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The geodiversity of crime: Evidence from British Columbia
Applied Geography 34 (2012) 180e188
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Applied Geography journal homepage: www.elsevier.com/locate/apgeog
The geodiversity of crime: Evidence from British Columbiaq Richard Frank a, Martin A. Andresen a, *, Marcus Felson b a b
School of Criminology, Institute for Canadian Urban Research Studies, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada Department of Criminal Justice, 601 University Drive, Texas State University, San Marcos, TX 78666, USA
a b s t r a c t Keywords: Geodiversity Mobility triangle Geometry Journey to crime
Crime mapping has established central tendencies, e.g., that crime trips tend to be certain lengths. But this is only one-half of the convergence that leads to a crime. Crime mobility research, however, considers the simultaneous movements of both offenders and victims. In this paper, we consider the geodiversity of crime mobility: there are variations in the amount of area covered by various crimes depending on the variations of criminal opportunity. Extending the crime mobility research to consider co-offending, co-victimization, and area covered rather than typologies, we find strong evidence for geodiversity in crime. This geodiversity varies across crime types within a single municipality as well as across municipalities within a single crime type. Ó 2011 Elsevier Ltd. All rights reserved.
Introduction
1979; Felson & Cohen, 1980, 1981). In order for a crime to occur, a motivated offender and a suitable target must converge in time and space with the lack of a capable guardian. This is a necessary condition, but not sufficient for a crime to occur. Therefore, the presence of these fundamental components may be thought of as crime’s geodiversity; the manifestation of crime itself is then its biodiversity, and the greater crime’s geodiversity the greater its corresponding biodiversity.1 In more conventional criminological language, we say: where there is more opportunity there is more crime. Therefore, though we may expect the same, or similar, spatial crime patterns in different places, variations in crime’s resource base (opportunity) is expected to lead to variations in the spatial behavior of crime. One branch of the geography of crime literature that could consider this variation is the journey to crime literature (Wiles & Costello, 2000). This literature shows that the journey to crime is short, particularly for violent crime, but only represents one-half of the convergence in time in space. A related branch of literature considers the simultaneous movements of the offender and the victim, converging in spacedmobility triangle research. This research investigates the geographic proximity of the offender’s residence, the victim’s residence, and the crime location.2 In all studies known to the authors, mobility triangles are
Geographical theories of crime state that the way one moves throughout the environment impacts offending behavior as well as when and where one may be a victim of crime. Consequently, crime and its geography are not only measurable, but predictable. We can then, for example, use geographical information (the locations of crimes) to help locate certain types of offenders as well as predict geographic patterns, more generally (Rossmo, 2000). Despite the regularities in crime patterns, is there diversity in other geographic terms? Geodiversity is a term used in the natural sciences to describe the abiotic aspects of our environment: climate, topography, geology, and hydrology (Gray, 2004, 2008). These aspects combine to generate the resources necessary for biodiversity, flora and fauna (Parks & Mulligan, 2010); and the greater the geodiversity within an area the greater its corresponding biodiversity (Dufour, Gadallah, Wagner, Guisan, & Buttler, 2006). As such, greater opportunity for life (a greater presence of resources) leads to a greater presence of life. But does this relate to crime? The fundamental components for crime, its resources, are best understood within a routine activities approach (Cohen & Felson,
q This work was done in the ICURS Laboratory at Simon Fraser University under terms of a joint Memorandum of Understanding between the Institute for Canadian Urban Research Studies, Simon Fraser University, “E”-Division of the Royal Canadian Mounted Police, and the British Columbia Ministry of Public Safety and Solicitor General. We would like to thank three anonymous reviewers for their comments that have improved our paper. * Corresponding author. E-mail addresses: [email protected] (R. Frank), [email protected] (M.A. Andresen), [email protected] (M. Felson). 0143-6228/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apgeog.2011.11.007
1 Though not discussed in terms of geodiversity, Johnson et al. (2007) find evidence for geodiversity in their cross-national study of near-repeat victimization. 2 These analyses implicitly or explicitly assume that the residences of the offender and victim are the starting points of their journey to crime and victimization, respectively. This assumption, however, may be problematic. See Townsley and Sidebottom (2010) for a discussion of this issue.
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Table 1 Mobility triangle classifications, Normandeau (1968). Mobility triangle type
Definition
Percentage of offenses (robbery)
Crime neighborhood triangle
Offender’s residence, victim’s residence, and crime location all in the same neighborhood/communitya Victim’s residence and crime location in the same neighborhood/community Offender’s residence and crime location all in the same neighborhood/community Offender’s and victim’s residence in the same neighborhood/community Offender’s residence, victim’s residence, and crime location all in different neighborhoods/communities
14
Offender mobility triangle Victim mobility triangle Offense mobility triangle Total mobility triangle a
17 19 12 38
Normandeau (1968) defines a neighbourhood/community using census tract boundaries.
calculated for a single municipality. However, because of crime’s underlying geodiversity, there is no reason to believe that this geometry of crime is the same from place to place. In this paper we contribute to the mobility triangle literature in three ways. First, we do not concern ourselves with the categories used in previous researchdthese categories are discussed below. As outlined by Groff and McEwen (2007), there may be difficulties when social boundaries are not considered in the assessment of the geometry of crime, but in order for new insight to be gained it is necessary to break from the 80-year-old classification system. Rather, we calculate the mobility area for offending and victimization. This allows for a more detailed and more geographical comparison between crime classifications and within crime classifications for different offending and victimization patterns. Second, we explicitly consider the geometry of co-offending and co-victimization.3 Groff and McEwen (2007) do include co-offenses or co-victimization in their analysis of homicide, but independently calculate a mobility triangle for each of the offenders and victims. We consider the geometry of offenses with up to two offenders and two victims. And third, not only do we break down the analysis by crime classification, we also compare the geometry of offenses in three different municipalities, two urban and one rural. Measuring crime’s geodiversity: theory and empirics of the geometry of crime The presence of a geometric component to crime is obvious when one considers the geographical theories of crime. Routine activity theory (Cohen & Felson, 1979; Felson & Cohen, 1980, 1981), though initially concerned with temporal changes, states that understanding the convergence in time and space of an offender, a victim, and the lack of a capable guardian is critical to understanding criminal incidents. Though not a specific requirement for routine activity theory, the offender comes from a place, the victim comes from a place, and the two intersect at another place.4 The geometric theory of crime (Brantingham & Brantingham, 1981, 1993a), invokes the concepts of nodes, paths, and edges from Lynch (1960), stating that the vast majority of crime occurs within the offender’s awareness and activity space. Therefore, it is the convergence of offender and victim awareness spaces that leads to incidents of crime (Brantingham & Brantingham, 1995).5 Though developed after the original mobility triangle research, these two theoretical frameworks provide support for the existence
3 Co-offending is defined as the presence of two or more offenders during the criminal event; similarly for co-victimization. 4 Of course, it is possible that the criminal incident may occur at the residence of the offender or the victim, such is the case in domestic violence. 5 The geometric theory of crime and routine activity theory are also components of the meta-theoretic framework crime pattern theory (Brantingham & Brantingham, 1993b). In the current context, we are concerned with the specific aspects of these theories. As such, we do not consider crime pattern theory in the current analysis, per se.
of mobility triangles. Mobility triangles represent the geometry of the offender’s residence, the victim’s residence, and the location of the criminal incidentdthese locations each represent a vertex of the triangle. Though the original context was sexual promiscuity, not crime, Burgess (1925) describes three types of mobility triangles: delinquency triangles (offenders’ residence, victim’s residence, and crime location all in the same neighborhood/community), mobility triangles (offender’s and victim’s residence in the same neighborhood, but the crime location is elsewhere), and promiscuity triangles (all points are in different neighborhoods). Once these locations are classified, offenderevictim movement patterns can then be mapped and compared across different social groups, gender, and crime classifications. The first known research to apply Burgess’ (1925) mobility triangle typology to crime in an empirical context was Lind’s (1930) analysis of crime in Honolulu. However, Lind (1930) did not consider the victim’s residence. As such, a mobility triangle only emerged with multiple offenders. Lind’s (1930) general results were that the delinquency triangle most often occurred within low socioeconomic status neighborhoods and that the mobility of offenders (delinquency / mobility / promiscuity triangles) increased with age. It was another thirty years before another study of mobility triangles emerged. From an empirical perspective, Normandeau (1968) introduced the victim into mobility triangle research, only considering solo-offenders. More significantly, Normandeau (1968) also expanded the typology of mobility triangles into five classifications. This new typology allowed much more insight into the geometry of crime to be gathered. For example, in column 3 of Table 1 (reproduced from Normandeau 1968), the offender and the victim reside in the same neighborhood 26 percent of the time, the offender’s residence and the crime location are in the same neighborhood 33 percent of the time, and the victim’s residence and the crime location are in the same neighborhood 32 percent of the time. Consequently, there is a strong geographical bias in the commission of crime. That bias may be finding victims close to the offender’s home, or finding victims close to their own home. Amir (1971) investigated rape in Philadelphia, finding that 68 percent of the time the crime neighborhood triangle was present, and in 82 percent of all cases the offender and victim had residences in the same neighborhood. In a comparison of robbery and rape, these two different crime classifications exhibited very different dominating mobility triangle types. The next advancement in this literature occurred with Rand’s (1986) analysis of nine different crime classifications: total crime, homicide, rape, robbery, aggravated assault, burglary, larceny, vehicle theft, and simple assault. She finds that 31 percent of offenders find their targets in their home neighborhood (census tract); however, there is large variation across crime classifications: as low as 15 percent (larceny) and as high as 53 percent (homicide and rape). Generally speaking, the total mobility triangle is the most prevalent (45 percent), and the offense mobility triangle is the
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least prevalent (5 percent). Additionally, property crimes have a tendency to be total mobility triangles and violent crimes have a tendency to be neighborhood triangles. Rand’s (1986) results reiterate the importance of analyzing detailed crime classifications, when comparing the work of Amir (1971) to Normandeau (1968). More recently, Tita and Griffiths (2005) analyzed the mobility triangles of homicide. Tita and Griffiths (2005) use the same 5 classification typology as Normandeau (1968), but with different naming conventions. Homicides tend to either be total mobility triangles (28 percent) or crime neighborhood triangles (27 percent). The primary contribution of Tita and Griffiths (2005) is to show that the mobility patterns of homicide depend on: participant characteristics, victimeoffender relationships, motive, and event characteristics. Similar to the tenets of situational crime prevention (Clarke, 1980), in order to understand mobility triangles the analysis needs to be crime specific, not only in terms of the crime type, but also with regard to the characteristics of the crime itself. The most recent analysis of mobility triangles, Groff and McEwen (2007), replicates Tita and Griffiths (2005) showing the importance of understanding the nature of homicide when classifying the type of mobility triangle. Additionally, Groff and McEwen (2007) advance the literature through the incorporation of distance measures to classify mobility triangles.6 Groff and McEwen (2007) identify limitations when incorporating the actual distance between offender’s residence, victim’s residence, and the crime location to classify the mobility triangles. For example, having an offender cross a road (very short distance) may be socially significant. Regardless, they believe the benefits of their methodology outweigh the limitations. Groff and McEwen (2007) use one-quarter mile in order to classify near and far. With this criterion, they subsequently use the 5 category classification system to label criminal incidents. In their analysis, offenders find victims in their own neighborhood 46 percent of the time, victims are victimized in their own neighborhood 51 percent of the time, and both offenders and victims live in the same neighborhood 31 percent of the time. This literature, albeit small, clearly shows the importance of separately analyzing different crime classifications, the importance of other characteristics specific to crimes, and that incorporating other geographical information contributes to understanding criminal mobility. We incorporate this insight into our analyses. On the basis of Rand’s (1986) results, we analyze 12 crime classifications; in order to incorporate the importance of characteristics we analyze criminal mobility in three different municipalities, interpreting results in this context7; and we consider additional geographic information that provides further insight into criminal mobility.
Data and measurement method Criminal incident data The data employed in the current analysis are from three municipalities (police jurisdictions) in British Columbia, Canada’s western-most province. The entire province of British Columbia has approximately 4 million residents living in 186 police jurisdictions, with the Royal Canadian Mounted Police (RCMP) being responsible
6 Westerberg, Grant, and Bond (2007) also investigate mobility triangles for automotive theft. However, their research considers the offender’s home location, the theft location, and the vehicle disposal site. Consequently, we do not review Westerberg et al. (2007) here. 7 We do not have access to the detailed crime characteristics analyzed by Tita and Griffiths (2005).
for policing 174 of the 186 police jurisdictionsd67 percent of the provincial population, approximately 2.7 million persons. The municipalities we include in the analysis are from within the Metro Vancouver region (Coquitlam and Surrey), and one municipality outside the Metro Vancouver region (Prince George). We include these three municipalities because of their size (there is a lot of data for these municipalities) and to provide different types of urban form in the analysis to investigate the geodiversity of crimedthe inclusion of more municipalities would greatly expand the data presented in the tables. Coquitlam is a relatively small municipality covering 121 square kilometers, with approximately 115,000 persons and a population density of 942 persons per square kilometers; Surrey is a municipality covering 317 square kilometers, has approximately 400,000 persons and a population density of 1245 persons per square kilometer; Prince George is a municipality covering 316 square kilometers, has approximately 71,000 persons and a population density of 225 persons per square kilometers in the rural area of British Columbia. Both municipalities within Metro Vancouver have urban sprawl, light industry, strip development and malls, apartments, and single family dwellings, but the locations of these facilities are quite different for each municipality. Coquitlam essentially has one commercial district centered on a large shopping area. The area also contains a major transportation hub, and direct train-line to downtown Vancouver, a library, a college campus and a sports complex. This commercial district not only attracts residents of Coquitlam, but residents from neighboring municipalities because of its size. In contrast, Surrey has multiple commercial districts and regional shopping areas, each large enough to attract residents from neighboring municipalities as well. Of course, this is in part because of Surrey’s greater population. Prince George, located in the center of the province, is included to provide a more nonmetropolitan example. Similar to Coquitlam, Prince George has one commercial district and draws populations from the surrounding rural areas to serve their needs. Because of the different sizes of the municipalities, data availability does vary: we cannot make comparisons across all municipalities, crime types, and offenderevictim combinations. Despite these limitations, we are able to investigate some interesting comparisons. The use of different types of municipalities (in terms of population density, commercial areas, etc.) allows us to compare geodiversity not only in terms of crime types, but different types of municipalities. The data used in the analyses below are incident-based and extracted from the RCMP Police Information Retrieval System (PIRS). These data cover the period August 1, 2002 through July 31, 2006 and represent the complete set of incidents dealt with by the RCMP. With our ability to combine 48 consecutive months of the PIRS database, any unusual features of any given year or month are ironed out. The entire PIRS database contains approximately 5 million contacts with the police that involve approximately 9 million individualsdoffenders, victims, complainants, and witnesses. Of these 5 million police contacts, approximately 750,000 are common criminal offenses. In our analysis we consider both solo-offenses and co-offenses, with a co-offense being defined as an incident with more than one person classified as suspect, chargeable, or charged.8
8 A suspect is someone whom the RCMP believe committed the crime, but they do not (at the time of entry) have supporting evidence to pursue a charge; charged is for a person whom the RCMP believe committed the crime and for which there is supporting evidence; chargeable is for a person whom the RCMP believe committed the crime and for which there is supporting evidence, but who is not charged for a variety of reasons, such as being under the age of criminal responsibility.
R. Frank et al. / Applied Geography 34 (2012) 180e188 Table 2 Summary statistics, crime type classifications.
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Table 3 Summary statistics, types of polygons.
Crime type
Count
Percent
Offenders
Victims
Count
Percent
Aggravated assault Assault Homicide Sexual assault Armed robbery Robbery Commercial burglary Other burglary Residential burglary Theft Theft from motor vehicle Theft of motor vehicle Total
1096 2923 80 751 462 318 66 86 337 490 245 503 7357
14.9 39.7 1.1 10.2 6.3 4.3 0.9 1.2 4.6 6.7 3.3 6.8 100.0
1 1 2 2 Total
1 2 1 2
5321 912 902 222 7357
72.3 12.4 12.3 3.0
From this large incident-based data set, we extract twelve crime classifications that represent the majority of property and violent crimes: homicide, sexual assault, aggravated assault,9 assault, robbery, armed robbery, burglary (residential, commercial, and other10), theft, theft of motor vehicle, and theft from motor vehicle. However, because of small numbers of observations, not all crime classifications are reported in each set of results. In order for the geometry of these offenses to be calculated a further data restriction had to be made: only crimes that contain the offender’s home location, the victim’s home location, and the crime location are analyzed. This subset of data includes 7357 offenses, outlined in Table 2. Though most crimes investigated by the RCMP are property crimes, violent crimes dominate this particular subset of data because of the location restrictions stated above. Property crimes often do not have the victim present, as such the offender’s identity (and the offender’s home address) is not known as often as with violent crimes. This is one reason why clearance rates for property crimes tend to be rather low compared to violent crimes.11 However, as shown in Table 2, a large number of crimes are analyzed for all property crime classifications aside from Commercial and Other Burglary. In all calculations, these data are separated into categories based on the number of offenders and victims. In order to avoid small samples we do not consider crimes with more than two offenders or two victims. In almost all cases that have more than two offenders and/or victims there are fewer than ten observations. In fact, many of our results for two offenders and/or two victims are based on fewer than ten observations; these particular results should, therefore, be interpreted with caution. The counts within each of these categories are shown in Table 3. Immediately obvious from Table 3 is that crimes with one offender and one victim dominate, over 72 percent of the data. Some research has shown that co-offending dominates offending patterns, particularly in youth (Andresen & Felson, 2010; Carrington, 2009), but our data does not make any demarcations by age. Additionally, the presence of more than one offender only exacerbates the issue regarding offender identity and home address, discussed above.
9 For these purposes, aggravated assault combines aggravated assault and assault with a weapon. 10 Most often, “other burglary” refers to a burglary at a structure such as a vacation cottage or a trailer. 11 These statements are based on clearance data from the RCMP that are not publically available.
Measuring the geometry of co-offending and co-victimization Since the publication of Breckenridge and Abbott (1912), cooffending has been known to be an important aspect in the study of crime. The earliest studies of co-offending found that co-offending is commonplace for youth offending: Shaw and McKay (1931) found almost 82 percent of youth offending is co-offending in Chicago, Illinois; Gold (1970) found 75 percent in Flint, Michigan; and in a review of eleven studies, Erickson (1971) found that 85 percent of offenses involved co-offending. There has been some recent research that questions the degree of co-offending (Carrington, 2002; van Mastrigt & Farrington, 2009; Stolzenberg & D’Alessio, 2008), but there is substantial evidence that offending, particularly youth offending, is a group phenomenon. Additionally, a number of scholars find that those who co-offend tend to commit criminal offenses more frequently and more serious offenses (Hindelang, 1976; Sarnecki, 2001), “early starters” that co-offend commit more crimes later (McCord & Conway, 2002), and exposure to violence through cooffending leads to more violent crimes later in a criminal career (Conway & McCord, 2002).12 Lastly, Felson (2003) argues that cooffending causes more harm to youth, ethnic minorities, and cities. Needless to say, there is substantial evidence for the incorporation of co-offending into any analysis of crime, including its geometry. As stated above, we do not concern ourselves with categories, or typologies, of mobility triangles. Rather, we wish to be able to directly compare the mobility of different crime classifications. For example, Rand (1986) found that offenders did not have to leave their neighborhood to find their victims in 53 percent of homicide and rape incidents. However, this does not mean that the mobility of homicide and rape offenders is identical. Consider the following example. Fig. 1 shows two examples of mobility triangles that have the same classificationdtotal mobility triangles. However, it should be clear that such a classification scheme, though instructive, is limited in its ability to describe the geometry of these two crimes. In Fig. 1a, the actual distances traveled to offending and victimization are short, whereas a much greater distance is traveled for both offender and victim in Fig. 1b. Though these neighborhood boundaries may still be significant because crossing a particular street may have social significance (Groff & McEwen, 2007), much geographical information is lost with such classification schemes.13 In order to address this issue, we calculate the mobility area. This allows for a more precise comparison between different crime classifications, and within a crime classification but across cooffending and co-victimization patterns. Because we consider up to two offenders and two victims with a crime location, we analyze triangles, quadrilaterals, and pentagons. Fig. 2 shows the general area calculation for co-offending with a triangle and
12 Carrington (2002) warns about these generalizations because there are some studies that counter these claims. 13 The social significance of boundaries was indeed of critical importance to Burgess (1925). However, much, if not all, of the mobility triangle research is undertaken considering census tracts that may not necessarily be representative of actual neighborhoods.
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a quadrilateraldsimilar figures are available to show higher order polygons, and co-victimization. In Fig. 2, all offenders’ home locations are necessary for the calculation of the mobility area. This may not be the case in practice. Fig. 3 shows that two offenders may actually create a mobility triangle (Fig. 3a) rather than a mobility quadrilateral. One possible solution to this complication is to use all locations as vertices for the mobility area. However, this too has a complication that is evident in Figs. 3bed. In the case of only two offenders, one of whom lives within the mobility triangle of the other offender, the researcher must choose from three possible area calculations. Evident from Figs. 3bed, each of these possibilities may have a different mobility area. This becomes even more complex when there are more offenders and victims involved with a single criminal incident. We avoid this complication by calculating a minimum bounding area for each offense. The minimum bounding area is the smallest area that will enclose (either as vertices or interior points) all offenders’ home locations, the victims’ home locations, and the crime location. When all locations are in positions similar to those in Fig. 2 there is no areal bias. However, the mobility area is biased upwards when one vertex is contained by the others. This bias is minimized by averaging all mobility areas.
Fig. 1. a. Distance versus area-based mobility triangles. b. Distance versus area-based mobility triangles.
The mobility areas are calculated by fitting a convex hull around the event and home locations involved in each crime. A customwritten VB.NET program was used to retrieve the data from the database and calculate the relevant XY coordinates for each crime. Qhull (http://www.qhull.org) was then used to calculate the set of points that make up the convex hull, or mobility area, for each crime. Once these points were known, the area of the convex hull was calculated by our VB.NET algorithm as follows. First, an arbitrary XY coordinate was selected inside the mobility polygon by averaging all the XY coordinates that make up the convex hull. Second, triangles were constructed such that one of the vertices was the arbitrary coordinate from the previous step, the other two being two adjacent points in the convex hull. The area of the convex hull is calculated by summing the areas of the respective triangles (Barber, Dobkin, & Huhdanpaa, 1996). An alternative calculation that avoids the use of categories/ typologies is some combination of the distances for the journey to crime and the journey to victimization. The most obvious calculation is adding the two distances together to obtain the total journey to the criminal event. However, such a method has difficulties. Consider a total journey to the criminal event that sums to 20 units. Though 10 þ 10 and 5 þ 15, etc. all sum to 20, the areas of these triangles are all different. As such, only considering the linear nature of the journeys provides limited information. This is the reason why we choose area for the calculations below.
Fig. 2. a. Measuring the geometry of co-offending, triangle. b. Measuring the geometry of co-offending, quadrilateral.
There is one final methodological consideration regarding area. Though all necessary locations may be available, an area may not always be calculated. This may occur in two types of situations. First, both home locations (offender and victim) and the location of the crime may be at the same address. This example may be a domestic assault or involve three (or more) units in an apartment complex. This situation results in the mobility area being a point with an area of zero. Second, all home locations and the crime location can be on the same street, but all at different street numbers. In this situation, the mobility area is a line, also with an area of zero. In these cases an arbitrary area could be assigned to minimize data loss: a point could be assigned a value of 0.01 square kilometers and a line could be assigned a value of 0.01 square kilometers multiplied by the length of the line. However, rather than imposing bias on the area calculations these crimes are omitted from the study. This causes little concern as the number of such mobility polygons is small: a total of 17, or 0.23 percent.
R. Frank et al. / Applied Geography 34 (2012) 180e188
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Fig. 3. Methodological issues with the geometry of offending and victimization, two offenders.
Results The output from the crime mobility polygon calculations is reported in Tables 4e7. Though we only report the median mobility area, other statistics are available to the interested reader from the authors. This measure of central tendency is chosen because of some extreme values that impacted the calculations of the means, particularly for Prince George. The results for the crime mobility polygons for one offender and one victim (mobility triangles) are shown in Table 4. Even for this more common crime mobility polygon, there are fewer than ten observations in four of the twelve crime classifications in Coquitlam: homicide, commercial burglary, other burglary, and residential burglary. As such, these results are not discussed. In the context of violent crime classifications, the median crime mobility area is approximately two square kilometers, except for sexual assault which is approximately four square kilometers. Generally speaking, the median crime mobility area for property
Table 5 Median crime mobility area, by crime type, one offender and two victims.
Table 4 Median crime mobility area, by crime type, one offender and one victim. Crime classification
Aggravated assault Assault Homicide Sexual assault Armed robbery Robbery Commercial burglary Other burglary Residential burglary Theft Theft from motor vehicle Theft of motor vehicle
Coquitlam
Prince George
crime classifications tends to be greater. Though theft from motor vehicle has a small crime mobility area (0.4 square kilometers), theft (4.6) and theft of motor vehicle (6.3) are much greater than the values for the violent crime classificationsdthe three burglary classification all have large crime mobility areas, but as mentioned above, this is based on small samples. Therefore, in Coquitlam, the crime mobility areas for property crime classifications tend to be greater than the crime mobility areas for violent crime classifications. This is a result similar to the journey to crime literature: the journey to crime is short, but even shorter for violent crime classifications. The results for Prince George are rather different from those in Coquitlam. First, only other burglary has fewer than ten observations, but its results are not out of line from the other crime classifications. Second, and most significantly, the median crime mobility areas are substantially smaller than in Coquitlam for most crime classifications.
Crime classification
Coquitlam
Prince George
Surrey
Median
n
Median
n
Median
n
1.9 2.2 64.8 3.8 1.2 2.6 16.9 33.9 2.9 4.6 0.4 6.3
92 300 3 64 61 24 3 3 7 38 23 29
1.0 0.7 1.0 1.7 1.2 0.7 3.2 0.4 0.4 0.8 3.0 4.4
222 570 12 172 52 55 16 7 48 94 52 55
1.0 1.2 2.7 4.0 3.2 2.3 0.8 1.4 0.2 2.0 2.1 5.1
439 1483 36 338 186 127 23 37 77 228 100 245
Median Aggravated assault Assault Homicide Sexual assault Armed robbery Robbery Commercial burglary Other burglary Residential burglary Theft Theft from motor vehicle Theft of motor vehicle
Surrey
n
Median
n
Median
n
4.3 6.6
16 33
21.6 7.6 2.5 67.2 0.1 0.1 9.8 58.7 44.4
14 16 4 3 1 7 3 2 8
1.3 1.3 0.9 1.3 3.0 4.5
46 81 1 44 13 16
0.5 0.1 4.7 1.6 1.6
3 22 12 7 5
3.0 2.5 14.5 3.3 5.2 6.3 25.5 0.5 1.9 8.4 0.4 11.8
105 185 11 80 39 30 4 8 28 22 10 33
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Table 6 Median crime mobility area, by crime type, two offenders and one victim. Crime classification
Aggravated assault Assault Homicide Sexual assault Armed robbery Robbery Commercial burglary Other burglary Residential burglary Theft Theft from motor vehicle Theft of motor vehicle
Coquitlam
Prince George
Surrey
Median
n
Median
n
Median
n
1.8 2.8 0.6 18.4 9.5 4.8 3.7 106.1 1.5 2.5 6.0 17.1
13 31 3 2 11 8 3 1 15 8 3 6
3.1 1.7 0.6 8.9 3.8 2.7 11.8
37 61 2 11 20 14 5
0.9 0.8 1.1 2.6
43 31 23 23
2.3 3.0 4.1 4.8 4.6 7.1 21.9 9.1 2.1 1.6 12.3 6.6
82 136 8 17 33 32 6 20 57 41 16 80
For the violent crime classifications, the median crime mobility areas are all approximately one square kilometerdsexual assault is 1.7 square kilometers, but assault and robbery are 0.7 square kilometers. As such, the median crime mobility areas in Prince George are approximately one-half of those in Coquitlam. A similar result holds for the property crime classifications. Other burglary, residential burglary, and theft all have median crime mobility areas less than one square kilometer; commercial burglary, theft from motor vehicle, and theft of motor vehicle all have median crime mobility areas greater than 3 square kilometers. On average, similar to Coquitlam, property crime classifications in Prince George have greater median crime mobility areas than violent crime classifications. The greater median crime mobility areas for commercial burglary, theft from motor vehicle, and theft of motor vehicle are likely the result of the built environment in Prince George: most of the targets for these crime classifications are in the central business district which most offenders must travel to in order to commit their crime. Turning to Surrey, the results are similar to those of Coquitlam and Prince George but there is less of a distinction between violent and property crime classifications. Aggravated assault and assault have low median crime mobility areas, but the other violent crime classifications are of a similar magnitude to the property crime classifications. Sexual assault (4 square kilometers) and theft of motor vehicles (5.1 square kilometers) have the largest median crime mobility areas which is most likely because of the need for offenders to travel further to find targets. Based on the nature of the built environment in Surrey, it is not a surprise that the median crime mobility areas are all low. As mentioned above, Surrey has multiple residential and commercial areas through the city that
means most offenders do not have to travel a great distance for the commission of any crime classification, property or violent. The results for the crime mobility polygons for one offender and two victims (mobility quadrilaterals) are shown in Table 5. In the context of Coquitlam many of the crime classifications no longer have enough observations to make meaningful inferencesdhomicide is no longer present. However, aggravated assault, assault, sexual assault and armed robbery all have more than ten observations. The median crime mobility areas for these four crime classifications have all increased substantially, particularly sexual assault. The median crime mobility areas have doubled for aggravated assault, tripled for assault, and increased five- and six-fold for sexual assault and armed robbery, respectively. However, such increases are not unexpected. As shown in Fig. 4, if two victims live close to one another the area can easily double. In the case of a mobility triangle, area A represents the crime mobility area, but area A plus area B if the victims live in close proximity. Turning to the results for Prince George, the changes are much different. To begin with, only four crime classifications (homicide, other burglary, theft from motor vehicle, and theft of motor vehicle) have fewer than ten observations. More importantly, there is very little change for most of the crime classifications with regard to the median crime mobility areas. Aggravated assault, assault, homicide, sexual assault, other burglary, and residential burglary all have very little change when a second victim is present. The median crime mobility areas for theft from motor vehicle and theft of motor vehicle are one-half and one-third, respectively, of the values in Table 4, but the number of observations in both cases are now less than ten so any inference here must be made with caution. However, notable increases are present for armed robbery, robbery, and theft. Regardless, these increases are at magnitudes that arise in situations similar to that shown in Fig. 4. And with the small number of property crime classification results, little may be said regarding the median crime mobility area being smaller or greater for violent crime classifications. The results for Surrey are similar to those for Prince George in the sense that only a few crime classifications have fewer than ten observations and the increases in the median crime mobility areas are moderate for those crime classifications with more than ten observations. Similar to Prince George, little may be said regarding the median crime mobility areas for violent versus property crime classifications. Three of the six property crime classifications have lower median crime mobility areas than all of the violent crime classifications, but the median crime mobility areas of the other three property crime classifications are substantially greater. Consequently, there is not a discernable pattern to be discussed.
Table 7 Median crime mobility area, by crime type, two offenders and two victims. Crime classification
Aggravated assault Assault Homicide Sexual assault Armed robbery Robbery Commercial burglary Other burglary Residential burglary Theft Theft from motor vehicle Theft of motor vehicle
Coquitlam
Prince George
Surrey
Median
n
Median
n
Median
n
11.1 7.8
5 6
12.9 6.6
3 3
87.7 6.3
6 1
2.8 2.2 0.1 1.1 6.4 11.1 20.2 1.6 5.1 2.0 4.3 8.0
7 9 1 2 6 2 2 1 11 4 5 5
5.2 7.7 16.8 1.5 13.4 4.9 5.6 13.5 0.7 8.3 98.7 19.0
32 28 3 7 22 3 1 5 16 8 4 14 Fig. 4. Area calculations when increasing offenders.
R. Frank et al. / Applied Geography 34 (2012) 180e188
The results for co-offending (two offenders and one victim) are shown in Table 6. Once again, Coquitlam suffers from many crime classifications with few observations. However, the increases in the median crime mobility areas are most often rather modest. Only armed robbery (with eleven observations) has a substantial increase in its median crime mobility area. This result implies that co-offenders in Coquitlam tend to reside close to one another. The median crime mobility areas for Prince George exhibit similar changes to those in Coquitlam when a second offender is included in the analysis: moderate increases in the median crime mobility areas. In fact, in the cases of theft, theft from motor vehicle, and theft of motor vehicle the median crime mobility area has decreased. And similar to the results for one offender and two victims, little may be said regarding the relative values for median crime mobility areas for violent and property crime classifications. Turning to the results for Surrey, results similar to those discussed above are present as well: moderate increases in the median crime mobility areas for those crime classifications with more than ten observations. Only theft from motor vehicle has a large increase (six-fold) in the median crime mobility area. The last set of results represents co-offending and covictimization (Table 7), two offenders and two victims: pentagons. For all three municipalities the number of observations for most crime classifications is too small to identify any patterns in the changes. Coquitlam has fewer than seven observations in all cases and will not be discussed, Prince George has fewer than ten observations for all crime classifications except for residential burglary that has eleven observations, but Surrey does have more than ten observations for five crime classifications. Aggravated assault and assault have notable increases in their median crime mobility areas, approximately doubling, whereas the median crime mobility area of residential burglary decreased. Perhaps most worthy are the significant increases in the median crime mobility areas for armed robbery and theft of motor vehicle.
Discussion and conclusions In this paper we contribute to the mobility triangle literature by incorporating co-offending and co-victimization into the analysis.14 Because of this contribution, we are dealing not only with mobility triangles, but mobility quadrilaterals and pentagonsdmobility polygons. We also contribute to this literature by introducing the crime mobility area rather than relying on the traditional categories used to describe mobility triangles. Our methodology provides more details into the patterns of mobility polygons. With this greater detail, geographical comparisons between crime classifications and within crime classifications may be made for different offending and victimization patterns. Lastly, we consider the geography of this geometric dimension of crime by comparing the results of three different municipalities, measuring geodiversity. In general, we find that median crime mobility areas are small. There are some large increases as more offenders and victims are added to the analysis, but most often these large increases coincide with crime classifications that have few observations. Though we are not always able to make this claim, the median crime mobility areas for violent crime classifications are smaller than the median crime mobility areas for property crime classificationsdthis phenomenon is definitely present for the mobility triangles, Table 4.
14 Because of our data limitations we must provide caveats when the number of observations is lowdsometimes not reporting results. However, we are confident it is critical to report these results because such an analysis has not been undertaken before. Future research that has more observations may be able to confirm or deny these findings.
187
Perhaps most interesting is the geographic component of the analysis. In the cases of both violent and property crime classifications, the median crime mobility areas in Coquitlam are generally greater than those in Prince George and Surrey. This is particularly interesting because Coquitlam is approximately one-half the size of both Prince George and Surrey. Consequently, one would expect that offenders would not need to travel as far in Coquitlam to find targets. However, it is the location of the crime that we use to make municipal assignments so it is possible that offenders and victims from other municipalities travel to Coquitlam. Inspection of maps in neighboring municipalities (Pitt Meadows and Maple Ridge) shows that this is the case. Despite there being many targets in these two municipalities, the target-rich area of Coquitlam draws offenders across municipal boundaries. Such a phenomenon may be occurring in Prince George and Surrey as well, but probably less frequently in Prince George. This is also consistent with Prince George having the lowest median crime mobility areas overall. Another explanation for the differences in the median crime mobility areas is the nature of the built environments in these different municipalities, another example of geodiversity. Though Prince George and Surrey are approximately the same official size, Prince George has far more area that is relatively uninhabited space: the core of Prince George is only about ten percent of the total area for the municipality. Surrey also has some uninhabited spaces (agricultural land, for example), but much of this municipality is occupieddSurrey has almost seven times the population of Prince George in the same official area. Therefore, the smaller median crime mobility areas in Prince George are likely a result of two things: its small core area and that it only has one primary commercial area. Generally speaking, Surrey has smaller median crime mobility areas than Coquitlam and Coquitlam is smaller, but Surrey has a denser population. As such, target density in Surrey is greater than in Coquitlam lessening the need for longer journeys to crime and, therefore, larger crime mobility areas. The results of this analysis contribute to the applied geographical literature as well, particularly geographic profiling (Rossmo, 2000). From the perspective of geographic profiling, these results are instructive when considering a “spatial profile”. A spatial profile may be considered as how far an offender travels to commit the crime; this information may be used to prioritize a list of potential suspects similar to geographic profiling proper. For example, in cases when there are multiple offenders, some crime classifications exhibit greater crime mobility polygon areas than other crime classifications. There are a number of future research directions for this type of analysis. The first is to replicate the methodology in other municipalities to find if the results presented here are generalizable, in terms of different crime classifications, numbers of offenders and numbers of victims. It would be most useful for any such replications to also analyze multiple municipalities to enable comparisons of different sized and differently built municipalities. Second, from a methodological perspective, the impact of areal bias needs to be investigated. As noted above, using a minimum bounding area necessarily imposes an upward bias in the area calculations. It is important to obtain information regarding how much areal bias is present because increasing the number of offenders and victims tends to increase the median crime mobility area. This area does not increase substantially in most cases when another individual is added to the calculation, but this increase may be partially due to the areal bias. Third, a more detailed analysis of the mobility polygons is in order. In particular, it would be interesting to know if co-offenders are recruited in close proximity from each other and if the age of the offenders has an impact on the median crime mobility area. And last, future research should investigate this phenomena within the context of theory. Though our analysis is motivated by theory, our
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contribution is more methodological. However, that does not mean that different sized polygons in different places, for different crime types, and varying offender-victim combinations do not have a priori expectations. References Amir, M. (1971). Patterns of forcible rape. Chicago, IL: University of Chicago Press. Andresen, M. A., & Felson, M. (2010). The impact of co-offending. British Journal of Criminology, 50, 66e81. Barber, C. B., Dobkin, D. P., & Huhdanpaa, H. T. (1996). The Quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software, 22, 469e483. Brantingham, P. L., & Brantingham, P. J. (1981). Notes on the geometry of crime. In P. J. Iin Brantingham, & P. L. Brantingham (Eds.), Environmental criminology (pp. 27e53). Beverly Hills, CA: Sage Publications. Brantingham, P. L., & Brantingham, P. J. (1993a). Nodes, paths and edges: considerations on the complexity of crime and the physical environment. Journal of Environmental Psychology, 13, 3e28. Brantingham, P. L., & Brantingham, P. J. (1993b). Environment, routine and situation: toward a pattern theory of crime. In R. V. Clarke, & M. Felson (Eds.), Routine activity and rational choice: Advances in criminological theory, Vol. 5 (pp. 259e294). New Brunswick, NJ: Transaction Publishers. Brantingham, P. J., & Brantingham, P. L. (1995). Environmental criminology and crime prevention. In P.-O. H. Wikstrom, R. V. Clarke, & J. McCord (Eds.), Integrating crime prevention strategies: Propensity and opportunity (pp. 207e240). Stockholm: National Council for Crime Prevention Sweden. Breckenridge, S. P., & Abbott, E. (1912). The delinquent child and the home. NewYork, NY: Russell Sage Foundation Charities Publication Committee. Burgess, E. W. (1925). Can neighborhood work have a scientific basis? In R. E. Park, E. W. Burgess, & R. D. McKenzie (Eds.), The city: Suggestions for investigation of human behaviors in the urban environment (pp. 142e155) Chicago, IL: University of Chicago Press. Carrington, P. (2002). Group crime in Canada. Canadian Journal of Criminology, 44, 277e315. Carrington, P. J. (2009). Co-offending and the development of the delinquent career. Criminology, 47, 301e335. Clarke, R. V. G. (1980). Situational crime prevention: theory and practice. British Journal of Criminology, 20, 136e147. Cohen, L. E., & Felson, M. (1979). Social change and crime rate trends: a routine activity approach. American Sociological Review, 44, 588e608. Conway, K. P., & McCord, J. (2002). A longitudinal examination of the relation between co-offending with violent accomplices and violent crime. Aggressive Behavior, 28, 97e108. Dufour, A., Gadallah, F., Wagner, H. H., Guisan, A., & Buttler, A. (2006). Plant species richness and environmental heterogeneity in a mountain landscape: effects of variability and spatial configuration. Ecography, 29, 573e584. Erickson, M. (1971). The group context of delinquent behaviour. Social Problems, 19, 114e129. Felson, M. (2003). The process of co-offending. In M. J. Smith, & D. B. Cornish (Eds.), Theory for practice in situational crime prevention, crime prevention studies, Vol. 16 (pp. 149e167). Monsey, NY: Criminal Justice Press.
Felson, M., & Cohen, L. E. (1980). Human ecology and crime: a routine activity approach. Human Ecology, 8, 398e405. Felson, M., & Cohen, L. E. (1981). Modeling crime trends: a criminal opportunity perspective. Journal of Research in Crime and Delinquency, 18, 138e161. Gold, M. (1970). Delinquent behavior in an American city. Belmont, CA: Brooks/Cole. Gray, M. (2004). Geodiversity: Valuing and conserving abiotic nature. Chichester: Wiley. Gray, M. (2008). Geodiversity: developing the paradigm. Proceedings of the Geological Association, 119, 287e298. Groff, E. R., & McEwen, T. (2007). Integrating distance into mobility triangle typologies. Social Science Computer Review, 25, 210e238. Hindelang, M. J. (1976). ‘With a little help from their friends: group participation in reported delinquent behaviour. British Journal of Criminology, 11, 109e125. Johnson, S. D., Bernasco, W., Bowers, K., Elffers, H., Ratcliffe, J., Rengert, G., et al. (2007). Space-time patterns of risk: a cross national assessment of residential burglary victimization. Journal of Quantitative Criminology, 23, 201e219. Lind, A. W. (1930). Some ecological patterns of community disorganization in Honolulu. American Journal of Sociology, 36, 206e220. Lynch, K. (1960). The image of the city. Cambridge, MA: MIT Press. McCord, J., & Conway, K. P. (2002). Patterns of juvenile delinquency and cooffending. In E. Waring, & D. Weisburd (Eds.), Crime and social organization. Advances in criminological theory, Vol. 10 (pp. 15e30). New Brunswick, NJ: Transaction Publishers. van Mastrigt, S. B., & Farrington, D. P. (2009). Co-offending, age, gender and crime: implications for criminal justice policy. British Journal of Criminology, 49, 552e573. Normandeau, A. (1968). Patterns in robbery. Criminology, 6, 2e16. Parks, K. E., & Mulligan, M. (2010). One the relationship between a resource based measure of geodiversity and broad scale biodiversity patterns. Biodiversity and Conservation, 19, 2751e2766. Rand, A. (1986). Mobility triangles. In R. M. Figlio, S. Hakim, & G. F. Rengert (Eds.), Metropolitan crime patterns (pp. 117e126). Monsey, NY: Criminal Justice Press. Rossmo, D. K. (2000). Geographic profiling. Boca Raton, FL: CRC Press. Sarnecki, J. (2001). Delinquent networks: Youth co-offending in Stockholm. Cambridge, UK: Cambridge University Press. Shaw, C. T., & McKay, H. D. (1931). Report on the causes of crime, Vol. 2. Washington, DC: Government Printing Office. Stolzenberg, L., & D’Alessio, S. J. (2008). Co-offending and the age-crime curve. Journal of Research in Crime and Delinquency, 45, 65e86. Tita, G., & Griffiths, E. (2005). Traveling to violence: the case for a mobility-based spatial typology of homicide. Journal of Research in Crime and Delinquency, 42, 275e308. Townsley, M., & Sidebottom, A. (2010). All offenders are equal, but some are more equal than others: variation in journeys to crime between offenders. Criminology, 48, 897e917. Westerberg, K., Grant, T., & Bond, J. W. (2007). Triangulation mobility of autotheft offenders. Journal of Investigative Psychology and Offender Profiling, 4, 109e120. Wiles, P., & Costello, A. (2000). The ‘road to nowhere’: The evidence for travelling criminalsIn Home Office Research Study, 207. London: Research: Development and Statistics Directorate, Home Office.
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Applied Geography journal homepage: www.elsevier.com/locate/apgeog
The geodiversity of crime: Evidence from British Columbiaq Richard Frank a, Martin A. Andresen a, *, Marcus Felson b a b
School of Criminology, Institute for Canadian Urban Research Studies, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada Department of Criminal Justice, 601 University Drive, Texas State University, San Marcos, TX 78666, USA
a b s t r a c t Keywords: Geodiversity Mobility triangle Geometry Journey to crime
Crime mapping has established central tendencies, e.g., that crime trips tend to be certain lengths. But this is only one-half of the convergence that leads to a crime. Crime mobility research, however, considers the simultaneous movements of both offenders and victims. In this paper, we consider the geodiversity of crime mobility: there are variations in the amount of area covered by various crimes depending on the variations of criminal opportunity. Extending the crime mobility research to consider co-offending, co-victimization, and area covered rather than typologies, we find strong evidence for geodiversity in crime. This geodiversity varies across crime types within a single municipality as well as across municipalities within a single crime type. Ó 2011 Elsevier Ltd. All rights reserved.
Introduction
1979; Felson & Cohen, 1980, 1981). In order for a crime to occur, a motivated offender and a suitable target must converge in time and space with the lack of a capable guardian. This is a necessary condition, but not sufficient for a crime to occur. Therefore, the presence of these fundamental components may be thought of as crime’s geodiversity; the manifestation of crime itself is then its biodiversity, and the greater crime’s geodiversity the greater its corresponding biodiversity.1 In more conventional criminological language, we say: where there is more opportunity there is more crime. Therefore, though we may expect the same, or similar, spatial crime patterns in different places, variations in crime’s resource base (opportunity) is expected to lead to variations in the spatial behavior of crime. One branch of the geography of crime literature that could consider this variation is the journey to crime literature (Wiles & Costello, 2000). This literature shows that the journey to crime is short, particularly for violent crime, but only represents one-half of the convergence in time in space. A related branch of literature considers the simultaneous movements of the offender and the victim, converging in spacedmobility triangle research. This research investigates the geographic proximity of the offender’s residence, the victim’s residence, and the crime location.2 In all studies known to the authors, mobility triangles are
Geographical theories of crime state that the way one moves throughout the environment impacts offending behavior as well as when and where one may be a victim of crime. Consequently, crime and its geography are not only measurable, but predictable. We can then, for example, use geographical information (the locations of crimes) to help locate certain types of offenders as well as predict geographic patterns, more generally (Rossmo, 2000). Despite the regularities in crime patterns, is there diversity in other geographic terms? Geodiversity is a term used in the natural sciences to describe the abiotic aspects of our environment: climate, topography, geology, and hydrology (Gray, 2004, 2008). These aspects combine to generate the resources necessary for biodiversity, flora and fauna (Parks & Mulligan, 2010); and the greater the geodiversity within an area the greater its corresponding biodiversity (Dufour, Gadallah, Wagner, Guisan, & Buttler, 2006). As such, greater opportunity for life (a greater presence of resources) leads to a greater presence of life. But does this relate to crime? The fundamental components for crime, its resources, are best understood within a routine activities approach (Cohen & Felson,
q This work was done in the ICURS Laboratory at Simon Fraser University under terms of a joint Memorandum of Understanding between the Institute for Canadian Urban Research Studies, Simon Fraser University, “E”-Division of the Royal Canadian Mounted Police, and the British Columbia Ministry of Public Safety and Solicitor General. We would like to thank three anonymous reviewers for their comments that have improved our paper. * Corresponding author. E-mail addresses: [email protected] (R. Frank), [email protected] (M.A. Andresen), [email protected] (M. Felson). 0143-6228/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apgeog.2011.11.007
1 Though not discussed in terms of geodiversity, Johnson et al. (2007) find evidence for geodiversity in their cross-national study of near-repeat victimization. 2 These analyses implicitly or explicitly assume that the residences of the offender and victim are the starting points of their journey to crime and victimization, respectively. This assumption, however, may be problematic. See Townsley and Sidebottom (2010) for a discussion of this issue.
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Table 1 Mobility triangle classifications, Normandeau (1968). Mobility triangle type
Definition
Percentage of offenses (robbery)
Crime neighborhood triangle
Offender’s residence, victim’s residence, and crime location all in the same neighborhood/communitya Victim’s residence and crime location in the same neighborhood/community Offender’s residence and crime location all in the same neighborhood/community Offender’s and victim’s residence in the same neighborhood/community Offender’s residence, victim’s residence, and crime location all in different neighborhoods/communities
14
Offender mobility triangle Victim mobility triangle Offense mobility triangle Total mobility triangle a
17 19 12 38
Normandeau (1968) defines a neighbourhood/community using census tract boundaries.
calculated for a single municipality. However, because of crime’s underlying geodiversity, there is no reason to believe that this geometry of crime is the same from place to place. In this paper we contribute to the mobility triangle literature in three ways. First, we do not concern ourselves with the categories used in previous researchdthese categories are discussed below. As outlined by Groff and McEwen (2007), there may be difficulties when social boundaries are not considered in the assessment of the geometry of crime, but in order for new insight to be gained it is necessary to break from the 80-year-old classification system. Rather, we calculate the mobility area for offending and victimization. This allows for a more detailed and more geographical comparison between crime classifications and within crime classifications for different offending and victimization patterns. Second, we explicitly consider the geometry of co-offending and co-victimization.3 Groff and McEwen (2007) do include co-offenses or co-victimization in their analysis of homicide, but independently calculate a mobility triangle for each of the offenders and victims. We consider the geometry of offenses with up to two offenders and two victims. And third, not only do we break down the analysis by crime classification, we also compare the geometry of offenses in three different municipalities, two urban and one rural. Measuring crime’s geodiversity: theory and empirics of the geometry of crime The presence of a geometric component to crime is obvious when one considers the geographical theories of crime. Routine activity theory (Cohen & Felson, 1979; Felson & Cohen, 1980, 1981), though initially concerned with temporal changes, states that understanding the convergence in time and space of an offender, a victim, and the lack of a capable guardian is critical to understanding criminal incidents. Though not a specific requirement for routine activity theory, the offender comes from a place, the victim comes from a place, and the two intersect at another place.4 The geometric theory of crime (Brantingham & Brantingham, 1981, 1993a), invokes the concepts of nodes, paths, and edges from Lynch (1960), stating that the vast majority of crime occurs within the offender’s awareness and activity space. Therefore, it is the convergence of offender and victim awareness spaces that leads to incidents of crime (Brantingham & Brantingham, 1995).5 Though developed after the original mobility triangle research, these two theoretical frameworks provide support for the existence
3 Co-offending is defined as the presence of two or more offenders during the criminal event; similarly for co-victimization. 4 Of course, it is possible that the criminal incident may occur at the residence of the offender or the victim, such is the case in domestic violence. 5 The geometric theory of crime and routine activity theory are also components of the meta-theoretic framework crime pattern theory (Brantingham & Brantingham, 1993b). In the current context, we are concerned with the specific aspects of these theories. As such, we do not consider crime pattern theory in the current analysis, per se.
of mobility triangles. Mobility triangles represent the geometry of the offender’s residence, the victim’s residence, and the location of the criminal incidentdthese locations each represent a vertex of the triangle. Though the original context was sexual promiscuity, not crime, Burgess (1925) describes three types of mobility triangles: delinquency triangles (offenders’ residence, victim’s residence, and crime location all in the same neighborhood/community), mobility triangles (offender’s and victim’s residence in the same neighborhood, but the crime location is elsewhere), and promiscuity triangles (all points are in different neighborhoods). Once these locations are classified, offenderevictim movement patterns can then be mapped and compared across different social groups, gender, and crime classifications. The first known research to apply Burgess’ (1925) mobility triangle typology to crime in an empirical context was Lind’s (1930) analysis of crime in Honolulu. However, Lind (1930) did not consider the victim’s residence. As such, a mobility triangle only emerged with multiple offenders. Lind’s (1930) general results were that the delinquency triangle most often occurred within low socioeconomic status neighborhoods and that the mobility of offenders (delinquency / mobility / promiscuity triangles) increased with age. It was another thirty years before another study of mobility triangles emerged. From an empirical perspective, Normandeau (1968) introduced the victim into mobility triangle research, only considering solo-offenders. More significantly, Normandeau (1968) also expanded the typology of mobility triangles into five classifications. This new typology allowed much more insight into the geometry of crime to be gathered. For example, in column 3 of Table 1 (reproduced from Normandeau 1968), the offender and the victim reside in the same neighborhood 26 percent of the time, the offender’s residence and the crime location are in the same neighborhood 33 percent of the time, and the victim’s residence and the crime location are in the same neighborhood 32 percent of the time. Consequently, there is a strong geographical bias in the commission of crime. That bias may be finding victims close to the offender’s home, or finding victims close to their own home. Amir (1971) investigated rape in Philadelphia, finding that 68 percent of the time the crime neighborhood triangle was present, and in 82 percent of all cases the offender and victim had residences in the same neighborhood. In a comparison of robbery and rape, these two different crime classifications exhibited very different dominating mobility triangle types. The next advancement in this literature occurred with Rand’s (1986) analysis of nine different crime classifications: total crime, homicide, rape, robbery, aggravated assault, burglary, larceny, vehicle theft, and simple assault. She finds that 31 percent of offenders find their targets in their home neighborhood (census tract); however, there is large variation across crime classifications: as low as 15 percent (larceny) and as high as 53 percent (homicide and rape). Generally speaking, the total mobility triangle is the most prevalent (45 percent), and the offense mobility triangle is the
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least prevalent (5 percent). Additionally, property crimes have a tendency to be total mobility triangles and violent crimes have a tendency to be neighborhood triangles. Rand’s (1986) results reiterate the importance of analyzing detailed crime classifications, when comparing the work of Amir (1971) to Normandeau (1968). More recently, Tita and Griffiths (2005) analyzed the mobility triangles of homicide. Tita and Griffiths (2005) use the same 5 classification typology as Normandeau (1968), but with different naming conventions. Homicides tend to either be total mobility triangles (28 percent) or crime neighborhood triangles (27 percent). The primary contribution of Tita and Griffiths (2005) is to show that the mobility patterns of homicide depend on: participant characteristics, victimeoffender relationships, motive, and event characteristics. Similar to the tenets of situational crime prevention (Clarke, 1980), in order to understand mobility triangles the analysis needs to be crime specific, not only in terms of the crime type, but also with regard to the characteristics of the crime itself. The most recent analysis of mobility triangles, Groff and McEwen (2007), replicates Tita and Griffiths (2005) showing the importance of understanding the nature of homicide when classifying the type of mobility triangle. Additionally, Groff and McEwen (2007) advance the literature through the incorporation of distance measures to classify mobility triangles.6 Groff and McEwen (2007) identify limitations when incorporating the actual distance between offender’s residence, victim’s residence, and the crime location to classify the mobility triangles. For example, having an offender cross a road (very short distance) may be socially significant. Regardless, they believe the benefits of their methodology outweigh the limitations. Groff and McEwen (2007) use one-quarter mile in order to classify near and far. With this criterion, they subsequently use the 5 category classification system to label criminal incidents. In their analysis, offenders find victims in their own neighborhood 46 percent of the time, victims are victimized in their own neighborhood 51 percent of the time, and both offenders and victims live in the same neighborhood 31 percent of the time. This literature, albeit small, clearly shows the importance of separately analyzing different crime classifications, the importance of other characteristics specific to crimes, and that incorporating other geographical information contributes to understanding criminal mobility. We incorporate this insight into our analyses. On the basis of Rand’s (1986) results, we analyze 12 crime classifications; in order to incorporate the importance of characteristics we analyze criminal mobility in three different municipalities, interpreting results in this context7; and we consider additional geographic information that provides further insight into criminal mobility.
Data and measurement method Criminal incident data The data employed in the current analysis are from three municipalities (police jurisdictions) in British Columbia, Canada’s western-most province. The entire province of British Columbia has approximately 4 million residents living in 186 police jurisdictions, with the Royal Canadian Mounted Police (RCMP) being responsible
6 Westerberg, Grant, and Bond (2007) also investigate mobility triangles for automotive theft. However, their research considers the offender’s home location, the theft location, and the vehicle disposal site. Consequently, we do not review Westerberg et al. (2007) here. 7 We do not have access to the detailed crime characteristics analyzed by Tita and Griffiths (2005).
for policing 174 of the 186 police jurisdictionsd67 percent of the provincial population, approximately 2.7 million persons. The municipalities we include in the analysis are from within the Metro Vancouver region (Coquitlam and Surrey), and one municipality outside the Metro Vancouver region (Prince George). We include these three municipalities because of their size (there is a lot of data for these municipalities) and to provide different types of urban form in the analysis to investigate the geodiversity of crimedthe inclusion of more municipalities would greatly expand the data presented in the tables. Coquitlam is a relatively small municipality covering 121 square kilometers, with approximately 115,000 persons and a population density of 942 persons per square kilometers; Surrey is a municipality covering 317 square kilometers, has approximately 400,000 persons and a population density of 1245 persons per square kilometer; Prince George is a municipality covering 316 square kilometers, has approximately 71,000 persons and a population density of 225 persons per square kilometers in the rural area of British Columbia. Both municipalities within Metro Vancouver have urban sprawl, light industry, strip development and malls, apartments, and single family dwellings, but the locations of these facilities are quite different for each municipality. Coquitlam essentially has one commercial district centered on a large shopping area. The area also contains a major transportation hub, and direct train-line to downtown Vancouver, a library, a college campus and a sports complex. This commercial district not only attracts residents of Coquitlam, but residents from neighboring municipalities because of its size. In contrast, Surrey has multiple commercial districts and regional shopping areas, each large enough to attract residents from neighboring municipalities as well. Of course, this is in part because of Surrey’s greater population. Prince George, located in the center of the province, is included to provide a more nonmetropolitan example. Similar to Coquitlam, Prince George has one commercial district and draws populations from the surrounding rural areas to serve their needs. Because of the different sizes of the municipalities, data availability does vary: we cannot make comparisons across all municipalities, crime types, and offenderevictim combinations. Despite these limitations, we are able to investigate some interesting comparisons. The use of different types of municipalities (in terms of population density, commercial areas, etc.) allows us to compare geodiversity not only in terms of crime types, but different types of municipalities. The data used in the analyses below are incident-based and extracted from the RCMP Police Information Retrieval System (PIRS). These data cover the period August 1, 2002 through July 31, 2006 and represent the complete set of incidents dealt with by the RCMP. With our ability to combine 48 consecutive months of the PIRS database, any unusual features of any given year or month are ironed out. The entire PIRS database contains approximately 5 million contacts with the police that involve approximately 9 million individualsdoffenders, victims, complainants, and witnesses. Of these 5 million police contacts, approximately 750,000 are common criminal offenses. In our analysis we consider both solo-offenses and co-offenses, with a co-offense being defined as an incident with more than one person classified as suspect, chargeable, or charged.8
8 A suspect is someone whom the RCMP believe committed the crime, but they do not (at the time of entry) have supporting evidence to pursue a charge; charged is for a person whom the RCMP believe committed the crime and for which there is supporting evidence; chargeable is for a person whom the RCMP believe committed the crime and for which there is supporting evidence, but who is not charged for a variety of reasons, such as being under the age of criminal responsibility.
R. Frank et al. / Applied Geography 34 (2012) 180e188 Table 2 Summary statistics, crime type classifications.
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Table 3 Summary statistics, types of polygons.
Crime type
Count
Percent
Offenders
Victims
Count
Percent
Aggravated assault Assault Homicide Sexual assault Armed robbery Robbery Commercial burglary Other burglary Residential burglary Theft Theft from motor vehicle Theft of motor vehicle Total
1096 2923 80 751 462 318 66 86 337 490 245 503 7357
14.9 39.7 1.1 10.2 6.3 4.3 0.9 1.2 4.6 6.7 3.3 6.8 100.0
1 1 2 2 Total
1 2 1 2
5321 912 902 222 7357
72.3 12.4 12.3 3.0
From this large incident-based data set, we extract twelve crime classifications that represent the majority of property and violent crimes: homicide, sexual assault, aggravated assault,9 assault, robbery, armed robbery, burglary (residential, commercial, and other10), theft, theft of motor vehicle, and theft from motor vehicle. However, because of small numbers of observations, not all crime classifications are reported in each set of results. In order for the geometry of these offenses to be calculated a further data restriction had to be made: only crimes that contain the offender’s home location, the victim’s home location, and the crime location are analyzed. This subset of data includes 7357 offenses, outlined in Table 2. Though most crimes investigated by the RCMP are property crimes, violent crimes dominate this particular subset of data because of the location restrictions stated above. Property crimes often do not have the victim present, as such the offender’s identity (and the offender’s home address) is not known as often as with violent crimes. This is one reason why clearance rates for property crimes tend to be rather low compared to violent crimes.11 However, as shown in Table 2, a large number of crimes are analyzed for all property crime classifications aside from Commercial and Other Burglary. In all calculations, these data are separated into categories based on the number of offenders and victims. In order to avoid small samples we do not consider crimes with more than two offenders or two victims. In almost all cases that have more than two offenders and/or victims there are fewer than ten observations. In fact, many of our results for two offenders and/or two victims are based on fewer than ten observations; these particular results should, therefore, be interpreted with caution. The counts within each of these categories are shown in Table 3. Immediately obvious from Table 3 is that crimes with one offender and one victim dominate, over 72 percent of the data. Some research has shown that co-offending dominates offending patterns, particularly in youth (Andresen & Felson, 2010; Carrington, 2009), but our data does not make any demarcations by age. Additionally, the presence of more than one offender only exacerbates the issue regarding offender identity and home address, discussed above.
9 For these purposes, aggravated assault combines aggravated assault and assault with a weapon. 10 Most often, “other burglary” refers to a burglary at a structure such as a vacation cottage or a trailer. 11 These statements are based on clearance data from the RCMP that are not publically available.
Measuring the geometry of co-offending and co-victimization Since the publication of Breckenridge and Abbott (1912), cooffending has been known to be an important aspect in the study of crime. The earliest studies of co-offending found that co-offending is commonplace for youth offending: Shaw and McKay (1931) found almost 82 percent of youth offending is co-offending in Chicago, Illinois; Gold (1970) found 75 percent in Flint, Michigan; and in a review of eleven studies, Erickson (1971) found that 85 percent of offenses involved co-offending. There has been some recent research that questions the degree of co-offending (Carrington, 2002; van Mastrigt & Farrington, 2009; Stolzenberg & D’Alessio, 2008), but there is substantial evidence that offending, particularly youth offending, is a group phenomenon. Additionally, a number of scholars find that those who co-offend tend to commit criminal offenses more frequently and more serious offenses (Hindelang, 1976; Sarnecki, 2001), “early starters” that co-offend commit more crimes later (McCord & Conway, 2002), and exposure to violence through cooffending leads to more violent crimes later in a criminal career (Conway & McCord, 2002).12 Lastly, Felson (2003) argues that cooffending causes more harm to youth, ethnic minorities, and cities. Needless to say, there is substantial evidence for the incorporation of co-offending into any analysis of crime, including its geometry. As stated above, we do not concern ourselves with categories, or typologies, of mobility triangles. Rather, we wish to be able to directly compare the mobility of different crime classifications. For example, Rand (1986) found that offenders did not have to leave their neighborhood to find their victims in 53 percent of homicide and rape incidents. However, this does not mean that the mobility of homicide and rape offenders is identical. Consider the following example. Fig. 1 shows two examples of mobility triangles that have the same classificationdtotal mobility triangles. However, it should be clear that such a classification scheme, though instructive, is limited in its ability to describe the geometry of these two crimes. In Fig. 1a, the actual distances traveled to offending and victimization are short, whereas a much greater distance is traveled for both offender and victim in Fig. 1b. Though these neighborhood boundaries may still be significant because crossing a particular street may have social significance (Groff & McEwen, 2007), much geographical information is lost with such classification schemes.13 In order to address this issue, we calculate the mobility area. This allows for a more precise comparison between different crime classifications, and within a crime classification but across cooffending and co-victimization patterns. Because we consider up to two offenders and two victims with a crime location, we analyze triangles, quadrilaterals, and pentagons. Fig. 2 shows the general area calculation for co-offending with a triangle and
12 Carrington (2002) warns about these generalizations because there are some studies that counter these claims. 13 The social significance of boundaries was indeed of critical importance to Burgess (1925). However, much, if not all, of the mobility triangle research is undertaken considering census tracts that may not necessarily be representative of actual neighborhoods.
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a quadrilateraldsimilar figures are available to show higher order polygons, and co-victimization. In Fig. 2, all offenders’ home locations are necessary for the calculation of the mobility area. This may not be the case in practice. Fig. 3 shows that two offenders may actually create a mobility triangle (Fig. 3a) rather than a mobility quadrilateral. One possible solution to this complication is to use all locations as vertices for the mobility area. However, this too has a complication that is evident in Figs. 3bed. In the case of only two offenders, one of whom lives within the mobility triangle of the other offender, the researcher must choose from three possible area calculations. Evident from Figs. 3bed, each of these possibilities may have a different mobility area. This becomes even more complex when there are more offenders and victims involved with a single criminal incident. We avoid this complication by calculating a minimum bounding area for each offense. The minimum bounding area is the smallest area that will enclose (either as vertices or interior points) all offenders’ home locations, the victims’ home locations, and the crime location. When all locations are in positions similar to those in Fig. 2 there is no areal bias. However, the mobility area is biased upwards when one vertex is contained by the others. This bias is minimized by averaging all mobility areas.
Fig. 1. a. Distance versus area-based mobility triangles. b. Distance versus area-based mobility triangles.
The mobility areas are calculated by fitting a convex hull around the event and home locations involved in each crime. A customwritten VB.NET program was used to retrieve the data from the database and calculate the relevant XY coordinates for each crime. Qhull (http://www.qhull.org) was then used to calculate the set of points that make up the convex hull, or mobility area, for each crime. Once these points were known, the area of the convex hull was calculated by our VB.NET algorithm as follows. First, an arbitrary XY coordinate was selected inside the mobility polygon by averaging all the XY coordinates that make up the convex hull. Second, triangles were constructed such that one of the vertices was the arbitrary coordinate from the previous step, the other two being two adjacent points in the convex hull. The area of the convex hull is calculated by summing the areas of the respective triangles (Barber, Dobkin, & Huhdanpaa, 1996). An alternative calculation that avoids the use of categories/ typologies is some combination of the distances for the journey to crime and the journey to victimization. The most obvious calculation is adding the two distances together to obtain the total journey to the criminal event. However, such a method has difficulties. Consider a total journey to the criminal event that sums to 20 units. Though 10 þ 10 and 5 þ 15, etc. all sum to 20, the areas of these triangles are all different. As such, only considering the linear nature of the journeys provides limited information. This is the reason why we choose area for the calculations below.
Fig. 2. a. Measuring the geometry of co-offending, triangle. b. Measuring the geometry of co-offending, quadrilateral.
There is one final methodological consideration regarding area. Though all necessary locations may be available, an area may not always be calculated. This may occur in two types of situations. First, both home locations (offender and victim) and the location of the crime may be at the same address. This example may be a domestic assault or involve three (or more) units in an apartment complex. This situation results in the mobility area being a point with an area of zero. Second, all home locations and the crime location can be on the same street, but all at different street numbers. In this situation, the mobility area is a line, also with an area of zero. In these cases an arbitrary area could be assigned to minimize data loss: a point could be assigned a value of 0.01 square kilometers and a line could be assigned a value of 0.01 square kilometers multiplied by the length of the line. However, rather than imposing bias on the area calculations these crimes are omitted from the study. This causes little concern as the number of such mobility polygons is small: a total of 17, or 0.23 percent.
R. Frank et al. / Applied Geography 34 (2012) 180e188
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Fig. 3. Methodological issues with the geometry of offending and victimization, two offenders.
Results The output from the crime mobility polygon calculations is reported in Tables 4e7. Though we only report the median mobility area, other statistics are available to the interested reader from the authors. This measure of central tendency is chosen because of some extreme values that impacted the calculations of the means, particularly for Prince George. The results for the crime mobility polygons for one offender and one victim (mobility triangles) are shown in Table 4. Even for this more common crime mobility polygon, there are fewer than ten observations in four of the twelve crime classifications in Coquitlam: homicide, commercial burglary, other burglary, and residential burglary. As such, these results are not discussed. In the context of violent crime classifications, the median crime mobility area is approximately two square kilometers, except for sexual assault which is approximately four square kilometers. Generally speaking, the median crime mobility area for property
Table 5 Median crime mobility area, by crime type, one offender and two victims.
Table 4 Median crime mobility area, by crime type, one offender and one victim. Crime classification
Aggravated assault Assault Homicide Sexual assault Armed robbery Robbery Commercial burglary Other burglary Residential burglary Theft Theft from motor vehicle Theft of motor vehicle
Coquitlam
Prince George
crime classifications tends to be greater. Though theft from motor vehicle has a small crime mobility area (0.4 square kilometers), theft (4.6) and theft of motor vehicle (6.3) are much greater than the values for the violent crime classificationsdthe three burglary classification all have large crime mobility areas, but as mentioned above, this is based on small samples. Therefore, in Coquitlam, the crime mobility areas for property crime classifications tend to be greater than the crime mobility areas for violent crime classifications. This is a result similar to the journey to crime literature: the journey to crime is short, but even shorter for violent crime classifications. The results for Prince George are rather different from those in Coquitlam. First, only other burglary has fewer than ten observations, but its results are not out of line from the other crime classifications. Second, and most significantly, the median crime mobility areas are substantially smaller than in Coquitlam for most crime classifications.
Crime classification
Coquitlam
Prince George
Surrey
Median
n
Median
n
Median
n
1.9 2.2 64.8 3.8 1.2 2.6 16.9 33.9 2.9 4.6 0.4 6.3
92 300 3 64 61 24 3 3 7 38 23 29
1.0 0.7 1.0 1.7 1.2 0.7 3.2 0.4 0.4 0.8 3.0 4.4
222 570 12 172 52 55 16 7 48 94 52 55
1.0 1.2 2.7 4.0 3.2 2.3 0.8 1.4 0.2 2.0 2.1 5.1
439 1483 36 338 186 127 23 37 77 228 100 245
Median Aggravated assault Assault Homicide Sexual assault Armed robbery Robbery Commercial burglary Other burglary Residential burglary Theft Theft from motor vehicle Theft of motor vehicle
Surrey
n
Median
n
Median
n
4.3 6.6
16 33
21.6 7.6 2.5 67.2 0.1 0.1 9.8 58.7 44.4
14 16 4 3 1 7 3 2 8
1.3 1.3 0.9 1.3 3.0 4.5
46 81 1 44 13 16
0.5 0.1 4.7 1.6 1.6
3 22 12 7 5
3.0 2.5 14.5 3.3 5.2 6.3 25.5 0.5 1.9 8.4 0.4 11.8
105 185 11 80 39 30 4 8 28 22 10 33
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Table 6 Median crime mobility area, by crime type, two offenders and one victim. Crime classification
Aggravated assault Assault Homicide Sexual assault Armed robbery Robbery Commercial burglary Other burglary Residential burglary Theft Theft from motor vehicle Theft of motor vehicle
Coquitlam
Prince George
Surrey
Median
n
Median
n
Median
n
1.8 2.8 0.6 18.4 9.5 4.8 3.7 106.1 1.5 2.5 6.0 17.1
13 31 3 2 11 8 3 1 15 8 3 6
3.1 1.7 0.6 8.9 3.8 2.7 11.8
37 61 2 11 20 14 5
0.9 0.8 1.1 2.6
43 31 23 23
2.3 3.0 4.1 4.8 4.6 7.1 21.9 9.1 2.1 1.6 12.3 6.6
82 136 8 17 33 32 6 20 57 41 16 80
For the violent crime classifications, the median crime mobility areas are all approximately one square kilometerdsexual assault is 1.7 square kilometers, but assault and robbery are 0.7 square kilometers. As such, the median crime mobility areas in Prince George are approximately one-half of those in Coquitlam. A similar result holds for the property crime classifications. Other burglary, residential burglary, and theft all have median crime mobility areas less than one square kilometer; commercial burglary, theft from motor vehicle, and theft of motor vehicle all have median crime mobility areas greater than 3 square kilometers. On average, similar to Coquitlam, property crime classifications in Prince George have greater median crime mobility areas than violent crime classifications. The greater median crime mobility areas for commercial burglary, theft from motor vehicle, and theft of motor vehicle are likely the result of the built environment in Prince George: most of the targets for these crime classifications are in the central business district which most offenders must travel to in order to commit their crime. Turning to Surrey, the results are similar to those of Coquitlam and Prince George but there is less of a distinction between violent and property crime classifications. Aggravated assault and assault have low median crime mobility areas, but the other violent crime classifications are of a similar magnitude to the property crime classifications. Sexual assault (4 square kilometers) and theft of motor vehicles (5.1 square kilometers) have the largest median crime mobility areas which is most likely because of the need for offenders to travel further to find targets. Based on the nature of the built environment in Surrey, it is not a surprise that the median crime mobility areas are all low. As mentioned above, Surrey has multiple residential and commercial areas through the city that
means most offenders do not have to travel a great distance for the commission of any crime classification, property or violent. The results for the crime mobility polygons for one offender and two victims (mobility quadrilaterals) are shown in Table 5. In the context of Coquitlam many of the crime classifications no longer have enough observations to make meaningful inferencesdhomicide is no longer present. However, aggravated assault, assault, sexual assault and armed robbery all have more than ten observations. The median crime mobility areas for these four crime classifications have all increased substantially, particularly sexual assault. The median crime mobility areas have doubled for aggravated assault, tripled for assault, and increased five- and six-fold for sexual assault and armed robbery, respectively. However, such increases are not unexpected. As shown in Fig. 4, if two victims live close to one another the area can easily double. In the case of a mobility triangle, area A represents the crime mobility area, but area A plus area B if the victims live in close proximity. Turning to the results for Prince George, the changes are much different. To begin with, only four crime classifications (homicide, other burglary, theft from motor vehicle, and theft of motor vehicle) have fewer than ten observations. More importantly, there is very little change for most of the crime classifications with regard to the median crime mobility areas. Aggravated assault, assault, homicide, sexual assault, other burglary, and residential burglary all have very little change when a second victim is present. The median crime mobility areas for theft from motor vehicle and theft of motor vehicle are one-half and one-third, respectively, of the values in Table 4, but the number of observations in both cases are now less than ten so any inference here must be made with caution. However, notable increases are present for armed robbery, robbery, and theft. Regardless, these increases are at magnitudes that arise in situations similar to that shown in Fig. 4. And with the small number of property crime classification results, little may be said regarding the median crime mobility area being smaller or greater for violent crime classifications. The results for Surrey are similar to those for Prince George in the sense that only a few crime classifications have fewer than ten observations and the increases in the median crime mobility areas are moderate for those crime classifications with more than ten observations. Similar to Prince George, little may be said regarding the median crime mobility areas for violent versus property crime classifications. Three of the six property crime classifications have lower median crime mobility areas than all of the violent crime classifications, but the median crime mobility areas of the other three property crime classifications are substantially greater. Consequently, there is not a discernable pattern to be discussed.
Table 7 Median crime mobility area, by crime type, two offenders and two victims. Crime classification
Aggravated assault Assault Homicide Sexual assault Armed robbery Robbery Commercial burglary Other burglary Residential burglary Theft Theft from motor vehicle Theft of motor vehicle
Coquitlam
Prince George
Surrey
Median
n
Median
n
Median
n
11.1 7.8
5 6
12.9 6.6
3 3
87.7 6.3
6 1
2.8 2.2 0.1 1.1 6.4 11.1 20.2 1.6 5.1 2.0 4.3 8.0
7 9 1 2 6 2 2 1 11 4 5 5
5.2 7.7 16.8 1.5 13.4 4.9 5.6 13.5 0.7 8.3 98.7 19.0
32 28 3 7 22 3 1 5 16 8 4 14 Fig. 4. Area calculations when increasing offenders.
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The results for co-offending (two offenders and one victim) are shown in Table 6. Once again, Coquitlam suffers from many crime classifications with few observations. However, the increases in the median crime mobility areas are most often rather modest. Only armed robbery (with eleven observations) has a substantial increase in its median crime mobility area. This result implies that co-offenders in Coquitlam tend to reside close to one another. The median crime mobility areas for Prince George exhibit similar changes to those in Coquitlam when a second offender is included in the analysis: moderate increases in the median crime mobility areas. In fact, in the cases of theft, theft from motor vehicle, and theft of motor vehicle the median crime mobility area has decreased. And similar to the results for one offender and two victims, little may be said regarding the relative values for median crime mobility areas for violent and property crime classifications. Turning to the results for Surrey, results similar to those discussed above are present as well: moderate increases in the median crime mobility areas for those crime classifications with more than ten observations. Only theft from motor vehicle has a large increase (six-fold) in the median crime mobility area. The last set of results represents co-offending and covictimization (Table 7), two offenders and two victims: pentagons. For all three municipalities the number of observations for most crime classifications is too small to identify any patterns in the changes. Coquitlam has fewer than seven observations in all cases and will not be discussed, Prince George has fewer than ten observations for all crime classifications except for residential burglary that has eleven observations, but Surrey does have more than ten observations for five crime classifications. Aggravated assault and assault have notable increases in their median crime mobility areas, approximately doubling, whereas the median crime mobility area of residential burglary decreased. Perhaps most worthy are the significant increases in the median crime mobility areas for armed robbery and theft of motor vehicle.
Discussion and conclusions In this paper we contribute to the mobility triangle literature by incorporating co-offending and co-victimization into the analysis.14 Because of this contribution, we are dealing not only with mobility triangles, but mobility quadrilaterals and pentagonsdmobility polygons. We also contribute to this literature by introducing the crime mobility area rather than relying on the traditional categories used to describe mobility triangles. Our methodology provides more details into the patterns of mobility polygons. With this greater detail, geographical comparisons between crime classifications and within crime classifications may be made for different offending and victimization patterns. Lastly, we consider the geography of this geometric dimension of crime by comparing the results of three different municipalities, measuring geodiversity. In general, we find that median crime mobility areas are small. There are some large increases as more offenders and victims are added to the analysis, but most often these large increases coincide with crime classifications that have few observations. Though we are not always able to make this claim, the median crime mobility areas for violent crime classifications are smaller than the median crime mobility areas for property crime classificationsdthis phenomenon is definitely present for the mobility triangles, Table 4.
14 Because of our data limitations we must provide caveats when the number of observations is lowdsometimes not reporting results. However, we are confident it is critical to report these results because such an analysis has not been undertaken before. Future research that has more observations may be able to confirm or deny these findings.
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Perhaps most interesting is the geographic component of the analysis. In the cases of both violent and property crime classifications, the median crime mobility areas in Coquitlam are generally greater than those in Prince George and Surrey. This is particularly interesting because Coquitlam is approximately one-half the size of both Prince George and Surrey. Consequently, one would expect that offenders would not need to travel as far in Coquitlam to find targets. However, it is the location of the crime that we use to make municipal assignments so it is possible that offenders and victims from other municipalities travel to Coquitlam. Inspection of maps in neighboring municipalities (Pitt Meadows and Maple Ridge) shows that this is the case. Despite there being many targets in these two municipalities, the target-rich area of Coquitlam draws offenders across municipal boundaries. Such a phenomenon may be occurring in Prince George and Surrey as well, but probably less frequently in Prince George. This is also consistent with Prince George having the lowest median crime mobility areas overall. Another explanation for the differences in the median crime mobility areas is the nature of the built environments in these different municipalities, another example of geodiversity. Though Prince George and Surrey are approximately the same official size, Prince George has far more area that is relatively uninhabited space: the core of Prince George is only about ten percent of the total area for the municipality. Surrey also has some uninhabited spaces (agricultural land, for example), but much of this municipality is occupieddSurrey has almost seven times the population of Prince George in the same official area. Therefore, the smaller median crime mobility areas in Prince George are likely a result of two things: its small core area and that it only has one primary commercial area. Generally speaking, Surrey has smaller median crime mobility areas than Coquitlam and Coquitlam is smaller, but Surrey has a denser population. As such, target density in Surrey is greater than in Coquitlam lessening the need for longer journeys to crime and, therefore, larger crime mobility areas. The results of this analysis contribute to the applied geographical literature as well, particularly geographic profiling (Rossmo, 2000). From the perspective of geographic profiling, these results are instructive when considering a “spatial profile”. A spatial profile may be considered as how far an offender travels to commit the crime; this information may be used to prioritize a list of potential suspects similar to geographic profiling proper. For example, in cases when there are multiple offenders, some crime classifications exhibit greater crime mobility polygon areas than other crime classifications. There are a number of future research directions for this type of analysis. The first is to replicate the methodology in other municipalities to find if the results presented here are generalizable, in terms of different crime classifications, numbers of offenders and numbers of victims. It would be most useful for any such replications to also analyze multiple municipalities to enable comparisons of different sized and differently built municipalities. Second, from a methodological perspective, the impact of areal bias needs to be investigated. As noted above, using a minimum bounding area necessarily imposes an upward bias in the area calculations. It is important to obtain information regarding how much areal bias is present because increasing the number of offenders and victims tends to increase the median crime mobility area. This area does not increase substantially in most cases when another individual is added to the calculation, but this increase may be partially due to the areal bias. Third, a more detailed analysis of the mobility polygons is in order. In particular, it would be interesting to know if co-offenders are recruited in close proximity from each other and if the age of the offenders has an impact on the median crime mobility area. And last, future research should investigate this phenomena within the context of theory. Though our analysis is motivated by theory, our
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