valuable suggestions to regional planning and design of social policies more aligned with demographic change (Lerch 2014; Salvati et al. 2016; Carbonaro et al. 2018).

Formation of new family structures, aging, gentrification of inner cities, migration and social filtering, were important phenomena that can be more effectively managed through integrated socioeconomic policies in metropolitan areas (Buzar et al. 2005; Arapoglou and Sayas 2009; Lauf et al. 2012). At the same time, recent processes of re-densification of central districts are intimately dependent on demographic dynamics and should be considered in strategies aimed at regulating urban growth (Haase et al. 2010; Kabisch and Haase 2011; Kroll and Kabisch 2012), e.g. through containment of settlement sprawl in suburban locations (Munafò et al. 2013; Colantoni et al. 2015; Duvernoy et al. 2018; Zambon et al. 2018).

From the methodological perspective, the increased availability of small-scale data, and improvements in demographic indicators, analytical approaches and spatial techniques, allowed a refined analysis of regional fertility trends. Although the approach proposed in this study is eminently descriptive and exploratory, it proved suitable to identify the intimate linkage between urban transformations and changes in the spatial structure of local fertility. By integrating descriptive statistics, parametric and non-parametric inference and multivariate exploratory techniques, this approach can be adopted in demographic investigation of other socioeconomic contexts characterized by (more or less) rapid changes in the spatial regime of fertility (Morelli et al. 2014). More specifically, the adopted framework support the use of spatially explicit and implicit techniques that can be applied to urban studies in other Southern European countries. Novelty of our approach lies in the complete integration of spatially explicit and implicit exploratory approaches in a common analysis of regional demography.

Especially when geo-referenced data are available that cover a sufficiently long time period representative of important urban transformations, results of the analytical framework proposed in this study may integrate findings from econometric models grounded on economic growth theories and the empirical knowledge derived from application of urban theories (Michielin 2004; Chi and Zhu 2008; Cazzola et al. 2016). Compared to such models, the proposed approach seems to be particularly appropriate in the study of similarities (or differences) in fertility patterns at different geographical scales—from urban (local) to metropolitan (regional). This will definitely contribute to a refined understanding of multi-scale socio-demographic dynamics typical of contemporary cities (Salvati et al. 2016). Results of our study finally outline the importance of geo-referenced data covering long time intervals. Availability of vital statistics at disaggregated spatial scales (e.g. municipalities) since the early 1950s allows a more accurate investigation of the spatial regime underpinning demographic changes at both national, regional and local scale in Europe. The extensive knowledge provided by empirical studies that develop a spatial interpretation of demographic dynamics vis-à-vis urban change may also contribute to improve accuracy of regional population projections (Bocquier 2015).

5 Conclusion

The empirical results of this study highlight important changes in the spatial pattern of fertility rates in the Athens’ metropolitan region. In particular, the spatial structure of local fertility identified homogeneous areas with similar birth rates in the period between 1956 and 1980. Being the result of accelerated population growth, urbanization was associated with an evident fertility divide in urban and rural districts, especially at the end of the urbanization wave (1980). The highest population concentration in the Greater Athens’ area and the most intense socioeconomic disparities between urban and rural areas were observed at that time. The progressive decline of spatial clustering in local fertility observed in the 1980s coincided with suburbanization. Consequently, the spatial structure of fertility was less dependent on the urban gradient in the subsequent time period. Spatial segregation of population with similar fertility behaviors was increasingly reduced, outlining a less polarized (and more heterogeneous) spatial structure during counter-urbanization. In this time period, spatial heterogeneity was associated with a huge fertility decline.

Based on an exploratory approach, our work demonstrates that territorial divides in fertility levels (1) are influenced by background socioeconomic conditions—resulting in specific socio-spatial structures at the metropolitan scale—and (2) respond (more or less rapidly) to long-term urban dynamics, being less sensitive to short-term economic shocks. These findings corroborate earlier studies focusing on the effect of economic cycles on fertility patterns and trends. While country/regional fertility rates are sensitive to economic downturns, the local-scale spatial structure of fertility was demonstrated to be a more stable attribute of complex socioeconomic systems influenced by medium-term changes that reflect individual stages of a complete urban cycle. The socioeconomic context underlying such transformations—and the implications for population dynamics at various spatial scales—should be investigated further adopting comparative approaches based on descriptive, inferential and multivariate analysis of demographic indicators. This will contribute to a truly multi-dimensional interpretation of metropolitan change and socioeconomic transformations shaping urban complexity in advanced economies.