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Spatial dynamics and crime

Andresen, M.A. (2015). Spatial dynamics and crime. In J.D. Wright (Ed.), International encyclopedia of social and behavioral sciences (2nd ed.), Volume 23 (pp. 142 – 147). Oxford, UK: Elsevier.

Published onJan 01, 2015
Spatial dynamics and crime


Crime and its spatial dynamics have a long history dating back to the early 1800s in France. In this entry I review four sub-fields of research within spatial criminology that explicitly consider crime and its spatial dynamics: spatially-referenced crime rates, location quotients, geographic profiling, and crime and place. The latest research from these sub-fields are reviewed with some discussion of their future directions in understanding spatial dynamics and crime.


Ambient population; crime and place; crime measurement; crime rates; environmental criminology; geographic profiling; geometric theory of crime; location quotient; population at risk; rational choice theory; routine activity theory; spatial criminology


Crime and its spatial dynamics have been studied for close to 200 years since the work of André-Michel Guerry (1833) and Adolphe Quetelet (1842), French and Belgian, respectively. Their work was not only important for spatial criminology, but positivist criminology, more generally. Since this time, a large body of research has emerged that investigates the spatial dynamics of crime at a variety of scales and contexts.

There are many dimensions of spatial criminology that are of particular interest at this time, including: understanding the role of police foot patrol and car patrol in reducing crime, understanding the crime drop of the 1990s, furthering the understanding of relationships such as unemployment and crime, and helping to understand the transition economies in central and eastern Europe. However, in this entry I will discuss four areas of research in spatial criminology that are explicitly concerned with the spatial dynamics of crime: spatially-referenced crime rates, the location quotient, geographic profiling, and crime and place. Though these may not be the only aspects of spatial criminology that are explicitly concerned with the spatial dynamics of crime, they have all received a lot of interest within the field and continue to offer fruitful avenues of research in the future.

Spatially-Referenced Crime Rates

In order to calculate a crime rate, there are two pieces of data that are necessary: crime data and population at risk data, shown in Equation 1. The crime count is the literally the count of criminal events in some defined geographic area. This count is most often based on official crime data, emerging from some aspect of the criminal justice system. The most well-known official crime data are the Uniform Crime Reporting (UCR) data. These data had its beginning in the United States in 1930 and now nearly all law enforcement agencies in the United States provide data to the Federal Bureau of Investigation for the UCR counts (Mosher et al., 2012; FBI, 2012). In Canada, the UCR began later, in 1962, and is gathered by the Canadian Centre for Justice Statistics—responding to the UCR survey in Canada is mandatory. In 1988, a new version of the UCR in Canada was started that added information regarding incidents, victims, and accused persons. This new UCR is referred to as UCR2; equivalent data in the United States are collected under the National Incident-Based Reporting System (NIBRS), that began in 1987 (FBI, 2012; Statistics Canada, 2012). Another form of official crime data is calls for service data from the police. Though often considered unofficial because these data are not dependent upon a criminal charge and often represent police activity, these are very useful data because a geographic location and time is most often included and the calls for service can be separated to only include the calls that the police identify as a criminal event (Sherman et al., 1989).

(Crime countPopulation at risk)Scalar\left( \frac{\text{Crime\ count}}{\text{Population\ at\ risk}} \right)*Scalar


Despite the widespread availability of these official crime data, there are a number of limitations. First, crime reporting can vary from police detachment to police detachment. This may be due to factors such as the local policing and/or population culture considering factors such as (a lack of) tolerance on particular issues. Second, not all criminal events are reported to the police. In Canada, only 31 percent of criminal victimization was reported to the police in 2009, down from 34 percent in 2004 and 37 percent in 1999 (Perreault and Brennan, 2010). This is of critical importance in spatial criminology because if the spatial patterns of crime for official data are different from the spatial patterns of crime more generally, all inference from official data may be spurious. However, very little can be done regarding these first two limitations.

A third limitation is in regard to the need for population at risk data to calculate the crime rates. In spatial criminology, that often uses the census tract as it spatial unit of analysis, the most common source of population at risk data is the census—resident population. These data are very easy to obtain and high quality, but there are two issues with using these data. First, censuses are only undertaken every 5 (Canada) or 10 years (United States and United Kingdom) in most countries. Consequently, depending on the date of the crime data obtained there may be as many as 9 years discrepancy between crime count and population at risk data. If populations are stable over long periods of time this isn’t problematic, per se, but in cities that grow this could lead to significant overestimates of crime rates if crime counts are for a later year than the resident population.

The second issue with using the resident population from a census as the population is risk is whether or not it is an accurate representation of where people are. This is a critical question in spatial criminology because if the crime rate is to represent an overall measure of risk (Boggs, 1965) the variable representing the population at risk should measure where people actually are. Recent research on this issue has shown that the ambient population can be quite different from the resident population leading to changes in inference regarding spatially-referenced crime rates (Andresen, 2006, 2013; Andresen and Jenion, 2010). In this work, data from the Oak Ridge National Laboratory was used to measure the ambient population that was defined as the number of people in a square kilometer averaged over a 24-hour period for any typical day of the year—see Andresen (2006) for details of these data.

In an investigation of the similarity between maps of resident-based and ambient-based crime rates, Andresen and Jenion (2010) found that, despite the visual appearance of similar spatial patterns and a statistically significant relationship, resident-based crime rates were very poor predictors of ambient-based crime rates. Though we do not discuss this prediction, this is what we assume when we use the resident population: it may not be the best measure, but it is representative of the true population at risk. Moreover, places that attract populations throughout the day, measured using the ambient-resident population ratio, are commercial/shopping areas and major transportation routes.

In subsequent research, Andresen (2011, 2013) showed that ambient-based crime rates exhibited significant differences to resident-based crime rates in the context of local analysis, local Moran’s I. In this work, not only did the spatial pattern of clustering change with some units of analysis changing statistical significance, but also when statistically significant in both analyses the classifications in some places would be completely different—most often, high crime areas remained high crime areas and low crime areas remained low crime areas, but the units of analysis contained within each of those classifications changed. In a spatial regression context, the similarity of results for resident- and ambient-based crime rates differed on the year of data and the size of the unit of analysis. In some cases, the results from the ambient-based crime rates outperformed the resident-based crime rate results in the context of: greater (pseudo) R2 values, more reasonable parameter estimates, more statistically significant relationships, and a better concordance with theoretical expectations. In other cases, there were very few differences with limited consequences to the results.

Overall, this research shows that there are good theoretical reasons to question the use of the commonly used resident population in spatially referenced crime rates—crime rate calculations for what may be considered a “closed system” of population movement such as a metropolitan area or a subnational unit (province or state) will most probably be unaffected. Though there may not necessarily be an impact on the results, such an impact is definitely possible and alter any interpretations. Moreover, just because there is no impact for one year of data and one spatial unit of analysis, an impact may be present for a different year of data and/or a different spatial unit of analysis even in the same city.

A Spatial Alternative Measure of Crime: Location Quotient

As should be clear from the preceding section, the calculation of crime rates has two sources of measurement issues: the criminal event counts and the population at risk. There is an alternative to the crime rate that only relies upon criminal event data, however, that has been used in spatial criminology for 20 years but is arguably under-utilized—the location quotient. The location quotient is a specifically geographic statistic that measures the over- or under-representation of some activity in a spatial unit of analysis relative to the entire study area. The location quotient is calculated as follows:

LQin=CinCtnn=1NCinn=1NCtn\text{LQ}_{\text{in}} = \frac{\frac{C_{\text{in}}}{C_{\text{tn}}}}{\frac{\sum_{n = 1}^{N}C_{\text{in}}}{\sum_{n = 1}^{N}C_{\text{tn}}}}


where Cin is the count of crime i in sub-region n, Ctn is the count of all crimes in sub-region n, and N is the total number of sub-regions. The location quotient is a ratio of the percentage of a crime type in a sub-region relative to the percentage of that crime type in the region as a whole; neighbourhoods within a city, for example. If the location quotient is equal to one, the sub-region has a proportional share of a particular crime; if the location quotient is greater than one, the sub-region has a disproportionately larger share of a particular crime; and if the location quotient is less than one, the sub-region has a disproportionately smaller share of a particular crime. For example, if a sub-region has a location quotient of 1.20, that sub-region has 20 percent more of that crime than expected given the percentage of that crime in the region as a whole. Consequently, it can be said that this sub-region “specializes” in that particular crime type.

First introduced to the criminological literature by Brantingham and Brantingham (1993) as a descriptive tool, the location quotient has been used by subsequent researchers to investigate a number of phenomena such as drug markets, theory testing, shootings, and automotive theft markets—see Andresen (2013) for a review. The utility of the location quotient is that by using an alternative measure of criminal activity we are able to identify different patterns. For example, as outlined in Andresen (2013), the spatial patterns of crime rates versus location quotients are somewhat similar for a number of crime types, but notable differences emerge when considering specialization versus risk. In the case of assault in Vancouver, Canada, a crime rate map indicates that this crime type is highly concentrated in Skid Row. However, the east side of the city (and the north east side in particular) exhibits a lot of assault specialization. What does this mean? In order to answer this question, both the crime rate and the location quotient need to be considered. First, the risk of an assault is greatest in Vancouver’s Skid Row. But, given that an individual is going to be a victim of crime, it is more likely to be an assault on the east side of the city relative to the west side of the city. Similar differences in the spatial patterns of crime emerge for other crime types as well, but not always in the same places: robbery, sexual assault, theft (more specialization of this crime type is present on the western more affluent side of the city), theft from vehicle, and theft of vehicle.

Perhaps the most interesting application of the location quotient in Andresen (2013) is burglary. The burglary crime rate map indicates that burglary has its greatest risk in and around the central business district and skid row—standard social disorganization theory predictions. However, the location quotient map shows the burglary specializes the most on the relatively affluent west side of the city where the burglary rates are the lowest. Of course, this does not mean that burglary is more frequent on the west side of the city than the crime rate map indicates, but it does mean that if an individual is going to be a victim of a crime on the west side of Vancouver it is most likely going to be a burglary. Though no research has been undertaken to support this claim, it has been hypothesized that this may explain some aspects of the fear of crime in low crime neighbourhoods: though the burglary rate may be low, everyone whom an individual speaks to about criminal victimization has referred to a burglary of their home so other residents in the neighbourhood begin to fear that crime.

Another interesting application of the location quotient was an attempt to understand the increasing crime rate from east to west in Canada that has been present, but not well understood, for at least 50 years (Andresen, 2009). For decades, the western provinces have had greater than national average crime rates across most crime types. However, no such pattern emerged for the location quotient. In the cases of violent crime, there were location quotients with moderate over-representation, but for provinces in western, central, and eastern Canada; in the case of property crime, no province had notable over-representation. In fact, the territories that are historically characterized by the greatest violent and property crime rates had the lowest location quotients for property crime—all three territories were over-represented for violent crime, however. What this means is that the risk of criminal victimization is greatest in the west, but given that an individual is going to be a victim of crime, there is no spatial pattern that emerges to state that individual will be the victim of a particular crime type. In other words, the western provinces are not disproportionately violent than other areas in Canada; they simply have more of everything.

Lastly, Andresen (2013) also presented an inferential application of the location quotient (spatial regression) that produced some interesting results. Most important, the workhorse theories used in spatial criminology (social disorganization theory and routine activity theory) performed well in the context of crime specialization. However, because the dependent variable measured specialization not risk, the interpretations of the estimated parameters are different. In some circumstances these differences are subtle such that the estimated parameters have the same sign, but how one interprets the results changes; in other contexts, the sign is opposite from the expectation in a crime rate context (a negative relationship between burglary and the unemployment rate, for example) that requires a completely different, but theoretically justified, explanation.

In all of the applications of the location quotient, the researcher is forced to ask different questions with regard to the spatial pattern of crime, sometimes subtle and sometimes not. Asking these different questions, it is argued, allows the researcher to obtain a better understanding of the phenomena of crime. As such, the use of alternative measures of crime, particularly in a spatial context, should not be used to replace crime rates, but to supplement crime rates for a deeper understanding of the spatial dynamics of crime.

Geographic Profiling

One of the more well-known applications of the theories within spatial/environmental criminology is geographic profiling. Developed by D. Kim Rossmo, geographic profiling may be thought of as understanding the spatial dynamics of serial crime. Geographic profiling is an investigative methodology that uses the locations of a connected series of criminal events to determine the most probable area of the offender’s residence—technically geographic profiling is used to identify the anchor point from which a serial offender bases his or her movements, but this is most often the residence. Because geographic profiling uses a connected series of criminal events, the most common uses of geographic profiling are serial murder, rape, arson, and robbery. However, geographic profiling may also be used for non-serial crimes that involve multiple locations. The major function of geographic profiling is to prioritize a list of potential offenders to aid in a corresponding investigation. Geographic profiling has proven to and continues to be a useful tool for the practice of investigative policing as well as the understanding of serial offenders from an academic perspective. Some of the more interesting recent geographic profiling applications have included: cellular telephone switch tower sites in kidnapping cases, the stores in which bomb components have been purchased, and an historical analysis of the locations of anti-Nazi propaganda postcards in left in the streets of Berlin, Germany in the early 1940s (Rossmo, 2014). Additionally, there have been new applications of geographic profiling that have proven to be very instructive, but for different reasons: terrorism and biology/zoology and epidemiology (Rossmo, 2012).

As stated above, standard geographic profiling uses the related locations in a series of criminal events to help identify the offender’s residence. At this time, geographic profiling has been applied to help military analysts identify the location of enemy military bases (Brown et al., 2005), but it can also be used to identify the targets of terrorist attacks. The study of terrorist activities has identified the existence of “terrorist cell sites”. These terrorist cell sites may be meeting places, rented apartments, etc. that are used as part of the planning of a terrorist attack. As it turns out, there is a strong spatial component to these terrorist cell sites. The research undertaken by Rossmo and Harries (2011) goes through how geographic profiling may be used to identify terrorist targets using these terrorist cell sites. Effectively, this use of geographic profiling is undertaken by taking the method of geographic profiling and turning it on its head. Rather than attempting to help identify the offender, geographic profiling is used to help identify the victim, whether that victim is a place or a person. As it turns out, terrorist cell sites are set up along the same principles as other offending activities. A non-terrorist offender tends to search for criminal targets in known areas, close to home but not so close as to reveal his or her identify. A set of terrorist cell sites tend to be organized close to but not too close to the target of the attack. Consequently, if the terrorist cell sites are considered the “connected series of criminal events” the geographic profile can then be interpreted as helping to identify the target of the terrorist attack rather than the home of the offender. This new application of geographic profiling has obvious benefits to counterinsurgency and counterterrorism operations as another tool for identifying potential targets of terrorist attacks based on known terrorist cell site activities as well as the most probable locations of enemy military bases. This shows the reach and power of how the understanding of the spatial dynamics of crime may be useful in other domains of research and practice.

One of the other new applications of geographic profiling is in the realm of biology and zoology. In an analysis of two species of bats in Scotland, Le Comber et al. (2006) were able to show the utility of geographic profiling in analysing the foraging patterns of the different species. Specifically, the authors were able to show that based on the use of geographic profiling the two different species of bats exhibited different patterns of foraging. Raine et al. (2009) were able to show that geographic profiling could be used to identify the likely locations for the nests of bumblebees, including the consideration of flower (target) densities. And Martin et al. (2009) were able to use geographic profiling in order to discover that the spatial patterns of shark predation were not random. The authors were able to identify the search base (anchor point) for these sharks in South Africa and understand the predatory strategies of these sharks considering factors such as prey detection, capture rates, and competition from other sharks. Perhaps most interesting, Raine et al. (2009) found that smaller (younger) sharks exhibited significantly greater areas for their prey search patterns than larger (older) sharks. This suggests that as sharks age they learn, or at least refine, their hunting strategies. And lastly, geographic profiling has been applied to epidemiological research to identify the origins of infectious diseases such as contaminated water sources for cholera and mosquito breeding grounds for malaria (Le Comber et al., 2011), and identifying the source locations for invasive species (Stevenson et al., 2012), both using the current locations of these phenomena.

Despite the general interest of the newer applications of geographic profiling, and their direct implications for the safety and security of different human populations, there is another significant implication of this more recent research. Though there are many serial criminal investigations that allow for more data to be available to refine the practice of geographic profiling, waiting for another set of serial homicides, for example, is not the most pleasant way of thinking of future data. If, and it does appear to be the case, that the predatory behaviours of other animal species are similar to ours, this new research can be used to better understand the predatory behaviour of humans. For example, if humans, similar to sharks off the South African coast, also reduce the size of their search area as they age, this information may be useful for the ranking of potential offenders in a criminal investigation; in such a situation, it may be possible to solve a serial criminal investigation sooner because of a better understanding of spatial predatory behaviour, more generally.

Crime and Place

As mentioned above, spatial criminology as we know it today began almost 200 years ago with the work in France by Quetelet and Guerry. One of the trajectories of spatial criminology over these many years has been the identification of spatial heterogeneity within the common spatial units of analysis of the day. For many years, the standard spatial unit of analysis within this literature has been the neighbourhood (however defined) or census tract. One of the great advantages of these units of analysis is the availability of census data for analysis such as with the crime rate and location quotient studies discussed above. Twenty-five years ago, the use of yet another smaller spatial unit of analysis began to emerge, called the micro-place—this literature is often referred to as the crime and place literature. These micro-places could be addresses, street intersections, or street segments and became used for citywide analyses because it became apparent that neighbourhoods were far from being spatially homogeneous with regard to criminal activity.

From a theoretical perspective in spatial criminology, the micro-place makes a lot of sense. Within routine activity theory (Cohen and Felson, 1979), a criminal event occurs when a motivated offender and a suitable target converge in time and space. That convergence, of course, does not occur in a neighbourhood, but at a discrete location. In the geometric theory of crime (Brantingham and Brantingham, 1981), criminal events dominantly occur at our activity nodes and the pathways between them, but there are also particular places within these activity nodes where the majority of criminal events will occur. And lastly, rational choice theory (Clarke and Cornish, 1985) posits that criminal events are the result of context specific choices. That context can vary significantly within a “neighbourhood” such that the context of micro-places will be important for criminal decision-making.

The first known research study to systematically investigate the micro-place in a citywide analysis was Sherman et al.’s (1989) analysis of predatory crime in Minneapolis. In this study, Sherman et al. (1989) found that 50 percent of calls for police service were generated from 3 percent of street segments. This profound concentration of criminal events showed that even in the neighbourhoods with the greatest criminal event levels had areas within them that were crime free. Smith et al. (2000) investigated the integration of routine activity theory and social disorganization theory considering the micro-place rather than the more tradition census tract or other census-defined unit of analysis. They found that the integration of these two theories was far more successful using the micro-place. Weisburd et al. (2004) and Groff et al. (2009) analysed the micro-place in Seattle using trajectory analysis. Similar to Sherman et al. (1989) these authors found that 50 percent of all criminal events were accounted for by approximately 5 percent of street segments, over a 14-year period. Moreover, Groff et al. (2009) found that street segments with the same trajectory tended to cluster together.

Some of the more recent research in this area shows the importance of the micro-place in understanding the spatial dynamics of crime. Weisburd et al. (2013), in the context of crime prevention, showed that over a 16-year time period I percent of street segments in Seattle represented 23 percent of all criminal activity across the city. This is an incredible concentration of criminal events in any context. In another set of analyses in Canada, Andresen and Malleson (2011) and Andresen and Linning (2012) revealed how concentrated crime can be in two Canadian cities, Vancouver and Ottawa. In Vancouver, 2001, 50 percent of the criminal events under study (listed in Table 1) were accounted for by just over 5 percent of street segments—an almost identical result compared to the work done on Seattle. This concentration varied by crime type from approximately 1 percent of street segments (sexual assault and robbery) to almost 8 percent (burglary). In Ottawa, 2006, the concentrations were even greater: 50 percent of the criminal events under study were accounted for by 1.7 percent of street segments, ranging from 0.01 percent of street segments (commercial robbery) to 1.67 percent of street segments (burglary)—the average is greater than the range because different crime types have their concentrations at different places.

The second column of Table 1 shows the percent of street segments that have any criminal events. In Vancouver, just over 60 percent of street segments have any criminal events whereas less than 10 percent of street segments in Ottawa have any criminal events. This is an incredible concentration within Ottawa that may be due to the limited number of crime types under analysis, but is noteworthy nonetheless. The last column of Table 1 shows the percentage of street segments with any criminal events that account for 50 percent of criminal events—this column uses column 2 as the base for the percentage, not all street segments in each city. These percentages represent concentrations within concentrations and indicate that there are clearly hot spots of crime within hot spots of crime and that spatial heterogeneity can even be present considering the micro-spatial unit of analysis.

Table 1. Concentration (within concentrations) of crime, Vancouver and Ottawa, Canada

Percentage of Street Segments Accounting of 50 Percent of Crime

Percent of Street Segments that Have Any Crime

Percent of Street Segments with Crime that Account for 50 percent of Crime

Ottawa, 2006

Commercial Burglary




Residential Burglary




Total Burglary (Aggregate)




Commercial Robbery




Individual Robbery




Other Robbery




Total Robbery (Aggregate)




Theft of Vehicle




Total (without double counting)




Vancouver, 2001













Sexual Assault








Theft of Vehicle




Theft from Vehicle




Total (without double counting)




*actual value: 0.000823

Future Directions

Crime and its spatial dynamics is a dynamic field of research. Spatial criminology spans a wide range of research activities ranging from the practical analysis of police activities to the more abstract nature of theoretical testing—of course, better refined theories may serve better practical applications. The four subfields of spatial criminology reviewed above are still in their infancy, requiring a lot of future research to better understand the spatial dynamics of crime.

In the context of spatially-referenced crime rates, further applications of the Oak Ridge National Laboratory data to investigate its utility in other contexts is in order. Additionally, there are other sources of data that may be used to estimate the ambient population for more appropriate estimates of the population at risk. For example, the SENSEable City Lab at MIT <> uses cellular phone call data to estimate where people are. And with mobile technologies, more generally, using applications such as Facebook and Twitter with location data there are many possibilities to get a better understanding of where the population at risk may be. Moreover, considering data obtained from mobile devices, measurements of the population at risk may be generated for different days of the year and different times of the day. Research on the alternative measures of crime should involve a broader application of the location quotient in order to continue supplementing the more traditional crime rate. Additionally, the crime rate and location quotient are not the only available measures that can be applied to the study of crime and its spatial dynamics. Future research should investigate other alternatives to be found in other disciplines such as economics or geography.

Future research in geographic profiling should continue to apply its method to counterinsurgency and counterterrorism in order to increase the safety and security of the affected populations. Additionally, the application of geographic profiling to other predatory species may continue to offer insight into the predatory behaviour of human (criminal) activity. And lastly, continued research in crime and place will only serve to provide a better understanding of the spatial dynamics of crime, particularly at the micro-spatial scale. Future research should continue to apply the micro-spatial unit of analysis to other contexts, but also use finer crime type classifications. Much of this crime and place research uses aggregate crime types, but the research that does use more detailed crime types has revealed variations along this dimension as well.

Cross References

Decision and Choice: Bounded Rationality; Decision and Choice: Heuristics for Decision and Choice; Crime: Geography of; Quantitative Methods and Crime; Routine Activities Approach and Crime;


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