Background

Ninety years ago, Burgess (1925) noted that people often commit crimes in census tracts (CTs) where they do not reside. That early finding is relevant to a contemporary research question—why does urban crime concentrate in some places? Such concentrations have long been associated with social features of the residential population, but it is increasingly evident that daily nonresidential activities distribute crime unevenly over space, beyond residential effects.

Crime’s spatial concentration, without a temporal dimension

Clarke and Eck (2005) have stated a larger rule of concentration, the 80–20 rule, which tells us that crime is highly concentrated among offenders, victims, or places. In particular, the highly unequal distribution of crime over urban space has been well documented. Approximately 5 % of street segments produce at least half the crime in several cities (Weisburd et al. 2012). Crime concentration tendencies have been shown strongly in Britain (Johnson 2010, 2014), Australia (Townsley et al. 2014), and the Netherlands (Bernasco and Luykx 2003). In addition, Andresen and Malleson (2013) observed crime concentrations at three spatial scales in the same city: street segments, CTs, and dissemination areas.

Land use studies, implying a temporal dimension

Several studies have linked crime to variations in land use. Shaw and McKay (1942) and White (1932) included local land use variables in their analyses. The Brantinghams (1975, 1981) considered how certain local land uses set the stage for proximate crimes. Dennis Roncek related block-level crime to such land uses as secondary schools and bars (see Roncek and Bell 1981; Roncek and Lobosco 1983; Roncek and Fagianni 1985; Roncek and Maier 1991). An array of subsequent studies linked crime spatially to liquor establishments and other risky facilities (Bowers 2013; Franquez et al. 2013; Groff 2011; Romley et al. 2007; Zhu et al. 2004; Groff and Lockwood 2014; Roman and Reid 2012).

As several scholars have already recognized, these land use studies have a temporal dimension by implication (McCord and Ratcliffe 2009; Tompson and Townsley 2010). A barroom brings out people at night, while a school enhances daytime population. A workplace shifts population according to work schedule. Moreover, every type of land use producing inflows for one place also causes outflows from another location.

Land use is even more clearly related to crime when disaggregating by season (Andresen and Malleson 2013). For example, crime concentrates in summer near major parks and beaches, but elsewhere in other seasons when visitor patterns differ. Indeed, the relationship between land use and crime should be thought of in spatio-temporal terms. Despite all we have learned from land use analyses, more direct measures of daily population flows are desirable, but difficult to find. The current research will not be able to provide the ideal data for such purposes, but we will be able to offer an intermediate approach, using transportation surveys to measure daily activity flows, and then relate these flows to crime. Some existing theoretical ideas on spatio-temporal crime patterns prove useful for this analysis.

The “Funneling Hypothesis”

Patricia and Paul Brantingham (1975, 1981, 1995, 1999) established several principles for studying offender movements in urban space:

  1. 1.

    In daily life, offenders move around rather like non-offenders.

  2. 2.

    Each offender’s daily awareness space is defined by routine activity locations—home, workplace, school, shopping, and recreation—as well as by the routes linking these locations.

  3. 3.

    Offenders commit crimes within their awareness spaces, or near-by.

  4. 4.

    Extra crime occurs where larger numbers of people visit.Footnote 1

These basic principles tell us that an urban system could well shift crime risk unequally in space and time. We might view a city as a set of funnels, moving people into some areas and out of others on a daily basis. In the course of these movements, some people become crime participants outside their zone of residence (as Burgess had suggested in 1925). This “funneling hypothesis” implies that an appreciable share of crime within a CT might be generated by non-residents visiting on a frequent basis.

Groff and McEwen (2007) confirmed the Burgess point that many crimes occur at noteworthy distances from the home of offender and/or victim (see also Bernasco 2010; Bernasco and Block 2011; Rossmo et al. 2012; Townsley and Sidebottom 2010; Andresen et al. 2014; Johnson 2014; Pyle 1974; Hakim and Rengert 1981). Moreover, Frank et al. (2013) showed that offenders tend to go in certain directions, such as towards malls or entertainment zones. The directionality point is also highly relevant to crime concentrations on public transport (Newton 2008). In a logical sense, offender directionality further implies that an urban system funnels potential crime participants into some places and away from others. Although that conclusion seems to be non-controversial, there are reasons to question it and to verify whether and when it fits the data.

Arguments against the funneling hypothesis

Despite the strong arguments for a funneling process, there are at least four logical reasons to doubt the hypothesis:

  1. 1.

    Population movements within a city could cancel each other out, with CTs losing and gaining similar numbers of offenders or targets.

  2. 2.

    Residential effects could easily swamp visitor effects, given that residents tend to spend much more time in their home CT than do most visitors.

  3. 3.

    After leaving their home CT, residents could easily spread crime risk along their entire route, diluting any visitor effects at their destination CT.

  4. 4.

    In departing from their home CT, residents reduce local guardianship, perhaps increasing crime near home as much as they supplement crime elsewhere.

These doubts are mitigated by some preliminary evidence supporting a funneling process. Stults and Halbrouk (2015) compared crime rates for 166 American cities with over 100,000 inhabitants showing that commuters can have a major impact on rates. For example, taking account of commuters dropped Washington, D.C., from 14th to 23rd in its homicide rate. Localized analyses of population flows further justify the funneling argument. Andresen (2010) calculated that some Vancouver suburbs double their daily population, while others lose half of their population due to daily routines; these plusses and minuses affect crime risks. For the city of Ottawa, Larue and Andresen (2015) linked vehicle theft and burglary risks to inflows of 65,000 university students, instructors and staff for two large universities. Also consistent with the funneling hypothesis, Boivin (2013) documented high levels of visitor participation in burglary and non-domestic assaults.

Past measurement efforts

One half century ago, Boggs (1965) imagined a daily population census that could tell us how many people flow in urban space-time. Boggs used proxy measures, such as the area of sidewalks to estimate pedestrian inflows. Her goal was to find better denominators for measuring crime rates, a goal revisited by others (Harries 1991; Clarke 1984; Ratcliffe 2010; Cohen and Felson 1979; Stults and Halbrouk 2015).

Cohen and Felson (1979) estimated crime rates per billion person hours spent among strangers. The results were dramatic, but the categories were rather crude given the time use data available at the time. More recently, The American Time Use Survey made it possible to calculate national violent victimization rates with time denominators with more disaggregation (Lemieux 2010; Lemieux and Felson 2012). However, none of these publications were able to localize the impact of shifting population on crime concentration processes. More recent work by Stults and Halbrouk 2015) carried the spatio-temporal analysis one step farther. Their work showed that crime rates change greatly when commuter inflows are considered in the denominator of a city’s crime rate. However, they were unable to study within-city variations due to Census Bureau privacy limitations on releasing commuter data for small areal units.

The ideal study would contain all the blocks in a city, and would measure crime distributions and population flow details for all blocks. A city with 10,000 blocks would probably require interviewing at least 200,000 persons (20 per block) to obtain a reasonable map of population flows within a city. Given the prohibitive cost of such a study, we can understand why the studies cited earlier used land use indicators to classify blocks rather than attempting to measure population flows more directly. The current paper takes a different approach. Having found a very large transit survey, we worked at the census tract level. With approximately 500 CTs and 60,000 respondents, a mean of 120 respondents were found per spatial unit. Before proceeding to the data, their functional form is a matter for further discussion.

What form should the funneling function take?

Although offenders and targets tend to increase crime risk as they converge, guardians might play the opposite role.Footnote 2 Angel (1968) presented a curvilinear model of street robbery risk, stating that robbery is least likely at the lowest and highest levels. At the lowest levels too few targets are around for robbers to attack, while the highest street density levels bring sufficient guardians to make an attack more difficult. Although Clarke et al. (2007) did not support the hypothesis within the New York City subway stations, it remains plausible to argue that an influx of visitors includes offenders, Kurland et al. (2014) learned that the timing of crimes near and within football stadiums near kickoff time reflects some of Angel’s thinking.

In studying the impact of visitors on CT crime levels, we can imagine a mathematical function with more visitors producing more crimes up to a point, after which visitors create sufficient guardianship to produce something of a downward turn. Such a “concave-downward quadratic function” might describe how numbers of visitors and numbers of crimes relate over CTs. Alternatively, more visitors could lead to an upward curve in crime risk. Perhaps crowds of rowdy drinkers multiply violence risk, or very large numbers of parked cars have a disproportionate effect on vehicle theft by blocking the ability to see what offenders are doing. If so, the slope could take the form of a “concave-upward quadratic function.” However, it is also possible that a simple straight line can relate visitor flows to crime concentrations. First we inquire whether there is a relationship, and then we seek to measure its form.

Current data

Transportation surveys are a longstanding tool for urban planning, not normally applied to crime analysis. Unfortunately, transportation surveys seldom have large enough samples to study each CT within a city. We were fortunate to gain partial access to an exceptionally large local transportation survey for a major city in Eastern Canada and were able to link it to crime risks. The survey includes multiple transportation modes and produces counts of daily population inflows into each of 506 CTs, both from other CTs and from the suburban ring around the city. However, we are unable to measure tourist inflows or long-distance commuters from beyond the regular commuting zone.Footnote 3

The current crime analysis is limited to within-city offenses, excluding crime occurring in the surrounding suburbs. The suburban exclusion limits the socioeconomic range of analysis. Accordingly, this study does not specifically seek to address social disorganization theory. Instead, we focus solely on determining the viability of the funneling hypothesis as a supplementary approach. Our three data sources include:

  1. (a)

    A 2008 transportation survey of 66,100 households, including questions about locations where respondents work and shop, or engage in recreation and education. The survey allowed us to estimate daily population flows into each CT for those four purposes.

  2. (b)

    Police data on reported violent and property crimes by CT, made available for 2011.

  3. (c)

    Social data for CT residents from the 2006 Census.

Before proceeding, we note certain limitations of these data. We were unable to disaggregate educational trips by age or grade level. Thus educational flows include elementary school ages, not as likely to be crime participants. The social data were taken from the 2006 Census because the later census (2011) shifted policies and measurement procedures. The 2006 Census provides the percent of census tract households with low income before tax cut-offs,Footnote 4 the percent of census tract families that are single-headed, and the percent of census tract population who moved within the last 5 years.

Data analysis

Distributions of key variables over the city are examined in two ways. First, we examine whether a relatively small share of CTs concentrate either crimes or their correlates. Later, we use more conventional statistics to relate visitor inflows to crime levels.

Visitor concentrations

Table 1 examines the concentrations of five key variables, taken one at a time. Only 6 % of CTs concentrate 25 % of the property crimes. Only 9.5 % of CTs concentrate 25 % of violent crimes. About one-fourth of CTs concentrate about one half of crimes of both types (right column). Although these crime concentrations are not as extreme as found in studies based on block data, a considerable degree of inequality is found.Footnote 5

Table 1 Crime and visitor concentrations, 25 and 50 % levels, Eastern Canadian city
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Even more interesting is the concentration of non-residents visiting CTs during their daily routines. A mere 1 % of CTs account for one-fourth of all work visitors; 7 % of CTs monopolize one-half of work visitors. Two percent of CTs account for a quarter of shoppers and 9 % of CTs account for half of all shoppers. Recreation and education visitors also show noteworthy concentrations. This tells us that visitor concentrations are strong enough to influence crime concentrations, but the task remains to demonstrate the magnitude of influence.

Linking visitors concentrations to crimes concentrations

Table 2 looks at concentration in a different way. For each of the four activity variables, we separate the top 5 % of CTs in numbers of visitors (n = 25). We then calculate the share of crimes committed in these CTs with the most visitors of each type. Those 5 % of CTs with the most work visitors account for 16.2 % of the property crime, over three times what would be expected if work concentration were unrelated to crime concentration. CTs with the most workers and shoppers tend to have three times their share of property crimes and twice their share of violent crimes. Recreation effects are even stronger, but education visitors have a smaller impact on crime concentration.

Table 2 Share of crimes for top 5 % of census tracts, Eastern Canadian city
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Similar thinking is applied in Table 3 to the top 25 % of CTs (n = 125) for visitors of each type. These CTs have more than their share of crime, but the excesses are not dramatic. The weakest relationship is for education visitors, with the top quarter of CTs producing a third of property and violent crimes. However, the top tier of CTs for work, schooling and recreation range contain from 42 to 47 % of property crimes and 36 or 37 % of violent crimes. The data so far show that the funneling hypothesis remains viable as a supplementary explanation of crime concentrations in this city.

Table 3 Share of crimes for top 25 % of census tracts, Eastern Canadian city
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Further explorations of distributions

The 2006 Census allowed us to examine how social features of the residential population distribute over CTs. These comparisons are not exactly parallel to visitor data, because social variables are reported as percentages of other units, as described earlier. However, Table 4 shows that social features of the residential population are much more evenly distributed than numbers of visitors. The coefficient of variation is presented in the last column, showing that residential components have low standard deviations relative to their means. Moreover, the means and medians are very close, indicating rather symmetrical distributions of residential social features over 506 CTs. In contrast, the number of visitors varies a great deal over CTs, with high coefficients of variation. For three of the four visitor indicators, the standard deviations are double or triple the size of the mean. The exception is for recreation, whose coefficient of variation is 1.3, perhaps reflecting the possibility that recreational visits to family and friends do not flow into entertainment districts. For each visitor variable, there is quite a gap between mean and median, reflecting the lopsided concentrations of visitors for some CTs. To sum up, visitor flows over CTs are both disproportionate and skewed. The skewness of key variables is described in the following text table.

Table 4 Descriptive statistics for residents, visitors, and crimes, Eastern Canadian city
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Variable

Skewness value

Property crime

6.08

Violent crime

2.05

Work visitors

12.37

Shopping visitors

6.45

Recreation visitors

5.03

Education visitors

6.13

In contrast, social variables in this city are distributed over CTs within this city on a relatively more equal basis and with greater symmetry around the mean.

Correlating crime with visitor components

Next we correlate CT crime rates, visitor rates, and census social variables. For this analysis, all variables are calculated as a percent of residential population, except for low income (available only as a percent of households) and single parents (available only as a percent of families). Table 5 shows a striking contrast in magnitude of correlations. In the upper right hand section of the matrix, correlations between crime rates and three of the four visitor variables range from 0.72 to 0.95. On the other hand, education inflows only correlate around 0.5 with property and violent crime rates, perhaps reflecting our inability to separate flows of high school youths from flows of younger children who are less problematical. In contrast, the correlations between residence-based social variables and crime rates range from near 0 to 0.3. Table 5 is highly consistent with the funneling hypothesis, showing that it visitor variables have strong correlations with crime variables, and that visitor effects in this city exceed residential effects by a considerable margin.

Table 5 Pearson’s r matrix for visitor, residential, and crime variables, Eastern Canadian city
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Given the magnitude of the visitor-crime correlations, we conducted a sensitivity analysis (Table 6) with log and square root transformations. A strong correlation between visitors and crimes is consistently found. Opinion differs about whether or when to correlate ratio-level variables as opposed to counts (Chamlin and Cochran 2004), but the relationship remains strong in either case. For example, the correlations for work visitors and property crimes range from 0.69 to 0.95, depending on variable form. Half of the correlations are 0.80 or greater, with 0.57 the lowest of the 12 correlations, all of which are highly significant statistically. The funneling hypothesis clearly survives this sensitivity analysis. We next turn to the quadratic equations discussed earlier.

Table 6 Sensitivity analysis of Pearson’s r, between property crimes and visitors for work, shopping, and recreation, Eastern Canadian city
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Separate quadric equations for visitor flows and crimes

Our next goal is to determine whether visitors and crime relate in a concave downward quadratic function, a concave-upward quadratic function, or simply a straight line. The general equation form is

$$ {\text{Y }} = {\text{ a }} + {\text{ b X }} + {\text{ c X}}^{ 2} , $$

where Y is the number of crimes and X is the number of visitors. Coefficient c is most relevant for assessing the curvature of the line.

If the quadratic effect, c, is negative, the curve is concave-downward; if positive, the curve is concave upward; if coefficient c is non-significant, the relationship can then be described as a straight line. However, measuring a quadratic effect really requires a much larger sample than offered here, so we consider the results in Tables 7 and 8 as suggestive for its quadratic component.

Table 7 Quadratic equations relating crimes to visitors for work, shopping, recreation, and education, Eastern Canadian city
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Table 8 Quadratic equation relating crimes to visitors for work, shopping, and recreation, Eastern Canadian city
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Table 7 explores the equation for one visitor component at a time. Those visiting a CT for work, shopping, or education all have negative coefficients for the quadratic effect, hence concave-downward curves. This implies that the impact of visitors on crime begins with a good upward slope, but then begins to taper off as the number of visitors reaches higher levels. Note that the quadratic coefficient is multiplied by the number of visitors squared, so large crowds can at some point diminish crimes. The data clearly imply that more visitors make more crime as a general rule, with tapering when inflows reach high levels. That is consistent with the idea that sufficient visitors provide guardianship, somewhat offsetting the main effects of additional offenders and targets. Yet that rule does not apply for recreation visitors, whose slope is concave-upward for property crimes and a simple straight line for violent crimes.

Given the small number of cases used to fit this quadratic curve, we cautiously note that for all eight equations, the y-intercepts (coefficient a) are positive and significant. If the number of visitors goes to zero, an average CT will still have crime—predicted to be from 87 to 117 property crimes and from 28 to 36 violent crimes as baseline risk levels, likely generated by residential populations. The same equations indicate that every thousand workers “bring” 43 property crimes and five violent crimes. At the other extreme, every thousand recreation visitors correspond to 156 property crimes and 29 violent crimes. Apparently, recreation visitors have the greatest relative impact on local crime. The work visitor equation for property crime has highest Multiple-R (0.878) of all eight equations. The recreation equation has the strongest main effects for violent and property crimes, alike. The multiple R for education visitors is much smaller than the others, probably reflecting the data limitations already discussed. We drop the education variable from our summary analysis due to measurement limitations.

Summary equations relating CT crime counts to visitor flows

We now place three flows of visitors together, as presented in Table 8. Again, our N is too small to take the quadratic coefficient within this equation as definitive. The Multiple R for property crimes now passes 0.9, and that for violent crimes is 0.66. The main effects all appear strong and significant. In the final property crime equation, every thousand workers visiting a CT produce a surprising 828 additional property crimes there over a 1 year period. Bear in mind that this number is mitigated by the negative quadratic effect, which is especially strong when inflows are squared, offsetting the apparent impact of more workers on more crime. We cannot say how many of these crimes are against businesses or individuals; but we can say that the concentration of workers give certain CTs considerably higher risks of property crime.

Work visitors influence property crime, but add little to violent crime, with statistical significance is only at the 0.05 level. Instead, recreation inflows appear to be the main source of violent crime, with every thousand visitors to a CT adding 20 violent incidents locally. The quadratic effect remains, along with the concave downward slope, but only one variable per equation has a negative quadratic coefficient. Swelling numbers of work visitors tend to increase property crimes, but only up to the point when the quadratic effect becomes notable. We recommend caution in teasing apart the impact of different types of visitors due to high correlations among these variables (e.g., r = 0.68 between shopping and recreation variables.

Conclusion and comments

The funneling hypothesis is highly sustainable as an explanation of within-city crime concentration. We find strong correlations between visitor variables and crime over 506 CTs. Due to limited access to the transportation survey, we were unable to disaggregate the movements of different age groups or to explore specific time of day or day of week. Nor were we able to separate business from citizen victimizations. Nor could we detail more specific crime types than property or violent crimes. Nor can we say that these findings will generalize to other cities, or to suburban areas, or to newer cities during their growth period. In this city, high correlations among some visitor variables limit our ability to separate their independent contributions with certainty. We cannot say that the four types of visitors would produce the same relative contributions elsewhere, but we remain convinced that visitor effects are strong in this city and merit investigation elsewhere.

Emerging data are beginning to produce alternative measures of daily population flows relevant to crime. For example, the LandScan Global Population Database combines conventional sources with high resolution satellite imagery to estimate 24-h average population for many regions.Footnote 6 Andresen (2006, 2010, 2011) applied that technology to show that “ambient population” in Vancouver produces different crime rates maps than those based on simple residential population.

Two new reviews consider several ways that emerging technologies help measure crime risks (Bernasco 2014; Van Gelder and Van Daele 2014). Some researchers are beginning to apply smart phone technology (including apps and GPS) to locate crime and study swiftly shifting populations. Japanese criminologists have used GPS data to identify children’s activities and vulnerabilities after school and adult neighborhood watch activities (Amemiya et al. 2009).

On a much smaller scale, Rossmo et al. (2012) mapped the space-time paths of a few parolees required to wear location-tracking devices. A novel study in Leeds, UK, relates crime hotspots to rapid shifts in the volume of social media messaging (Malleson and Andresen 2015). Others have arranged for youths to describe their spatial movements and fears, using computer screens to simulate their journey home from school (Wiebe et al. 2014).Footnote 7 Both old and new technologies have shed light on how youths allocate time and the consequences for offending or victimization (see review in Hoeben et al. 2014).

We suggest that, on the one hand, emerging technologies offer great promise for detailed measurement of rapidly shifting population for a whole urban system. On the other hand, more conventional surveys might prove more suitable for gathering crime-relevant details about where people go; for what purposes; how much alcohol they drink in different places; their group sizes; and their roles as offender, target, or guardian. Unstructured interviews may also prove useful for determining where offenders search for visitors and how they decide to choose their specific targets. Metropolitan movements shift by hour of day in detailed ways not captured in the current study. These processes depend on local variations in transportation, road networks, and land use patterns. A large national research project is ill-suited to such research, which instead depends on incremental local studies taking into account the local topography and built environment.

From other literature and our own analyses, we conclude that the funneling hypothesis is highly viable, and that the spatio-temporal concentration of crime over urban space is greatly influenced by daily flows of people away from where they live and into other parts of a city.