Testing the role of barriers in shaping segregation profiles: The importance of visualizing the local neighborhood

Abstract

“Egocentric” segregation profiles allow researchers to avoid a reliance on a priori definitions of local neighborhoods that contribute an unknown amount of error to measures of segregation. To date, however, such profiles have used distance-decay techniques that rely on “as the crow flies” measures of space. Yet we know that major roads, railroads, and other physical attributes of space mean that such techniques may introduce error into the measurement and visualization of residential segregation. Here, I use a variation on standard smoothing techniques that allows the smoothing function to vary based on a second variable of interest, in this case, the location of major roads, railroads, and nonresidential land use. Using Philadelphia as a case study due to access to detailed land-use data, I show that barriers do not affect observed values of city-level racial and ethnic dissimilarity. Visualizing the impact of barriers on local neighborhoods, however, shows that while barriers may not affect city-wide indexes of segregation, they continue to powerfully shape local experiences of the city, including protecting new immigrant ethnic enclaves, wealthy white neighborhoods, and also isolating high-poverty, predominantly black neighborhoods in different parts of the city.

Keywords

Segregation boundaries visualization urban geography exploratory spatial data analysis

Residential segregation is, by definition, a spatial structure of inequality. Yet, until recently, its measurement has been primarily aspatial. By relying on the census tract as a proxy of residential neighborhoods, traditional measures of segregation do not adjust for the size, shape, or location of neighborhoods within a city in order to create a single metric for how segregated or integrated a city or region is. Social scientists have explicitly acknowledged the importance of physical space on residential patterns for generations. Perhaps most famously, Suttles' (1972) “defended neighborhoods” in Chicago relied not only on social actions and violence to build that defense, but also clearly demarcated neighborhood boundaries upon which individuals cognitively mapped the boundary between “good” and “bad” areas. More theoretically, scholars of ethnicity have emphasized the importance of creating cultural boundaries between identities over within-group similarities as perhaps the most important operative aspect of racial (or ethnic) formation (Brubaker, 2002; Wimmer, 2009). Those boundaries between groups are taken for granted in segregation research, yet rarely measured or mentioned, save for a few examples (e.g., Grannis, 2005).

Unfortunately, although spatial techniques have enhanced the toolkit of options for scholars to measure and visualize racial residential patterns, they have not incorporated boundaries adequately. “Egocentric” segregation profiles (Reardon et al., 2008), for example, allow researchers to avoid a reliance on a priori definitions of local neighborhoods that contribute an unknown amount of error to measures of segregation. To date, however, such profiles have used distance-decay techniques that rely on “as the crow flies” measures of space. In other words, these methods have advanced the use of spatial analysis but rely on continuous measures of social space. Yet we know that major roads, railroads, and other physical attributes of space mean that such techniques may also introduce error into the measurement and visualization of residential segregation. Socially, space is discontinuous but scholars have advanced methods so far that rely on assumptions of continuous spatial space.

That reliance made sense in light of Tobler's “first law of geography” that “everything is related to everything else, near things are more related than distant things” (Tobler, 1970: 236). If Tobler's law is accurate, then assuming a continuous spatial space makes both practical and conceptual sense. However, others argue that the law was never tested and in reality “near things are often more related than distant things, and some near things have more in common than others” (Harris et al., 2013: 902). In fact, Harris and colleagues demonstrate that near things can be unrelated, depending on the social and physical context of the space, and have introduced hierarchical spatial autoregressive models that can incorporate local variations in spatial autocorrelation in regression analyses (Dong and Harris, 2015; Harris, 2016). In a similar vein of research, the location of physical barriers is related to patterns of economic deprivation in Glasgow, but are not key drivers of those geographic patterns of deprivation (Mitchell and Lee, 2014).

With regard to American segregation patterns, Roberto's (2015) work on defining and measuring residential boundaries via levels of local diversity highlights how stark those divides between areas are and thus how important it is to take physical boundaries seriously in measuring, visualizing, and analyzing residential segregation. Legewie and Schaffer (2016) shows that locations without clear boundaries between racial groups in New York City are where residents are most likely to report noise complaints. Likely related to that, Tannen's (2016) analysis of gentrification patterns highlights the fact that gentrification is the process of boundary-crossing or spill-over across previously clear divides between neighborhoods, turning sharp boundaries into fuzzy ones like those Legewie and Schaffer highlight.

Here, I use a smoothing technique that functions as a variation on standard kernel density distance-decay functions that allows the decay function to vary based on a second variable of interest, in this case, the location of major roads, railroads, and major nonresidential land use to model a discontinuous version of social space. Using Philadelphia as a case study, I test whether or not incorporating local barriers into egocentric measures of segregation increases observed levels of segregation before identifying specific locations in which the incorporation of land use has more or less significant effects.

Space and segregation: What's the problem?

Social scientists measure segregation by examining the demographics of individual neighborhoods and comparing them to an ideal, integrated hypothetical city. Unfortunately, the “neighborhood” is much like Supreme Court Justice Potter's test for obscenity—we know neighborhoods when we see them, but we cannot create a universal, agreed upon definition of them (Durlauf, 2004; Galster, 2008). To date, defining “the neighborhood” has largely been an exercise in comparing different, inadequate geographic proxies for an ambiguous but important social concept, one that often varies depending on individual residential histories (Hwang, 2016). We know that individuals define their “neighborhood” not as singular, static entities but rather as shifting geographies based on the conceptual topic of interest such as one's social networks, economic activity, or home valuation (Hwang, 2016; Martin, 2003; Suttles, 1972). No matter the proxy used, the modifiable areal unit problem (MAUP) introduces a real but unknown amount of measurement error when defining neighborhoods that can have significant impacts on the identification of a city's segregation and inequality (Downey, 2006; Grengs, 2007; Openshaw and Taylor, 1979).

Even were we able to perfectly define neighborhoods, segregation research generally treats individual neighborhood as insular and isolated. Segregation works at the neighborhood level—via social geographic processes such as redlining, localized housing markets, and school catchment areas—to structure opportunity (Galster and Sharkey, 2017). However, neighborhood boundaries are not walls around fortresses, and as the research on spillover effects on crime demonstrates, “neighborhood effects” aren't necessarily only caused by one's own neighborhood, but also by proximate neighborhoods, and possibly the ones past that as well (Crowder and South, 2011; Peterson and Krivo, 2010; Sharkey, 2014).

In previous work (Kramer, 2017), I argue that an “externality space” approach to segregation built on work by Galster (1986) can resolve these difficulties by defining neighborhoods by their boundaries and the strength of those boundaries. An externality space is one in which residents perceive the location as altering their own residential well-being (be it use value, psychological or financial), and externality spaces have three attributes: congruence (does it relate to predefined geographies?), generality (do use value externalities map to psychological externalities, etc.), and accordance (do individuals agree on that externality space definition?). This definition offers researches a way to systematically conceptualize Suttles’ “defended neighborhood.”

More broadly, if the inclusion of physical barriers affects city-level measures of segregation, than the consensus that racial segregation is falling, albeit slowly, may be an artifact of the shift toward income over racial segregation in the United States (Reardon and Bischoff, 2011) combined with border effects that have not been adequately measured to date. Thus, this paper is both a confirmation of the accuracy of aspatial and spatial measures that assume continuous space and a test of how physical space shapes community and individual behaviors (Grannis, 2009).

Data and methods

While American urban sociology has traditionally centered the Chicago school, its birth can be traced to Du Bois' pioneering Philadelphia Negro (1996 [1899]; Morris, 2015). Beyond Philadelphia's symbolic role as the birthplace of American urban sociology, it is also a racially diverse and highly segregated city. By 2010, Philadelphia was the 50th (out of over 3000) most diverse county in the country and one of the top 10 most segregated cities in the country by most metrics. This paper focuses on the city of Philadelphia and not the larger metropolitan region, which includes 11 other counties spanning across four states and nearly six million residents, for two substantive reasons. First, although the city accounts for only 25% of the region's population, it accounts for over 45% of the area's total nonwhite population and more than half of the region's Black population in 2010. Second, by focusing on one municipality, I avoid the potential for local municipal boundaries to act as segregation boundaries via legal mechanisms such as maximum density requirements (Rothwell and Massey, 2009; Rugh and Massey, 2010).

Block-level demographic data for this project come from the 2010 Summary File 1 of the US Census. Census blocks are formed by the combination of physical features that can be used as boundaries (streets, streams, railroads, etc.) and/or legal boundaries if relevant to that location.¹ To identify boundaries, I combine the Census' TIGER shapefile definitions of major roads² (Grannis, 2005) with data from the Pennsylvania Spatial Data Access clearinghouse to identify the locations of rivers, parks, and railroad tracks that can also serve as potential physical boundaries between neighborhoods.

Raster smoothing

Similar to incorporating a “moving average” in a graph with noisy data, raster maps can be smoothed to better model changes across a space that may be obscured by noisy data. Kernel estimation (or kernel density analysis) was developed to obtain a smooth estimate of a probability density from an observed sample (Bailey and Gattrell, 1995). When an entire population has been mapped (such as the decennial censuses used in this paper), kernel density analysis is a form of data smoothing. As Lee et al. (2008) show, kernel density analysis can approximate the demographics of a local area around each raster cell in a given city or metro area. This paper builds on Lee and colleagues' process by allowing a second variable (in this case, aspects of the physical environment) to affect the variable of interest (the demographics of a raster cell's local area). The smoothing technique I use is empirically identical to the kernel density analysis used by Lee et al. (2008) but slightly simplified.

Non-Euclidean smoothing

Social space, in reality, is far from Euclidean. We expect physical attributes of a space to dramatically affect the ease of interaction in that space.³ For example, people who live on a small, tertiary street are likely to interact and be exposed to each other frequently, even if they live a number of blocks away from each other, because they walk along the same sidewalks, or frequent the same shops and restaurants in the neighborhood (Grannis, 2009). On the other hand, people living across an interstate highway from each other may be physically closer than the residents described above, but are much less likely to interact. We can consider these attributes of the physical space as a cost to travel—that is, it easy to cross a small, tertiary street but it takes more effort to find a way to cross a highway or railroad tracks. The only change is that the bandwidth, rather than being equal in all directions, is instead a function of a given friction function of the space (for further details on the methodology, see Kramer, 2012).⁴ I identify a variety of potential barriers to social interaction and integration. I include all major roads as identified by the US Census Bureau, bodies of water (where they are not crossed by small, tertiary roads), and all railroad tracks as identified by the Pennsylvania Spatial Data Access Clearinghouse. I additionally include any census block with no residents (excluding parks), as these blocks are typically large industrial or commercial buildings—often vacant—that can act as symbolic and physical barriers to interaction. A non-Euclidean kernel density analysis can be understood as a weighted moving average across space where the weighting is dependent on the cost of moving across a given space. In mathematical terms, kernel density analysis is defined as

\hat{λ} (s) = \sum_{i = 1}^{n} (1 / τ^{2}) k (\frac{s - s_{i}}{τ})

where k(i) is a symmetric density-decay function about the origin, τ is the bandwidth of a circle surrounding s in which any points (in this case, people of a given race) contribute to the kernel's estimate (for more details on the technique, see Lee et al. (2008).⁵

Figure 1 is an idealized comparison of a single iteration of Euclidean and non-Euclidean smoothing. The python script differently weights rooks case and queen case adjacent cells so that the smoothing creates a circular pattern and not the square in the example, but I skip that step in this figure for ease of interpretation. Imagine a cell populated with 63 people surrounded by cells with no population in them. In Euclidean smoothing, each cell would have the same population (7) after smoothing. To introduce the effect of a barrier, first we assign a “friction” value (F_i) to that barrier and a total friction (F). In this example, I assign a friction double that of other cells for four of the adjacent cells. Individual cell's friction are then converted to a receptiveness value (R_i), simply 1/F_i and each cell then receives a proportion of the population being shared equal to R_i/F. Larger bandwidths are created by repeating this process iteratively. For 50 m × 50 m raster cells, a 500 m bandwidth is 10 iterations, 20 iterations equals 1000 m bandwidths, etc.

Figure 1.

Comparison of Euclidean and non-Euclidean smoothing process. (a) Original values. (b) Euclidean smoothing (no friction). (c) Friction converted to receptiveness. (d) Proportion of total received. (e) End value, non-Euclidean smoothing.

To determine whether or not barriers affect citywide indexes, I report the results from three sets of non-Euclidean smoothings that include barriers with friction. In other words, k(i) is an asymmetric density-decay function and the asymmetry is defined by the existence of physical barriers. For example, in a simulation in which barriers have twice the friction of nonbarriers, individuals on opposite sides of a barrier have one half the impact on the egocentric neighborhood of each other compared to Euclidean values such as those used by Reardon et al. (2009) and Lee et al. (2008). The three friction values used are 2, 10, and 1000. Friction values were selected to represent ideal types and are not meant to imply that one value is more accurate or realistic than another. The 2 × friction was selected because of its conceptual simplicity: it is twice as hard to cross a barrier than a nonbarrier cell. The 10 × friction was selected for similar reasons. Finally, the 1000 × friction is designed to approximate a nearly impassable barrier: 1000 people across a barrier would have the same impact on a cell's observed racial segregation as a single person in a cell on the same side of the barrier. Future work should attempt to identify the correct impact of the typical barrier in order to more accurately capture the real impact of barriers as opposed to providing a range of potential impacts, dependent on a priori decisions about the strength of barriers.

Adding a positive friction value effectively reduces the kernel bandwidth by increasing the distance decay function dependent on that friction value.⁶ As such, the introduction of non-Euclidean smoothing should increase observed levels of segregation as smaller aggregation units have high reported rates of segregation, as smaller units implicitly includes segregation at higher scales (Duncan et al., 1961). In results not shown, this is not the case for the inclusion of friction for nonlinear local measures (Theil's H) because of the effect of smaller ethnic groups (Asians and Latinos) on the multi-group local score.⁷ To measure segregation, I focus on the most common measure of evenness, the two-group dissimilarity index D

D = 1 / 2 \sum [(\frac{b_{i}}{B}) - (\frac{w_{i}}{W})]

where b_i is the Black population in a subunit, B is the total Black population of the entire area, w_i is the White population in a given subunit, and W is the White population of the entire area.

Results

Evenness in Philadelphia

Like other major northeastern cities, Philadelphia's population has been shifting from majority White to plurality Black. In the last 30 years of the 20th century, Philadelphia lost almost 500,000 total residents before stabilizing. By 2010, Philadelphia's total population had stabilized as White and Black out-migration continued while in-migration by Hispanic and Asian immigrants to the city grew. Between 2000 and 2010, the Black population grew larger (or, more accurately, shrunk less) than the White population of Philadelphia. According to the 2010 census, Philadelphia is 42.2% non-Hispanic Black, 36.9% non-Hispanic White, 12.3% Latino, and 5.9% Asian.

I begin by comparing the dissimilarity measures in Table 1. Following Reardon et al. (2009), each raster cell's bandwidth (the circular area around the cell of interest used to calculate that cell's racial demographics) is measured at four sizes. The smallest has a radius (also known as a “bandwidth”) of 500 m and is comparable to an easily walkable neighborhood, unless there is a barrier. The second smallest radius is 1 km in each direction and is a larger but still walkable area. The two larger neighborhoods—2000 m and 4000 m in radius—are included to replicate previous research using kernel density analysis and because prior research (Bader and Ailshire, 2010) indicates that even at these distances, the racial composition of the population is associated with residential senses of fear or safety in their neighborhood.

Table 1.

Dissimilarity indices by smoothing bandwidth and friction levels.

Friction level	500 m Bandwidth		1000 m Bandwidth		2000 m Bandwidth		4000 m Bandwidth
Friction level	Value	% Difference from Euclidean value	Value	% Difference from Euclidean value	Value	% Difference from Euclidean value	Value	% Difference from Euclidean value
Black–White dissimilarity index
None	.750		.738		.723		.702
2×	.749	−0.1	.736	−0.2	.721	−0.3	.702	00
10×	.762	1.6	.753	2.0	.735	1.7	.709	1.0
1000×	.771	2.8	.777	5.2	.774	6.9	.771	10.1
Latino–White dissimilarity index
None	.623		.613		.600		.582
2×	.634	1.7	.626	2.1	.613	2.2	.598	2.7
10×	.638	4.3	.631	2.9	.620	3.3	.607	4.3
1000×	.634	7.5	.632	3.0	.633	5.3	.624	6.9
Asian–White dissimilarity index
None	.483		.465		.445		.420
2×	.488	1.0	.471	1.3	.454	2.0	.428	1.9
10×	.504	4.3	.502	8.0	.488	9.7	.483	15.0
1000×	.521	7.5	.515	10.0	.479	7.0	.445	5.2

Looking first at the replication of the methods used by Reardon et al. (2009) and Lee et al. (2008), I confirm their finding that Philadelphia is highly segregated with regard to Black–White evenness. Unsurprisingly, as research into the modifiable areal problem shows, defining the neighborhood in progressively larger terms led to progressively lower observed levels of segregation, albeit relatively slowly. At the 1000 m neighborhood definition, dissimilarity drops only .01. This impact of the neighborhoods' size continues at both the 2000 m radii neighborhoods and the 4000 m radii, to the point that the dissimilarity in 2010 at 4000 m is barely above .7, although that only represents a decrease of 10% from the 500 m results, indicating that not only is Philadelphia racially uneven, but its racial unevenness is highly clustered.

Making barriers have twice the “friction” of residential spaces never has even a 1% effect on the observed level of Black–White segregation in Philadelphia. Setting the friction at barriers to 10 times that of residential spaces at most has a 2% effect on the observed level of segregation. In short, barriers do not have even a marginal effect on the observed Black–White segregation even when friction is set at 10. The final row of the first panel reports results when friction is set to 1000. At a value of 1000, a barrier is virtually a vertical wall; 1000 people across a barrier have the same effect on one's neighborhood demographics as one person on the same side of the barrier. Here, we see the first consistent impact of including impassable barriers. The barriers keep dissimilarity constantly between .771 and .777 across all four radii, while the models without barriers sees the dissimilarity score drop from .750 at 500 m to .702 at 4000 m. As such, the inclusion of barriers leads to a 10% increase in the measured “macro-level” segregation at the 4000 m neighborhood definition. Overall, however, barriers do not appear to have a substantial impact on Black–White evenness, save for the largest definition of a neighborhood.

That finding may be due to the long history of extreme, legalized segregation between Black and White neighborhoods and the clustering of those neighborhoods in city regions. Philadelphia's Black and White neighborhoods are so well-established, large, clustered, and separate that while physical boundaries may or may not be related to those racial demographics, their impact on city-wide measures of Black–White segregation are low. On the other hand, Asian and Latino immigrant neighborhoods are smaller, more integrated, and less entrenched. Thus, we may expect that barriers would have substantial effects for Asians and Latinos, as newer residential groups may rely on physical barriers to shape their residential decision process more than groups with longer ties to the region. Thus, the other panels of Table 1 report segregation between Whites and Latino or Asians.

Euclidean results for Latino–White segregation are generally high (above .600) except at the 4000 m bandwidth (.582). Here, the double friction barriers never have more than a .02 effect on observed segregation at any bandwidth, at most an effect of 2.7% at the 4000 m bandwidth. Much like the earlier results for Black–White segregation, the 10 × friction results are largely similar, having at most a .025 point effect on the city-wide measure of segregation, or a 4.3% difference between the Euclidean and non-Euclidean score at the 4000 m bandwidth. At smaller bandwidths, the observed difference is roughly 3%. Once again, even the virtually impassable friction simulation (1000×) had only a small effect on observed segregation. At the smallest bandwidth, the gap between Euclidean and the impassable simulation is only .011, or 1.7%. That grows to a .019 gap at the 1000 m bandwidth or 3.0% and eventually reaches a .042 gap at the 4000 m bandwidth for a 6.9% gap.

White–Asian segregation, on the other hand, is the only two-group form of segregation for which 10 × level barriers have a noticeable effect. In absolute terms, the gap between Euclidean and non-Euclidean results at the 10 × barrier grow from .02 (4.3%) at the 500 m bandwidth, to .047 (8.0%) at the1000 m bandwidth, to .063 (4000 m), a full 15% increase in the observed segregation compared to the 4000 m bandwidth Euclidean smoothing results. This is likely caused by two factors. First, White–Asian segregation is substantially lower than the other two-group comparisons; it is the only dissimilarity score below .5 in the city. Second, Asians are the smallest group and primarily clustered in four specific neighborhoods in the city—historic Chinatown, University City near the Schuykill River, South Philadelphia near Washington Avenue, and Olney. As the next section demonstrates, many of those locations are very close to significant barrier effects on the observed Black and/or White populations. Because Asian immigrants are more likely to immigrate to the suburbs directly, they are often found in first ring suburbs just outside of the city. Combined with their relatively small population share in the city, those suburban populations have substantial effects on observed dissimilarity scores differently as they travel across municipal boundaries that are not also physical barriers. These first ring suburbs are adjacent to largely Black neighborhoods, so the additional of some Asian residents (2 × and 10 × barriers) into those Black neighborhoods—but not into nearby White neighborhoods across a second barrier—affects White–Asian dissimilarity but not Black–Asian dissimilarity. Segregation between non-White populations show similar patterns to those reported here (results available as online supplementary material).

In sum, the city-level measures of two-group segregation show little effect of barriers on observed evenness. However, those small effects may obscure the local effects of boundaries as the Asian–White results indicate. Next, I turn to mapping the change in smoothed populations to explore local effects of incorporating barriers into the measurement of segregation.

Local patterns of multigroup segregation

Incorporating barriers appears to have little substantive effect on Philadelphia's evenness, save for White–Asian dissimilarity. However, while Philadelphia as a whole may not be affected by the inclusion of barriers into the measure, that does not indicate that specific neighborhood demographics are unaffected by barriers. While the total population and most observed levels of two-group dissimilarity do not change after the inclusion of barriers, exactly who is included as sharing a local neighborhood with whom may change at the local level. To test the local effects of incorporating barriers, Figure 2 compares the percentage Black in one's non-Euclidean social space (1000 × friction at barriers) to the percentage Black in one's Euclidean social space (no friction coefficient at barriers) at the 1000 m bandwidth, considered the best estimate of a walkable neighborhood. Here, areas colored Black are locations where the percentage Black in the local neighborhood decreases by at least 10% after incorporating barriers into the smoothing. Gray areas are the opposite—the observed local percentage Black increases by at least 10% after incorporating barriers.

Figure 2.

Difference in percentage black after inclusion of physical barriers, 1000 m smoothing.

In general, most of Philadelphia is not affected by the incorporation of barriers, which helps explain the nonfinding reported in the previous section about dissimilarity scores. For most of the city, symbolic barriers decoupled from physical barriers drive racial segregation. While that is the most common result, there are still areas with substantial local change in the observed percentage Black. In particular, we see the large effect of rivers on shaping the segregation patterns of Philadelphia. To the West side of the city, the Schuylkill River divides the less prosperous Black neighborhoods of West Philadelphia from the wealthier White neighborhoods of Center City. To the East, on the other hand, the Delaware River serves as a municipal, state, and racial boundary between Philadelphia and towns in New Jersey across the river. In Figure 3(a) to (c), I focus on three areas where the incorporation of physical barriers has marked effects on local segregation patterns using the 1000 m bandwidth to demonstrate the variety of local effects of incorporating barriers on the smoothed estimate of local racial demographics.

Figure 3.

Local patterns of change in largest racial/ethnic group after inclusion of physical barriers, 1000 m smoothing. (a) Schuylkill River. (b) South Philadelphia. (c) Chinatown.

Figure 3(a) focuses on a section of the Schuykill River as a divide between the high poverty Black neighborhoods of Mantua (west of the river) and Strawberry Mansion (east of the River and north of Girard Avenue compared to the affluent White neighborhood of Fairmount (east of the River, south of Girard Avenue) and University City (populated by students). Here, we see two effects of incorporating barriers. First, the large area around the Schuykill River and Fairmount Park to the north where the inclusion of barriers (the River and I-76, a major highway) kept those nonresidential spaces from falsely being represented as containing residential populations that would then obscure the dividing effect of the river in the city. Along Girard, Haverford, and Spring Garden Avenues, on the other hand, we see a pattern of major roads separating Black neighborhoods from whiter, more affluent neighborhoods. Thus, on the north side of these roads the observed percentage Black increases substantially near the barriers while the observed Black population shrinks substantially in the more affluent areas. These are also areas of high racial tension over encroaching development of market-rate housing because these barriers also serve as symbolic boundaries to interaction.

Further illustrating the connection between contemporary debates over housing, gentrification, and barriers, Figure 3(b) focuses on South Philadelphia. Point Breeze, the neighborhood west of Broad Street, the main north-south corridor for the city, is a historically high poverty Black neighborhood currently under substantial gentrification pressure from residents pushing south from Center City across Washington Avenue and from the East Passyunk neighborhood across Broad street. Point Breeze is the site of political contestation about the speed of development as hundreds of market-rate houses are being built in a neighborhood that in 2010 was two-thirds Black and had roughly 30 percent poverty rate. Here, the barriers practically surround the neighborhood to the north, east, and south. To the west is another high poverty Black neighborhood, though a small White community lives just west of 25th and north of Snyder as well. Since 2010, Point Breeze demonstrates that gentrification can and does eventually overtake many physical barriers, but only after saturating neighboring areas first (Tannen, 2016). In this case, Girard Estates to the South, Graduate Hospital/Center City to the North and East Passyunk are either historically middle class White areas or gentrified over the past 10–20 years and are now encroaching on the remaining high poverty, Black neighborhood they surround. Though not mapped here, this gentrification was presaged by the emergence of a small Southeast Asian enclave in the Southeast corner of Point Breeze in 1990s and early 2000s. That population is not identifiable in maps in which Broad Street and Snyder Avenue are not treated as physical and symbolic boundaries because it is a community of less than 2000 residents in an area with a total population in the tens of thousands.

Focusing further on Asian communities in Philadelphia demonstrates the significant role physical barriers have for identifying ethnic enclaves. In Point Breeze, the Southeast Asian population of Point Breeze acted as a harbinger of in-migration in Point Breeze that would otherwise be obscured by Euclidean smoothing techniques. In Center City, Philadelphia's historic Chinatown is unidentifiable as such without barriers. Figure 3(c) shows the large, highly local effect of barriers on Chinatown and the edge of a secondary, smaller ethnic enclave in the Fishtown/Girard area in the northeast section of the map. Chinatown is a geographically small area in downtown Philadelphia. Traditional census tract-based analyses of Chinatown include large nonresidential buildings including the Pennsylvania Convention Center, a large parking lot and the Museum of African American history (the two large areas colored black on the map correspond to those nonresidential usage areas). This makes Chinatown appear both geographically larger and less densely populated by a majority Asian population. Further, because the areas around Chinatown are also densely populated and all are majority White, Euclidean smoothing misidentifies Chinatown as majority White, not majority Asian.

Further, the map identifies a larger Asian enclave than only focusing on Chinatown would identify. As the city developed areas surrounding the historic center of Chinatown (and proposed building a baseball stadium there as well in 1990s), the Asian population of the city continued to grow and expanded northward because of that development pressure. This expansion is visible on the map—the upper half of the grey area on the map is north of I-676, the major highway that is the traditional northern boundary of Chinatown. That area north of I-676 is currently contested between the expanding Asian population in the area (roughly 25%), in-migrating high wealth White residents (50%), and a historic working class Black community (25%). As such, debate rages about whether to call that area Northern Chinatown, the Loft District, or Callowhill depending on who is discussing the area.

Discussion

Social scientists' concerns over properly measuring and identifying the neighborhood size and shape for studying the amount of and effects of residential segregation in the city have rarely been tested. Some have attempted to test the impact of measurement error by comparing different census areal units (Hipp, 2007), while others have used kernel density analysis that does not take into account the discontinuous nature of social and racial space (for discussion of the nature of racial space, see Lipsitz, 2007; Lee et al., 2008; Neely and Samura, 2011; Reardon et al., 2009; Tickamyer, 2000). After introducing non-Euclidean smoothing, a method that allows researchers to set friction values to better simulate and approximate the discontinuous nature of social environments, I test whether or not barriers affect the dissimilarity index at three levels of discontinuity and four bandwidths.

Overall, the inclusion of barriers had little impact on the measured level of evenness for two-group segregation, similar to previous findings that barriers are related to deprivation in Glasgow but are neither necessary nor sufficient to explain inter-neighborhood SES differences (Mitchell and Lee, 2014). Philadelphia is highly segregated, whether one uses census tracts, Euclidean smoothing, or non-Euclidean smoothing. Barriers are not necessary for identifying the extremely high level of segregation between Black and White residents in the city. As a mathematical function, introducing discontinuity to the analysis should only heighten the measured segregation between two groups. As such, there may be a ceiling effect—Philadelphia's segregation overwhelms any measurement error introduced by what proxy is for neighborhoods.

Only White–Asian dissimilarity was substantially affected by the inclusion of barriers into the smoothing process. However, Whites and Asians are, in Philadelphia and in the United States in general, highly integrated and Asians are more likely than prior immigrant groups to migrate directly to the suburbs (Charles, 2003; Lacy, 2016). New immigrants are isolating and integrating themselves into the city in patterns that are structured by the geography of the city. In other words, White–Black and to a lesser extent White–Latino segregation is so entrenched into the cultural, political, and structural aspects of the city that it does not rely on barriers (Charles, 2006). Asian immigrants, on the other hand, are not deeply entrenched in Philadelphia and thus have used highly visible markers such as highways or railroad tracks as physical markers for building immigrant enclaves over the last 20 years. As such, the reported White–Asian dissimilarity score is affected by the small size of the Asian population and edge effects of first-ring suburbs with large Asian populations. Future research should compare the impact of barriers in less segregated cities and/or cities with longer histories of immigration such as San Francisco or New York or longer histories of including a sizable Hispanic population, like Miami or San Antonio. It is possible that cities with smaller Black populations or with a longer tradition of non-White immigration may have segregation patterns that are differently related to physical barriers.

Importantly, purely statistical analyses of spatial patterns of racial segregation oversimplify the complex realities of social spaces and neighborhoods. While not all, nor even most, barriers lie at the nexus between two racially distinct neighborhoods, a substantial number of barriers alter the local level of segregation. These barriers between racially distinct neighborhoods also correspond to local divides about gentrification, development, and racial inequality. The barriers define an area as a “defended neighborhoods” providing meaningful symbolic bases for collective identities and actions (Suttles, 1972; Kramer, 2017).

These findings highlight the importance of re-orienting the social science literature on residential segregation to study the local patterns of segregation as well as national or even metropolitan-region scale analyses. The analysis above shows that barriers substantially impact the observed levels of segregation near them, as the maps of local patterns of segregation show. Barriers have their impacts at the margins of these macro-scale measures; barriers only impact the scores for those residents who actually live near barriers. The bulk of society, however, does not live close to a major road or railroad track or river. As such, barriers may help define the edges of racially separated neighborhoods, but they do not define the totality of residential segregation.

In terms of policy, this is a rejoinder to social science and policy makers to reconsider the lessons of American Apartheid. Massey and Denton's (1993) statistical analyses were at the macro-scale, but their argument was focused on meso-level effects: racial residential segregation, for the individual resident, concentrates poverty in specific neighborhoods. It is those local inequalities—that poverty within Philadelphia is concentrated in Black neighborhoods like Strawberry Mansion and do not spread to the whiter neighborhood of Fairmount to the south—that made segregation a structural cause of inequality. Relieving that concentration by providing escape valves across barriers may help mitigate the causal impact of segregation. Isolating those barriers that have substantial local impacts on segregation can help policy makers focus efforts to redevelop those barriers (as opposed to barriers that are not related to residential segregation) into locales of cross-racial interaction and potentially sites for redevelopment as integrated communities (Anderson, 2011).

In sum, Philadelphia is segregated, regardless of whether one incorporates barriers in the analysis, but the local patterns that create Black–White segregation change substantially in response to the inclusion of barriers. Identifying segregating barriers also identifies leverageable spaces for policy and targeted investment to promote integration specifically to bring those physically proximate but socially distinct communities together at those boundaries in more equitable manners.

Supplemental Material

Supplemental material for Testing the role of barriers in shaping segregation profiles: The importance of visualizing the local neighborhood

Supplemental material for Testing the role of barriers in shaping segregation profiles: The importance of visualizing the local neighborhood by Rory Kramer in Environment and Planning B: Urban Analytics and City Science

Footnotes

Acknowledgements

The author would like to thank the editors and reviewers of Environment and Planning B: Urban Analytics for their valuable feedback. The author would also like to thank Camille Charles, Lindsay Mack, and participants at the 2017 ASA session for their guidance and support.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

Rory Kramer is Assistant Professor of Sociology and Criminology at Villanova University. His research focuses on spatial and symbolic racial boundaries and racial inequality in the United States.

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