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Geographic profiling was originally developed as a statistical tool in criminology, where it uses the spatial locations of linked crimes (e.g., murder, rape, and arson) to identify areas that are most likely to include the offender’s residence. In criminology, geographic profiling uses these crime locations to create a probability surface that is overlaid on the study area to produce a geoprofile. Geoprofiles do not provide an exact location for the criminal’s home, but allow the police to prioritize investigations by systematically checking suspects associated with locations in descending order of the height of these locations on the geoprofile, facilitating an optimal search process based on decreasing probability density. The technique has been extremely successful in this field, and it is now widely used by police forces and investigative agencies around the world. Recently, the same techniques have begun to be applied to biological data, initially in the field of animal foraging and hunting behavior, but also in epidemiology and invasive species biology, where geographic profiling can be used to locate the sources of infectious disease or of invasive plants and animals as a prelude to targeted control efforts. As the technique has now been shown to be useful in such divergent scenarios from those for which it was originally developed, it raises the intriguing possibility that geographic profiling could be a useful general tool for studying spatial patterns in biological data. Here, we review the work in this area, and suggest further avenues for future research. We go on to consider ways in which this highly successful transfer of ideas from criminology to biology might also work in the opposite direction.
Geographic profiling is well established in criminology, with a proven track record of success. It has recently begun to be applied to biological data. In this research paper, we will first of all outline the basic ideas underlying geographic profiling (section “Introduction”), before reviewing the existing studies of biological data using geographic profiling, and considering how these differ from the model’s application in criminology (section “From Criminology to Biology: Applications of Geographic Profiling to Biology”). Having discussed how ideas from geographic profiling have fed into biology, we will suggest ways in which ideas from biology might in turn feed-back into geographic profiling in general, and criminology in particular (section “From Biology to Criminology: Future Developments”).
Geographic profiling is a statistical technique used in criminology to prioritize large lists of suspects in cases of serial crime, such as murder, rape, or arson. The need for such a technique arises because criminal investigations often generate too many, rather than too few, suspects; for example, the enquiry into the Yorkshire Ripper murders in the UK between 1975 and 1980 generated 268,000 names (Doney 1990). Obviously, it will frequently be impractical to follow up all but a handful of these names. Clearly, any technique that allows police forces to prioritize such lists of suspects is likely to be of enormous value.
In essence, the model is simple and depends on two concepts: (1) distance decay and (2) the buffer zone (Rossmo 1999; Le Comber et al. 2006). The first concept relies on the fact that, because traveling incurs costs in time, effort, and/or money, most crimes occur relatively close to an “anchor point” (usually the criminal’s home or workplace) (for instance, 70 % of arsons occur within two miles of the arsonist’s home (Sapp et al. 1994)). However, the anchor point is also typically surrounded by an area (the buffer zone) in which offenses are relatively rare. This buffer zone arises partly because of increases in detection risk related to reduced anonymity within the criminal’s local neighborhood, and partly because the number of criminal opportunities increases geometrically with distance traveled from home. The size of the buffer zone is specific to an individual criminal and location, since it will be affected by the criminal’s willingness and ability to travel, and also the underlying distribution of opportunities for crime (the “target backcloth” (Rossmo 1999)).
Geographic profiling uses the opposing effects of distance decay and the buffer zone to calculate the probability of offender residence for each location within the study area, producing a three-dimensional probability surface (called a jeopardy surface). Locations in which it is more likely that the offender might live are indicated by higher points on the jeopardy surface. Overlaying the 3-D jeopardy surface on to a search area map produces a geoprofile. Hence, geoprofiles do not provide an exact location for the criminal’s home, but they allow the police to prioritize search locations by starting with the highest point on the jeopardy surface. Systematically checking locations in descending order of their height on the geoprofile probability surface describes an optimal search process based on decreasing probability density. Therefore, the better the geographic profiling model performs, the shorter the search before the real location of the offender’s home is found (Rossmo 1999).
Because geographic profiling seeks to describe an optimal search, the model’s performance can be assessed simply by asking how high up the jeopardy surface, the true anchor point lies. This measure, which is expressed in terms of the hit score percentage (HS%), is the proportion of the study area (in criminology, this is usually the area bounding the crimes, plus an additional 10 % of the area surrounding this, to allow offender source locations to come from outside the area of the crime sites) that must be searched before the true anchor point is found. The smaller the HS%, the more accurate is the geoprofile. A hit score of 50 % is what would be expected from a nonprioritized (i.e., random or uniform) search; thus, a hit score of 10 % describes a search which is five times more efficient than a random search (Rossmo 1999).
From Criminology To Biology: Applications Of Geographic Profiling To Biology
Although geographic profiling was originally designed to apply to crimes such as murder, rape, and arson, it has had numerous success in other areas, including burglary, counter-insurgency and piracy (see, e.g., Kucera (2005) and Rossmo and Harries (2011)). Based on its applicability to a range of problems in a variety of different fields, its application to biological data was an obvious next step. Given the similarities between criminal hunting behavior and animal behavior, it is perhaps not surprising that the first paper to apply geographic profiling in a biological context looked at animal foraging (Le Comber et al. 2006).
Geographic Profiling And Animal Foraging
Geographic profiling was introduced to biology in a 2006 paper in the Journal of Theoretical Biology (Le Comber et al. 2006). In this study, the authors used data from radio-tracking studies of two species of bat, the common and soprano pipistrelles (Pipistrellus pipistrellus and P. pygmaeus) in north-east Scotland. A previous study had identified both roost sites and foraging sites, and the authors fitted Rossmo’s criminal geographic targeting (CGT) model (Rossmo 1999) for each bat and showed that the fitted model parameters (B, f, and g) could be used to locate roost sites, using foraging sites as input, analogous to crime sites. Interestingly, the fitted values differed between the two species, despite their close genetic relatedness. This probably reflects their different foraging strategies; P. pygmaeus forages preferentially in riparian habitats (i.e., along the edges of rivers and lakes) that support higher numbers of insect taxa (Gressit and Gressit 1962; Townes 1962), while P. pipistrellus is more generalist. This specialization in P. pygmaeus is likely to mean that this species must forage over greater distances to locate sufficient prey items to satisfy its energetic demands. This was an intriguing result, suggesting that when anchor points such as nests, roosts, or dens are known, fitted CGT model parameters could provide a concise way of describing complicated foraging patterns.
The bat study was followed by a second study of animal foraging, this time in bees, but using laboratory data rather than field data (Raine et al. 2009). Bees were allowed to enter a flight arena approximately 1 m square, via a central hole, and allowed to forage on artificial flowers containing a sucrose solution. Again, the CGT algorithm successfully located this entrance. Fitting model parameters in the same way as in the bat study also showed that when the artificial flowers were presented at higher density, the size of the buffer zone decreased. This was of interest because, in criminology, little may be known about the target backcloth, since law enforcement agencies will have information on crimes committed, but not always on potential crimes that were not.
Another interesting extension of this study involved using “virtual” bees, in a similar experimental design to the real bees, using a variety of plausible foraging algorithms (including spiral searches, nearest-neighbor methods, and a variety of others). Just as the fitted model parameters could be used to differentiate between the foraging patterns of the two bat species, they could be used here to distinguish between different foraging rules. Crucially, for biologists, these could also be compared to the behavior of the real bees, allowing the authors to rule out some of the suggested foraging algorithms as inconsistent with the patterns observed in the real bees.
At about the same time, Martin et al. (2009) used geographic profiling to study great white shark predation on seals off the coast of South Africa. Again, much of the interest of this paper derived from aspects tangential to the main purpose of geographic profiling, that is, identifying sources for point pattern data. In this case, the study identified a well-defined search base or anchor point 100 m seaward of the seal’s primary island entry-exit point. This is not where the chances of intercepting seals are greatest, and the authors suggested that it represented a balance between prey detection, capture rates, and competition. In addition, the different geoprofiles observed for sharks of different ages showed that smaller sharks exhibited more dispersed search patterns and had lower success rates than larger sharks, suggesting either that hunting success improved with experience or that larger sharks excluded smaller sharks from the most profitable areas.
Geographic Profiling And Epidemiology
As noted above, animal foraging behavior has much in common with criminal hunting behavior. The extension of geographic profiling to epidemiological datasets, however, involves several important differences, notably the increased importance of multiple sources, and the possibility, for some diseases, of secondary sources. These issues are discussed in section “Differences Between Biology and Criminology.”
The application of geographic profiling to epidemiological data fills a surprising gap in epidemiology. As Buscema et al. (2009) pointed out, classical epidemiology tends to model the spread of infectious epidemic diseases, and few attempts have been made to identify the origin of the epidemic spread. This is surprising because, as Le Comber et al. (2011) noted, in many diseases, infection sources can be highly clustered: For example, malaria parasite transmission is strongly dependent on the location of vector breeding sites, and most transmission only occurs within short distances of these sites; in Africa, these distances are typically between a few hundred meters and a kilometer, and rarely more than 2–3 km (Carter et al. 2000). Because of this clustering, untargeted control efforts are highly inefficient. Although source reduction of mosquito larval habitats can dramatically mitigate malaria transmission (Yohannes et al. 2005; Gu et al. 2006; Walker and Lynch 2007; Gu and Novak 2009), the transient nature and diversity of potential vector breeding sites makes the identification and control of breeding sites difficult (Carter et al. 2000). As a result, evidence-based targeting of interventions is more efficient, environmentally friendly, and cost-effective than untargeted intervention. This, of course, is exactly why the problem geographic profiling was designed to solve.
The first attempt to apply geographic profiling to epidemiological data was by Buscema et al. (2009). This study examined Chikingunya fever, foot and mouth disease, and cholera, but concluded that geographic profiling was less efficient than the authors’ preferred artificial intelligence method, the H-PST (Hidden-Pick and Squash Tracking) Algorithm. However, this study mistakenly used the distance between the peak of the geoprofile and the correct source as a measure of model performance. As Rossmo (1999) was careful to point out, geographic profiling does not attempt to provide a point estimate for the anchor point (here, the infection source), as methods such as spatial mean, spatial median, and center of minimum distance seek to do; rather, it describes an optimal search strategy. Because of the complexity of jeopardy surfaces, the distance from the peak of the geoprofile to the anchor point is irrelevant; what matters is what percentage of points within the study area have higher Z values than the anchor point. In fact, when there are multiple sources of infection (e.g., the malaria cases examined by Le Comber et al. (2011)) this is an important advantage of geographic profiling over the H-PST algorithm, since methods that provide point estimates of sources will typically perform poorly when there is more than one source. When Le Comber et al. (2011) revisited one of the case studies in the Buscema paper (John Snow’s data on the 1854 London cholera outbreak (Snow and Frost 1936)), geographic profiling performed extremely well.
Geographic Profiling And Invasive Species Biology
Another promising area for the application of geographic profiling to biological research concerns the spread of invasive species, an area with more in common with epidemiology (e.g., multiple and secondary sources) than with animal foraging. The issue is not trivial; invasive species are now viewed as the second most important driver of world biodiversity loss behind habitat destruction and have been identified as a significant component of global change (Vitousek et al. 1996; Wilcove et al. 1998). The cost of invasive species can run from millions to billions of dollars per occurrence (Mooney and Baker 1986; Pimentel et al. 2001), and invasive species have been shown to affect native species through predation and competition, modify ecosystem functions, alter the abiotic environment, and spread pathogens (Strayer et al. 2006; Ricciardi 2007). In addition, the problem is likely to get worse as climate change and anthropogenic influences lead to increased range shifts (Hulme 2007). For these reasons, prevention and control of invasive species has been identified as a priority for conservation organizations and government wildlife and agriculture ministries globally (Mooney and Baker 1986; Hulme 2006).
Although only one study has looked at invasive species and geographic profiling, the results are promising. Stevenson et al. (2012) analyzed historical data from the Biological Records Centre (BRC: http://www.brc.ac.uk/) for 53 invasive species in Great Britain, ranging from marine invertebrates to woody trees, and from a wide variety of habitats (including littoral habitats, woodland and man-made habitats). For 52 out of these 53 datasets, geographic profiling outperformed spatial mean, spatial median, and center of minimum distance as a search strategy. The study also compared fitted parameter values between different species, groups, and habitat types, with a view to identify general values that might be used for novel invasions where data are lacking, with some success.
Differences Between Biology And Criminology
The first applications of geographic profiling to biology involved fairly straightforward mapping of the basic concepts from criminology: In these studies, animal foraging sites were used to identify animal roosts (or other home locations) in the same way that crime sites are used to identify probable areas of offender residence in criminology. However, later extensions, and most notably studies of invasive species biology and epidemiology, differ in a number of areas.
In criminology, the application of geographic profiling will usually (or at least often) deal with the crimes of single individual with a single anchor point, often (hopefully!) over a short period of time. In contrast, biological data can involve multiple organisms (and hence multiple anchor points), secondary anchor points, and extended time periods.
Multiple Anchor Points
In criminology, although jeopardy surfaces may have several peaks, relating perhaps to the criminal’s home, work place, or a relative’s home (or, in the case of the Hillside Strangler, the two homes of the two cousins who committed the crimes together; Rossmo (1999)), it is usually assumed that the crimes are linked; that is, they are carried out by a single individual (some applications of geographic profiling to terrorist activities may be an exception). In invasive species biology or epidemiology, it is usually impossible, or at least impractical (e.g., perhaps requiring expensive genetic testing to identify particular strains of virus, or genotypes of individual plants or animals), to link events to individual sources. For example, the malaria cases in Le Comber et al. (2011) were treated as a single group of “crimes,” although it is possible that six or more An. sergentii breeding sites were involved. In this case, data was simply pooled and the heights of each potential source on the geoprofile examined separately; Stevenson et al. (2012) took a similar approach with invasive species. At this point, no studies have explicitly examined the effect of multiple sources on geographic profiling model performance, although the data in Le Comber et al. (2011) and Stevenson et al. (2012), along with some simulation data (unpublished), suggest that geographic profiling’s performance relative to simple measures of spatial center tendency (spatial mean, spatial median, center of minimum distance) will increase as the number of sources increases.
Secondary Anchor Points
Murder victims do not go out and commit murders; victims of arson do not go out and burn down other buildings. Similarly, in the context of animal foraging, seals predated upon by great white sharks do not then predate upon other seals. However, the sites of new biological invasions can go on to act as sources for further waves of invasion; similarly, in many disease systems, infected individuals will go on to affect other individuals. These secondary sources/anchor points may dramatically alter the spatial patterns observed.
Extended Time Periods
In criminal investigations, the persistence of a series of linked crimes over a number of years obviously represents a failure of law enforcement; cases such as Jeffrey Dahmer (1978–1991) or the Yorkshire Ripper (1975–1980) (Rossmo 1999) are, hopefully, an exception. In biology, this need not be the case, and longer-term datasets may in fact be highly desirable. Ecological datasets in particular can span decades or even centuries (Stevenson et al. 2012), and can involve multiple “outbreaks,” while criminal cases typically span shorter periods of time. In this sense, biological data may offer a distinct advantage over criminological data. Invasions and disease outbreaks have long histories and repeated outbreaks, so assuming that repeated invasions follow similar histories, previous outbreaks (perhaps with known sources) can be used to validate the geographic profiling model. Future spread can then be predicted using parameters established from the organism’s own invasion history.
From Biology To Criminology: Future Developments
Clearly, geographic profiling has already made important and interesting contributions to biology, in fields including animal foraging, invasive species biology, and epidemiology. In this section, we will consider how insights from biology might feedback into geographic profiling theory, and criminology generally. Broadly speaking, these fall into three classes: (1) mathematical developments; (2) spatial methods; and (3) experimental methods.
The underlying mathematics of geographic profiling has recently attracted attention, notably from O’Leary (2009, 2010). Here, we will briefly discuss four areas of interest. These are (1) incorporating a Bayesian framework; (2) fitting model parameters; (3) incorporating explicit models of behavior; and (4) considering different mathematical distributions in addition to the exponential functions used in the Rossmo model (Rossmo 1999).
Recent papers on the mathematics of geographic profiling, notably those of O’Leary (2009, 2010), highlight two different approaches to the subject. Because of its origins in criminology, one of these approaches is highly practical, concentrating on the model’s use as a tool in investigations of serial crimes such as murder, rape, and arson. Most applications of the model within biology to date have taken a similar approach, with the main results of the various studies (Le Comber et al. 2006; Martin et al. 2009; Raine et al. 2009) being to demonstrate the applicability of the model to different types of data. O’Leary’s papers take a different tack, considering the underlying mathematics themselves, with less attention paid to the model’s practical utility. It might be argued that these are two parallel avenues of research that are unlikely to intersect. However, our view is that it might be possible to bring these two strands together. The acid test, of course, will be whether different mathematical approaches (e.g., embedding the model within a Bayesian framework, or considering other underlying spatial distributions such as the Cauchy distribution (see below)) can improve the model’s performance.
Fitting Model Parameters
Rossmo’s (2009) model uses three parameters, B, f, and g. B is the width of the buffer zone, while f and g together determine first the increase in the probability of a crime occurring moving outward from the anchor point toward the edge of the buffer zone, and second the decrease moving further beyond this. In criminology, the width of the buffer zone is typically set at half the mean nearest-neighbor distance, with f and g set at 1.2. To date, studies in biology have either adopted this method (Martin et al. 2009; Le Comber et al. 2011), or attempted to fit spatial data to known anchor points (Le Comber et al. 2006, 2011; Raine et al. 2009). This may matter because multiple sources (see above) could lead to different patterns of “crime sites,” depending on their number and proximity to each other; there may also be some use in using fitted model parameters as descriptors of more complex spatial patterns, as in Raine et al. (2009). Thus, the issue of precisely how model parameters are fitted may be come of interest. Although to date published studies have used only simple methods (see, for instance, (Le Comber et al. 2006; Raine et al. 2009)), an obvious approach is to use Markov Chain Monte Carlo (MCMC) methods to explore parameter space. In our view, this is likely to be an interesting area of development, although care will have to be taken to avoid well-known problems of over-fitting (Hawkins 2004).
Incorporating Explicit Models Of Behavior
Current geographic profiling models are generic. They express simple geometric patterns such as exponential or normal decay. The Rossmo model incorporates B, an explicit parameter for the buffer zone, but f and g remain as exponential decay functions. Rather than fitting a generic statistical model, the aim of mathematical modeling is to find true relationships that underlie the data. Ideally we should have models that have parameters that explicating relate to some aspect of predator behavior, invasive species dispersal, or epidemic spread.
Models of offender behavior will obviously depend on the precise spatial distribution of crime sites. Canter and Hammond (Canter 2006) examined logarithmic, exponential, and quadratic functions, while the Rossmo model (Rossmo 1999) uses an exponential function, as does CrimeStat (Levine 2009). O’Leary (2010) introduced the idea of alpha as a single parameter from a normal distribution, suggesting that it could be used as a predictive parameter to represent average offense distance; the optimized parameter B in (Stevenson et al., 2012) fulfills similar criteria if f and g are fixed in the Rossmo model. In a later study, O’Leary (2010) compared single-and two parameter normal, and single-and two-parameter exponential functions, concluding that there was no difference between normal and exponential in the single-parameter models in Baltimore county burglaries; neither of the two-parameter models performed as well as the single-parameter models.
The distribution models appropriate for offender behavior are likely to be substantially different to models appropriate for disease and animal dispersal. Invasive species dispersal is likely to be strongly nonnormal; dispersal includes both short local dispersers and long escalated movements: for example, Levy flight (see, e.g., (Viswanathan et al. 2000; Viswanathan and Bartumeus 2002; Bartumeus 2009)). This type of dispersal is described by a Cauchy distribution (Viswanathan et al. 2000). The Cauchy distribution is related to normal distributions, in that dividing one normal distribution centered on zero by another centered on zero will yield a Cauchy distribution. In fact, the Cauchy distribution can be made to resemble a smoother version of the Rossmo distribution, but avoiding the latter’s sharp peak at the radius of the buffer zone. In addition, Cauchy distributions also allow the inclusion of a width or thickness parameter, gamma, which describes the “fatness” of the distribution’s tail, relating to the amount of longer dispersal events. A Cauchy distribution could also be used in criminology, and would relate to the occurrence of two different types of jumps already documented in the criminology literature, prowlers, and commuters (Rossmo 1999).
Running Models Forward In Time
Finally, one intriguing possibility following O’Leary’s work (2009, 2010) is that of running models forward in time – rather pleasingly, this would link current models of spatial epidemiology such as risk mapping (Leung et al. 2002) with geographic profiling, which is essentially retrospective in nature. O’Leary suggests using integration to generate a function that can then be used to predict future spread. The possibility of producing risk maps for offenders to predict possible sites of future burglaries or even more serious crimes is a real possibility, even when based on a small number of data points, in contrast to current hot spot mapping.
In the same way that mathematical studies are beginning to feed-back into geographic profiling, it seems likely that techniques from spatial epidemiology may offer interesting avenues for research; in fact, as noted above, O’Leary’s proposed approach (2009, 2010) may go some way toward allowing techniques from spatial epidemiology and spatial ecology to feed-back into geo graphic profiling.
One fruitful area is likely to be ecological niche mapping. Ecological niche mapping is used in invasion biology and macroecology to predict species spread based on associated habitat types (see, e.g., Kaschner et al. (2006)). Species found in particular ranges are associated with particular ecological factors; these can then be mapped to new ranges to predict spread based on these niche factors. We suggest that this type of modeling can be used to generate priors or hyperpriors for a Bayesian model of geographic profiling. True prediction requires knowledge of not only where the species is now and where it is dispersing to, but also what habitat is suitable for it to live in. Our prior estimation of where a species is capable of dispersing to will inform the geoprofile to produce a surface that includes both types of information. Obviously, this approach could also be applied to criminology, using information about neighborhood quality, street lighting, open spaces, frequency of police patrols, and so on.
One advantage the biologist has over the criminologist is that, in biology, experiments are far easier, and certainly less ethically problematic. For example, Raine et al. (2009) were able to manipulate the target backcloth in a study of bee foraging behavior that would simply not be possible in the context of crime. Thus, biology might be better placed to explicitly test some of the underlying assumptions and methodologies of geographic profiling.
A related point, alluded to above, is that in biology datasets, long-term datasets are more abundant, and replication is more exact: For example, in invasive species biology, it is possible, and even common, to have (1) repeated invasions of the same geographical area by the same species; (2) repeated invasions of different geographical areas by the same species; (3) repeated invasions of the same geographical area by different species. A rigorous comparison of these different cases may help to disentangle those aspects of any observed spatial patterns that are due to the invader’s behavior and/or biology, and the habitat’s own attributes. The analogous exercise – understanding what aspects of spatial patterns of crimes are due to the criminal’s behavior, and what aspects are due to the peculiarities of the target backcloth – is much more difficult.
Although the application of geographic profiling to biological datasets is still relatively new, the early indications are that the method’s considerable success in the field of criminology may be replicated in areas as seemingly diverse as animal foraging behavior, epidemiology, and invasive species biology. This is encouraging because, despite the obvious similarities between criminal hunting behavior and animal foraging behavior, there are several key differences that can arise in biology, notably the importance of multiple and secondary anchor points. To date, most studies using geographic profiling in biology have concentrated on demonstrating the method’s utility. In contrast, much of the mathematical research has pursued a parallel line of enquiry, ignoring the method’s application. Future work may bring these two seemingly distinct approaches closer together, and we suggest that, just as methods from criminology have proved of use in biology, some techniques from biology – for example, niche modeling, Levy flight, and optimization methods – may prove useful in criminology.
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