Geography of crime: population spillover problem in crime mapping

The problem

Consider the following scenario:

You live in a small low population suburb.  A complex of apartments is built in the neighbouring area.  The population density in the complex is very high, unlike the area in which you live.  Over time, you observe the frequency of petty crime increase in your neighbourhood.  You and your neighbours reason that this is mostly due to the residents of the new apartment complex.  Your complaints about crime germinate into hostile feelings to your apartment dwelling neighbours, and you start to form beliefs about them as people.  More specifically, since a disproportionate number of them also have a different cultural and ethnic background than people living in your neighbourhood, you start to believe that people with this background are more likely to commit crime.

In this scenario, let us assume that the following statements are objectively true:

  1. The number of crimes in the general area has gone up because of the people in the neighbouring apartment complex
  2. Risk of being a victim of crime has gone up in your neighbourhood because of the people in the neighbouring apartment complex

In spite of the above statements, it does not also follow that people in the apartment complex are more likely to commit crime than the people living in the low housing density neighbourhood nearby, or indeed, that there is any difference in anyone’s predilection to commit crime in the area generally.  If the reason for this isn’t obvious, I’ll elaborate on why this is the case below.  However, for the moment, it’s easy to see how a person could connect an increase in frequency of crimes with the predilection for committing crime based on a fairly reasonable and natural assessment of the facts.  The problem is that the frequency and rate of crime do not tell us about the people who commit crime; a geographical cluster of high crime rate can occur even if there is no geographic pattern in the likelihood that people will commit crime.

What is going on?

If all people committed crime in the neighbourhoods in which they lived, and crime rates were calculated only in neighbourhoods, then a neighbourhood’s crime rate could be a pretty good indicator of crime risk as well as the disposition to commit crime.  However, people do not restrict themselves to neighbourhood boundaries; offenders go where the opportunities present themselves, and for some types of crime, that could mean travelling some distance away from home.  There is empirical and theoretical research on how offenders travel to crime which varies by crime type, age and other factors.  For types of crime that are committed outside the home, where crime happens may tell us very little about where the offender is from.

The effect here is a ‘spillover’ in crime from higher population areas to lower population areas that can cause the apparent risk of crime in low population areas to be high even if the disposition to commit crime and the suitable targets for committing crime are geographically constant and non varying (‘spatially homogeneous’).  There has been considerable research [1,2,3,4]  into the spillover effect of public housing on crime in the US (most of which has found little relationship between public housing and crime in neighbouring areas) but I am not sure if anyone has analysed this population spillover effect specifically.

This diagram illustrates how this spillover can occur, and the effect on crime rate.

The two black squares are neighbourhoods–one small population (100 people) one large population (1000 people).  The curved black lines are the ‘trips’ that an offender takes from place of residence to where they commit the criminal offence.  The green circles are the residences, and the red squares are the offence locations.  In this example, the left hand square (a low population neighbourhood) has the same proportion of criminals as the right hand square (high population neighbourhood).  But because of the spillover effect, the crime rate is much higher in the low population area.

Why does this matter?

One of the consequences of this spillover is that it can lead to an inferential fallacy; the fact that crime rates are higher in the low population neighbourhood as a result of the high population neighbourhood could lead to incorrect generalisation about the individuals in the high population neighbourhood.  This spillover in crime could happen even if the people in the high population neighbourhood were less likely than average to commit crimes.  So at the very least, this should serve as a reminder that our intuitions–even when based on data–need to be carefully scrutinised, since we can be fairly easily mislead.

This spillover effect can also influence how we understand and attempt to explain patterns of crime.  I used data from the City of Edmonton to estimate the impact of the spillover on the risk of assault.  The interesting result is that neighbouring populations do seem to impact the risk of assault; the model I used (using 2016 crime and population data) suggests that for every 10,000 more people living in the regions surrounding your neighbourhood, there is between a 1.20 and 2.24 increased risk of assault.  To put this into perspective, the average person’s baseline annual risk of assault is 7 per 1000 (or 0.7% chance of being assaulted per year).  If you lived in a neighbourhood surrounded by a population of 20,000 people, then your risk of being assaulted is between 1% and 3.5% per year.

If you’d like to see how I did the analysis, follow this link to GitHub.


This population spillover effect is consequential for two reasons.  First, it may influence how people perceive their neighbours, but in ways that are almost certainly not helpful to social cohesion and sense of community.  Living next to an apartment building may slightly increase your risk of being a victim of some crimes, but this observation says nothing specifically about apartment dwellers’ dispositions to commit crime.  It could be that apartment dwellers as individuals are even slightly less likely to commit crime, and yet, could still be (as a geographical group) responsible for an increase in the rate of crime in nearby communities.  Come to think of it, this is an interesting example of the ecological fallacy!

My preliminary analysis also suggests that incorporating the effect of this spillover into our analyses could improve predictions of crime, although this is likely to vary by crime type.

Finally, the concept may be useful for indirectly estimating the range of criminal activity; it is possible that the presence/ absence of crime spillover may indicate how far people may travel to commit crime.  If there is no spillover effect, then crime may occur closer to home.  If the spillover effect is strong, then it could suggest that offenders travel to commit crime.  I modelled the spillover effect for assaults as well as thefts from inside vehicles, and the latter showed no spillover effect.  This could tell us something about the travel behaviour of offenders for these two types of crimes.