The foraging perspective in criminology: A review of research literature

In order to explain how crimes are carried out, and why at a particular place and time and against a specific target, crime studies increasingly harness theory from behavioural ecology, in particular Optimal Foraging Theory (OFT). However, an overview of their main findings does not exist. Given the growing focus on OFT as a behavioural framework for structuring crime research, in this article we review the extant OFT-inspired empirical crime research. Systematic search in Google Scholar and Web of Science yielded 32 crime studies, which were grouped into four categories according to their research topic. Empirical results largely support predictions made by OFT. However, there remains much potential for future OFT applications to crime research, in particular regarding the theoretical foundation of OFT in criminology, and through the application of contemporary extensions to OFT using specific tools developed for the study of animal foraging decisions.


Introduction
Environmental criminology concerns itself with explaining where and when crimes occur. In an effort to address why crime is unevenly and non-randomly distributed in time and space (Brantingham and Brantingham, 1993), researchers use the Rational Choice Perspective (RCP; Cornish and Clarke, 1986). Within RCP, criminal behaviour is framed as purposive behaviour. Actions are selected from a range of (legal and nonlegal) alternatives, based on an evaluation of the costs and benefits associated with each alternative. RCP is abstract, however, and 'requires supplementary empirical content through specification of the relevant aims and choice situations' (Bernasco, 2009). Crime researchers therefore increasingly supplement RCP with theoretical insights from Optimal Foraging Theory (OFT; see Brantingham, 2013;Johnson, 2014;Johnson et al., 2009b).
OFT is a behavioural ecology framework that studies how organisms' behavioural patterns of gathering food are the result of evolutionary and ecological forces (Stephens and Krebs, 1986). OFT offers a range of hypotheses and mathematical models, with many a priori predictions bearing close similarity to criminal decision-making (Bernasco, 2009;Felson, 2006;Johnson, 2014;Johnson and Summers, 2015). Crime studies increasingly adopt a foraging perspective when exploring criminal activities.
However, an overview of their main theoretical underpinnings and research findings does not exist, nor has the impact of OFT on criminology been evaluated. In this article we review the published OFT-inspired crime research and identify knowledge gaps, methodological limitations and opportunities for future research. The article is structured as follows. First, we discuss and frame OFT within the criminological literature. Second, we present the literature search strategy. Third, we discuss the selected studies' main objectives and findings. Finally, we discuss our findings and their implications for future OFT-inspired criminological theory and research.

Key elements
OFT is a behavioural ecology framework that studies the behaviour of animals when searching, selecting and processing food, while accounting for the costs and risks associated with their foraging behaviour (Davies et al., 2012;Stephens and Krebs, 1986). All animals must eat in order to sustain themselves, but they differ in what food they choose to eat and how they gather that food. OFT aims to explain these differences, assuming that ecological and individual constraints, in addition to evolutionary stress, pressure animals to optimize their foraging activities over extended periods of time.
The assumption of optimization is useful, because it allows us to rely on the wellestablished methods of optimality modelling (Parker and Smith, 1990) to predict how animals should behave. Like all optimality models, OFT models are composed of three components that are brought together in an algebraic formula (Stephens and Krebs, 1986): -Decision: the problem or choice to be optimized (for example, how long to stay in a food patch).
-Currency: the quantity in which the decision outcomes are evaluated (for example, energy, which is generated by food intake and spent by efforts to search and process food).
-Constraints: the limits on the available choice options and payoffs (for example, travel speed, hours of sunlight, food processing time, presence of competitors or predators).
In sum, OFT is a framework of mathematical models and a priori hypotheses with regard to what animals forage (Charnov, 1976b;Sih and Christensen, 2001), where animals forage (Nonacs, 2019), when animals forage and for how long (Charnov, 1976a;Marshall et al., 2013), how animals forage in groups (Giraldeau and Pyke, 2019;Waite and Field, 2007), and how animals move while foraging (Pyke, 2019a). Extensions of the classic models account for complications in foraging such as competition for and specialization in resources (Baird, 1991;Funk, 2019) and suboptimal behavioural strategies and irrational decision-making (Smith et al., 2016;Vasconcelos et al., 2015). Taken together, OFT offers a broad suite of behavioural rules and hypotheses, expressed in the language of mathematics, to address purposeful foraging behaviour.

Illustration: The marginal value theorem
To illustrate how, in OFT, hypotheses are derived from explicit propositions, in Table 1 we provide an example using a hypothesis known as the marginal value theorem (MVT; for a detailed description, see Charnov, 1976a). The MVT has been extensively studied and is regarded as the 'most successful empirical model in behavioural ecology' . It describes the behaviour of organisms foraging for food in a patchy environment, and predicts how long a forager will stay in a location to consume food. The rule for deciding how long a forager should stay in a location is assumed to be its long-term energy intake. By maximizing long-term energy intake, the forager maximizes its evolutionary fitness. In deriving hypotheses from the MVT, the constraints are crucial. For example, from assuming that a patch is depleted by consumption (that is, food is not replaced immediately upon consuming it) so that the rate of caloric intake drops over time, it follows that at some time it is more efficient to try to find another patch in the environment than to continue foraging at an ever-decreasing gain rate in the current patch. Other assumptions crucial for deriving the hypothesis relate to the search costs, the random nature of patch searches, and the similarity of the patches in terms of the resources they provide. Some assumptions are evidently unrealistic but are required to derive a straightforward hypothesis.

Application to criminal behaviour
OFT has been successfully used to study contemporary human behaviour, such as the way humans process digital information (Pirolli and Card, 1999) or as a model for shopping behaviour (Rajala and Hantula, 2000). The introduction of the metaphor that likens offenders' behaviour to that of foraging animals goes back to a number of • Patch-encounter rates are independent of the length (t) of stay in a patch. • Neighbourhood-encounter rates are independent of how long (t) the burglar has been committing burglaries in the same neighbourhood.
• The expected calory intake per time unit (for example, per month) is a well-defined gain function g(t) of time in the patch, with the following characteristics: • The expected value of stolen items per time unit (for example, per month) is a well-defined gain function g(t) of the time the burglar has been committing burglaries in the neighbourhood, with the following characteristics:  • All patches in the habitat are characterized by the same gain function (for example, all beech trees provide the same number of beechnuts). • All neighbourhoods in the city are characterized by the same gain function (for example, the neighbourhoods contain equal numbers of residential properties and do not differ in suitability for burglary).
Marginal value hypothesis A foraging organism will stay in a patch until the marginal gain rate in the patch has dropped to the average gain rate of the patches in its habitat. A residential burglar will continue committing burglaries in the same neighbourhood until the marginal gain rate in the neighbourhood has dropped to the average gain rate of the neighbourhoods in the city. works in criminology. Fagan and Freeman (1999) were probably the first to refer to foraging in a criminological context by comparing the switching between legal and illegal income-generating activities with the foraging decisions that animals face. 1 Later, Johnson and Bowers (2004b) compared burglars' subsequent target choices to foraging strategies, and Felson (2006) noted the similarities between aspects of criminal decision-making and questions addressed in animal ecology. Bernasco (2009) specifically outlined several established foraging models and how they can be applied to property crimes.

Method
We synthesized the extant literature by undertaking a 'systematic search and review' (Grant and Booth, 2009). This type of review combines the strengths of a comprehensive search and selection process with a more qualitative process of appraisal, synthesis, and analysis.
Studies are eligible for inclusion if they meet the following criteria: To identify relevant studies, we searched Google Scholar (GS) and Web of Science (WoS). We selected GS because this database consistently returns a larger number of publications than do traditional scientific databases, especially for the social sciences (Martín-Martín et al., 2018). To control for the lack of quality control and clear indexing guidelines, we combined it with a controlled database, in particular WoS (Halevi et al., 2017). For WoS, searches were conducted on 11 June 2019 using the following keywords: forag* AND (crim* OR delinq* OR offen*). A total of 189 hits were obtained this way. The use of Boolean operators is inconsistent for GS (Halevi et al., 2017). Therefore, we completed several separate search tasks in GS using combinations of the following keywords: forager/foraging/forage; crime/ criminal; delinquent/delinquency; offender/offending/offense. GS was consulted on 12 June 2019. Each combination resulted in an extraordinary number of hits. 2 This is partly owing to the fact that GS automatically searches for matching and similarmeaning words. However, the relevance of retrieved studies quickly dropped after the first 100 studies. For each combination of keywords, we evaluated only the first 250 studies (as ranked by GS), ensuring that the most relevant studies were included. In order to increase useful hits, we employed GS's cited by feature to find studies that referenced studies matching our criteria. To see whether these studies matched our inclusion criteria, we evaluated their title, abstract and contents (in that order). The two databases combined yielded 32 studies that matched the criteria outlined above. Searches and selections were conducted by the second author.

Results
The findings are presented according to the research topic being addressed. For each category, the research questions and underlying theoretical models are explained, followed by a discussion of the selected studies' research designs and a summary of their main findings. Table 2 summarizes the included studies.

Spatiotemporal clustering of crime and crime control
Research questions. Most OFT applications to offending investigate spatiotemporal clustering of crime, in particular the well-established phenomenon of repeat and nearrepeat victimization: following an offence, the risk of victimization is temporarily elevated for the original target and for nearby targets (Johnson andBowers, 2004a, 2004b;Johnson et al., 2009a). This phenomenon makes offences cluster in spacetime. In the majority of repeat and near-repeat offences, both the original and the subsequent offence involve the same offenders (Bernasco, 2008;Johnson et al., 2009b). In other words, events that represent repeat and near-repeat victimization are also instances of repeat and near-repeat offending. Offenders who repeatedly victimize the same or nearby targets bear a similarity to foraging animals that harvest patches, as described in the MVT (Charnov, 1976a). The MVT is thus a straightforward choice to frame predictions about offender behaviour. For example, can we predict how long an offender will continue offending in one place before moving on to a more lucrative location? Whereas in OFT assumptions are spelled out explicitly, OFT applications to offending are not all equally explicit about these assumptions.
First, in line with RCP, offender decision-making is assumed to involve weighing benefits, costs and risks, with offenders preferring alternatives that maximize the amount of resources obtained while minimizing efforts and apprehension risk (see also the section on 'Location choice'). Second, reflecting the first law of geography (Tobler, 1970), targets that are proximate to each other are on average more similar. Third, the adopted foraging perspective emphasizes that offenders learn about their environment when committing the first offence in a particular location (Bernasco et al., 2015;Johnson and Bowers, 2004b;Johnson et al., 2009a;Rey et al., 2012;Rosser et al., 2017;Sidebottom, 2012;Youstin et al., 2011). The acquired knowledge reduces offenders' uncertainty about targets near to previously targeted resources, in particular shortly after the first offence, when circumstances are less likely to have changed (Bernasco et al., 2015). This is similar to the sampling behaviour of animals exploring environments to evaluate whether they are worth the time, risk and effort (Stephens and Krebs, 1986). Finally, (re-)victimization risk is believed to decay over time because detection risk increases (Hering and Bair, 2014;Johnson and Bowers, 2004b;Johnson et al., 2009a;Rosser et al., 2017;Wheeler, 2012;Youstin et al., 2011). Additionally, as offenders continue foraging in the same area, resources become scarcer, which prompts offenders to move on to richer areas (Chainey and Silva, 2016;Hering and Bair, 2014;Johnson et al., 2009a). Combined, this leads to the hypothesis that optimally foraging offenders will continue offending in the same area after successfully committing a crime, until the perceived costs and risks outweigh the benefits. of crime and crime control: repeat and nearrepeat victimization Spatial clustering of burglary activity elevates the risk of further residential burglaries in the near future and in close proximity to the initial cluster.
(continued)  One study (Wheeler, 2012) addresses the related question of whether the location where offenders commit crime is conditional on where they live. It uses address changes of known offenders to compare offence locations of the same offenders before and after their address change. The study engages with OFT when discussing the tendency of offenders to re-offend where they offended before, but does not elaborate how offender home locations would fit in the OFT framework. The concept of central place foraging (Orians and Pearson, 1979), in which foraging is constrained by the need for animals to return to a fixed anchor point (for example, a nest), might have proven useful.
Another study focuses on spatiotemporal patterns of crime control (Sorg et al., 2017). It evaluates police behaviour during hotspot patrols. Hotspot policing aims to reduce aggregate crime levels by concentrating police efforts on high-crime areas (Weisburd, 2015). However, research suggests that the deterrent effect of police deployment decays over time (for example, Sherman, 1990). Sorg et al. (2017) examine the potential influence of changes in police effort on deterrence decay, and draw on MVT to hypothesize that officers might leave their assigned hotspots to patrol in other areas as time moves on, a mechanism they term dosage diffusion.
Many studies harness OFT to investigate spatiotemporal patterns in criminal and law enforcement activity, but the extent to which OFT is central to the research and which specific hypotheses are being tested differ. Li et al. (2014) refer to OFT as an explanatory framework for temporal clusters of crime, but do not explicitly test hypotheses from OFT. Yu and Maxfield (2013) state that foraging offenders are a possible mechanism in near-repeat victimization without much clarification. Bernasco et al. (2015) and Nobles et al. (2016) claim that OFT suggests that offenders should learn from previous offences. Sorg et al. (2017) are the only ones to operationalize the three components of optimality modelling (decision, currency and constraints). Direct tests of foraging behaviour measure either the extent of spatiotemporal clustering of crime (Chainey and Silva, 2016;Chainey et al., 2018;Johnson and Bowers, 2004b;Porter and Reich, 2012;Rey et al., 2012;Townsley and Oliveira, 2015), or whether individual offenders return to previously targeted areas (Bernasco et al., 2015;Hering and Bair, 2014;Porter and Reich, 2012). The distinction between the two approaches follows from the type of data available, that is, whether the data are aggregated or associated with individuals. Few studies test OFT hypotheses. More commonly, OFT informs predictive models of crime (Gerstner, 2018;Glasner et al., 2018;Johnson et al., 2009a;Rosser et al., 2017).
Discussion of study results. The findings of the studies focusing on criminal activity confirm that crime does cluster in space and time (Chainey and Da Silva, 2016;Johnson and Bowers, 2004b;Porter and Reich, 2012;Rey et al., 2012;Townsley et al., 2016), and that this observation is most likely the result of offenders deploying optimal foraging strategies (Bernasco et al., 2015;Johnson and Bowers, 2004b), especially at smaller temporal scales. Braithwaite and Johnson (2015) found that time-invariant risk heterogeneity and offenders returning to previously targeted areas are at play. Interestingly, Hering and Bair (2014) found results inconsistent with OFT: offender activity becomes more clustered as time progresses instead of becoming more dispersed.
One study (Johnson, 2014) examines the applicability of random walk models to sequential inter-crime trips of UK residential burglars. Random walks are mathematical models of moving objects that have been used to describe the search paths of foraging animals. When theorizing and describing animal foraging patterns, scholars in ecology often refer to and find evidence for two different types of random walk: Brownian motion and Lévy flight (for example, Humphries et al., 2010). Brownian motion is characterized by small variations in step length and appears optimal in environments where food is abundant, whereas Lévy flight is characterized by occasional large jumps and appears optimal in sparse environments. Both types of random walk generate movement patterns distinct from central place foraging, which is typical of the movement of animals that repeatedly return to an anchor point (for example, birds feeding their offspring) and also characterizes human mobility (Song et al., 2010). Johnson (2014) compares the empirical distributions of distances between burglary events with those generated by Lévy flight, by Brownian motion and by simple central place foraging. The findings suggest that central place foraging strategies alone cannot explain the observed distance distribution. Additionally, Johnson (2014) suggests that offenders most likely do not unequivocally stick with one of the two random walk strategies (Lévy flight or Brownian motion).
Finally, the results of the only study addressing law enforcement activity suggest that the amount of time spent patrolling outside assigned areas increases over time (Sorg et al., 2017). Additionally, they found that this process is hastened in areas that are faced with relatively little crime, or in areas adjacent to high-crime areas, a result in line with MVT's qualitative predictions (Charnov, 1976a).

Location choice
Research questions. Five studies reference OFT to explain how offenders choose where to offend (Bernasco, 2006(Bernasco, , 2010Bernasco and Nieuwbeerta, 2005;Medel et al., 2015;Pires and Clarke, 2011). Similar to a rational actor, an optimal forager prefers targets that maximize gains while minimizing effort and risk. By extension, areas containing valuable items, that are nearby and that are relatively easy to reach will be more attractive. It follows that optimally foraging offenders will attempt to maximize their revenues by selecting areas that are easy to navigate to and seem affluent, and where the risk of apprehension is small.
Discussion of study results. Study results are largely in line with OFT-inspired predictions. Burglars prefer areas that contain many dwellings (Bernasco, 2010;Bernasco and Nieuwbeerta, 2005), appear low in surveillance (Bernasco and Nieuwbeerta, 2005), contain more highly-valued properties (Bernasco, 2010), are physically accessible (Bernasco, 2006;Bernasco and Nieuwbeerta, 2005), and are in close proximity to offenders' homes (Bernasco, 2006(Bernasco, , 2010. Similarly, drug smuggling routes are selected to maximize profits and minimize costs and risks (Medel et al., 2015). Finally, the frequency of parrot species at illegal pet markets is likely the result of their overall abundance, accessibility to humans, and overall enjoyability as pets, indicating that parrot poachers might be acting as optimal foragers (Pires and Clarke, 2011).

Target choice
Research questions. Two studies (Badiora, 2017;Brantingham, 2013) investigate offender target choices and explicitly refer to the classic prey choice model (Charnov, 1976b). This model explains why animals would eat some types of prey while ignoring others. The model assumes discrete prey types that differ in value, in the effort it takes to capture and process them, and in their environmental abundance. Foragers are supposed to maximize the average gains per unit of time.
Applied to car theft, each make model can be ranked according to the ratio between its market value and the effort it takes to steal. Furthermore, car thieves should try to amass as much value as possible relative to effort by being selective in which make models they steal. When encountered, the highest-ranked make model should always be stolen given the opportunity. Since it is the best possible make model to steal, the time and effort spent can never be lost because there is no better alternative to spend it on. In fact, if this make model is abundant enough, there is no reason to pursue any other type. Such opportunities are rare, however, so that a car thief who specializes entirely in this make model will be left with few occasions to steal. Consequently, optimally foraging car thieves will add inferior car types to their 'diet', until doing so would no longer increase the average gains per unit of time.
The prey model thus predicts that offender specialization is normal, and that offenders should prefer a wider range of target types only when preferred targets become scarce (Araújo et al., 2011). This is a combination of rational decision-making (select the option that yields the greatest benefits relative to the costs) and the principle of lost opportunity (ignore targets if the probability of encountering higher-value targets is sufficiently great). This also leads to the somewhat unintuitive prediction that offenders' preference for a given target is independent of its abundance, but depends entirely on the abundance of higher-ranked targets.
Research designs. The two studies examine car thieves' choice to steal different car make models in Los Angeles, USA (Brantingham, 2013), and Lagos, Nigeria (Badiora, 2017). Instead of the more detailed predictions that can be generated under the Charnov (1976b) model, both studies use recorded crime data to test a conservative null hypothesis that, if all make models are ranked evenly (that is, if there is no preference for one model over another), each car type should be stolen about as frequently as they occur in the environment. This corresponds to a forager who targets opportunistically (Araújo et al., 2011). Both studies rely on correlational methods.
Discussion of study results. Both studies (Badiora, 2017;Brantingham, 2013) found a significant positive relationship between car theft and abundance, but also found that some models were targeted more often than expected based on their relative abundance (and vice versa). Brantingham (2013) additionally found that the higher theft rates of these models are associated with higher expected values but not with their handling costs (proxied by average break-in times). Both studies conclude that, although abundance is likely the primary predictor of car thieves' target choices, it is insufficient alone to explain theft rates. These findings suggest that offenders might have different target preferences, but do not offer conclusive evidence to suggest that individual specialization is widespread amongst offenders, as is the case in populations of foraging animals (Araújo et al., 2011;Bolnick et al., 2003).

Offender mobility
Research questions. One study examined the mobility of offenders and how this impacts their earnings (Morselli and Royer, 2008). Referring to strategic foraging (Felson, 2006), the authors claim that 'offenders will forage in patches somewhat farther away if additional booty makes it worth their while' (Morselli and Royer, 2008: 265). Mobility was operationalized as the perimeter within which offenders are active (akin to the operational range of foraging animals; see Felson, 2006). This is similar to questions in behavioural ecology where animals searching for patches containing food should prefer areas that contain many food items relative to the time and effort spent searching for them (MacArthur and Pianka, 1966). Travel distance is a cost that must be compensated for by the expected value of these areas.
Research designs. Morselli and Royer (2008) collected data on mobility and earnings through face-to-face interviews with incarcerated offenders in Quebec, Canada. Data were analysed through regression modelling.
Discussion of study results. Their findings (Morselli and Royer, 2008) suggest that increased mobility is compensated for by higher reported earnings, but that this relationship is stronger for predatory crime types (for example, burglary or robbery) than for market crimes (for example, drug dealing or fencing).

Discussion and conclusion
In this article, we reviewed the OFT-inspired empirical crime research, focusing on the underlying theoretical models and the generated findings. The 32 selected studies addressed four research topics, although foraging models are mostly applied to study the spatiotemporal clustering of crime (24 studies) and to a much lesser degree to the other research topics -location choice (five studies), target choice (two studies), and offender mobility (one study). The dominance of spatiotemporal phenomena in OFT applications in criminology is additionally highlighted by the observation that studies on 'location choice' and 'offender mobility' in fact also address spatiotemporal phenomena, including spatiotemporal clustering. The difference is in the unit of analysis. Research on spatiotemporal clustering uses spatial entities as the unit of analysis, whereas location choice and offender mobility research analyses individual offenders. Ultimately, all three topics address how aggregate spatiotemporal crime patterns arise. From this perspective, the distinction in topics we made is less clearcut than it seems.
Our review established that the application of OFT is mostly restricted to explaining spatiotemporal distributions of crime. It may further be noted that certain topics were not addressed from an OFT perspective despite OFT providing a potentially useful theory. For example, how offenders respond to variations in law enforcement, such as policing strategies, has not been studied systematically from a foraging perspective. However, answers to this research question could well profit from models that specify how animals mitigate predation risk (Verdolin, 2006). Another topic is cooperation and competition amongst offenders. Whereas models of social foraging account for the effects of intraspecies cooperation and competition (Giraldeau and Caraco, 2000), cooperation and competition between offenders has not been addressed in any of the selected crime studies. OFT may also provide a promising theoretical framework in this case.
Although spatiotemporal studies dominate OFT-inspired empirical crime research, the reverse is not true. Neither OFT nor RCT are dominant theories in criminological research that addresses spatiotemporal questions. Instead, scholars principally rely on the geometry of crime (Brantingham et al., 2016), a subset of Crime Pattern Theory (CPT; . The geometry of crime does not explicitly challenge the propositions of OFT, but there appears to be friction between the two perspectives. OFT is a generic behavioural theory with universal claims, whereas CPT is a criminological theory focused on criminal behaviour. OFT is built on first principles, whereas CPT builds on empirical regularities from other disciplines such as the concepts of activity space and awareness space. Because of these differences, the two theories offer different explanations for the same empirical phenomena. For example, OFT explains offenders' preference to commit crimes near their home as an outcome of the optimization of effort investment, whereas CPT explains it as resulting from the fact that humans spend most of their time close to their homes and therefore have more knowledge of nearby than of distant criminal opportunities. OFT is more closely related to RCP than it is to CPT. Both OFT and RCP have their roots in neoclassical economics and share the assumption of utility-maximizing behaviour. Why then would scholars turn to OFT when they have had RCP for decades already? The answer may be related to the fact that most individual-based crime research focuses on serial crime types, whereby one offender commits multiple offences. This aligns well with OFT's emphasis on the long-term fitness consequences of behaviour over sequences of decisions. Methodologically, it favours studies where a small number of animals are observed repeatedly (for example, Araújo et al., 2008;Tinker et al., 2012), which contrasts with crime research, which often relies on police recorded crime data where a large number of offenders are observed infrequently (Johnson, 2014). Finally, there is a focus on acquisitive crime, neglecting other crime types (but see Braithwaite and Johnson, 2015;Hering and Bair, 2014). This is unsurprising because it is more straightforward for acquisitive crime than for other crime to define the currency components of the crimeforaging problem (but see, for example, Burgason and Walker, 2013, who discuss an approach to identify the currency for Internet sex offending). Taken together, it seems evident that OFT was most influential for the study of repeat acquisitive offending.
Nonetheless, there might be some concerns about comparing the behaviour of offenders with that of foraging animals. First, for animals, the only alternative to eating is death. Offenders are not obliged to commit crime and have legal alternatives to choose from. Nevertheless, OFT has been successfully applied to human decision-making and behaviour that does not involve death as the ultimate alternative (Pyke and Stephens, 2019). In fact, offenders' decision-making to engage in legal or non-legal activities is acknowledged as a proper foraging problem that exhibits similarities with animals choosing between prey types or alternating between patches (Fagan and Freeman, 1999). Therefore, crime researchers should not refrain from harnessing OFT to study offender behaviour. Moreover, it seems appropriate to assume that optimal offending strategies are more likely than suboptimal strategies to thrive. Offenders who consistently make suboptimal choices are probably more likely to be arrested and convicted, and are also less likely to survive the competition with more successful offenders. Second, for many animals the search for food is a full-time activity, whereas offending is often part time (Bernasco, 2009;Pires and Clarke, 2011). However, efficient foraging increases fitness because excess time and energy can be spent on reproductive behaviour. This implies that offending does not have to be time-consuming in order to be studied using OFT. Finally, for animal diet choices the currency is seemingly straightforwardly identified, often the calorific intake rate over time (Charnov, 1976b). For offenders, the payoffs might not be apparent, especially when non-monetary gains are involved such as status or thrill-seeking (Goodwill, 2014). This challenges crime researchers to establish currencies or adopt sensible proxies thereof. In doing so, crime researchers could learn from the iterative approach that OFT researchers adopted to establish valid currencies (Burgason and Walker, 2013;Pyke, 2019b). In light of these concerns, we suggest referring to future OFT instalments in crime research as OFT-inspired instead of considering them as strict tests of the application of OFT to offending and law enforcement.
Despite these concerns, it cannot be ignored that research into animal behaviour has proven to be essential for advancing our understanding of human behaviour (Hager, 2010). For example, our insight into human individual, social and reproductive behaviours has dramatically improved owing to research into these behaviours in nonhuman primates (Brosnan, 2013;Burkart et al., 2018;Lindegaard et al., 2017;Muller and Wrangham, 2009). Indeed, OFT is increasingly being applied with success in a variety of disciplines that, at face value, bear little resemblance to the foraging decisions for which OFT was initially developed (Pyke and Stephens, 2019). For crime research in particular, the conceptual similarities between the situations faced by offenders and those encountered by foraging animals are apparent, and harnessing OFT offers important advantages to crime researchers.
First, criminology lacks a theoretical framework that is formulated in terms of mathematical propositions and is able to explain how, when, and where behavioural strategies are enacted (Bernasco, 2009). OFT provides such a theoretical background while also explaining why these patterns occur based on ecological and individual factors in addition to evolutionary stress. Therefore, OFT extends current criminological theory, in particular RCP, by offering criminologists a theoretical framework to translate qualitative hypotheses into quantitative predictions.
Second, the hypotheses formulated in OFT are compatible with hypotheses that have been formulated and tested in criminology (for example, offenders committing offences close to their home, and crime clustering in space and time). OFT is also appealing because it assumes neither that decision-making is perfect or deliberate nor that foragers are aware of the cognitive processes underlying their decision-making .
Furthermore, OFT is a theoretically rich and empirically vibrant field whose continuing theoretical, methodological, and analytical advances could inspire and enrich crime research. If nothing more, the heuristic value of the wide range of hypotheses that have been formulated through the years have already proven to be productive in generating new research directions for crime research (Brantingham, 2013). For example, the attention of OFT to how foraging decisions evolve over time has led to novel insights into the generation of spatiotemporal crime patterns (for example, Johnson et al., 2009a).
Finally, from a pragmatic point of view, the metaphor of the foraging criminal provides a highly visual image aiding communication with law enforcement agencies (Pease, 2014). Taken together, not only is OFT compatible with extant criminological theory and research hypotheses in environmental criminology but it also extends current theory within environmental criminology, offers crime researchers a mathematical framework with versatile modelling options, and could serve as the inspiration for future crime research.
Despite a growing number of crime studies referencing OFT, theoretical work is still needed to employ behavioural ecological insights in criminology beyond its heuristic value. A number of steps might be undertaken to further develop OFT as a framework in criminology.
First, if the strength of OFT lies in the 'specification of the relevant aims and choice situations' (Bernasco, 2009), crime researchers could be more explicit in the choice situations they are modelling, which currency foragers are expected to maximize, and under what constraints they operate. None of the selected studies elaborated on these core elements of optimality modelling that are central to OFT. In fact, studies that apply OFT rarely articulate why it is preferred over RCP. Two crime-foraging studies that use agentbased modelling (ABM) to test OFT hypotheses, but were not included in the literature review because they are not empirical studies (Malleson, 2012;Malleson et al., 2013), are a case in point. Both studies present the foraging criminal as an alternative to the rational offender, but it is not clear why one was chosen over the other. To illustrate, Malleson (2012) states that '[b]urglars act as "optimal forager", when they choose target areas because their decision is based on an analysis of potential rewards against risks'. Moreover, this approach places considerable emphasis on the process of arriving at a particular decision (that is, the analysis of rewards against risks), which is but one aspect of the concept of rationality in behavioural ecology (Kacelnik, 2006).
Second, researchers could leverage the interrelations between foraging models and different stages of offender decision-making. Bernasco (2006) noted the similarities between the choice processes of residential burglars and of foraging animals. Burglars are assumed to follow a spatially structured, sequential and hierarchical decision process in selecting their targets (Cornish and Clarke, 1986), which corresponds to selecting an area first and a suitable target second (Vandeviver and Bernasco, 2020). This resembles animals' decision hierarchy (Stephens, 2008), whereby they first select a foraging patch, which influences their subsequent prey selection in the patch (Charnov, 1976b) and how long they keep foraging in the patch (Charnov, 1976a). The interrelations between subsequent choices have not been evaluated from an optimal foraging perspective in criminology so far, but could help in the development of a comprehensive offender decision-making framework.
Finally, the relationship between evolutionary fitness and economic utility could be elaborated. Although fitness and utility are closely related concepts with similar roles in their respective disciplines (Schulz, 2014), they cannot be unambiguously equated with each other (Binmore, 2012). In fact, the relationship between the two concepts is the subject of behavioural ecological enquiry (Westneat and Fox, 2010), in part because the (a posteriori) utility maximization approach allows the modelling of trade-offs between, for example, safety and food intake (Stephens and Krebs, 1986). Clarifying if, and in what circumstances, principles of fitness maximization can be interpreted as utility maximization could guide crime researchers' decision about when it is appropriate to apply OFT models to offender behaviour. Similarly, clarifying the evolutionary basis of rationality helps integrate criminology with other disciplines.
At the same time, certain methodological issues specific to crime research limit the potential of applying OFT to criminological themes. Studies in behavioural ecology often collect data by directly observing the species' behaviour in situ (for example, Tinker et al., 2012). The nature of criminology's research subject, however, restricts direct observation of the foraging process (Van Gelder and Van Daele, 2014), although some notable exceptions exist (for example, Dabney et al., 2004). Not being able to directly observe criminal behaviour forces crime researchers to infer offenders' decisions from aggregated recorded crime data. Although some researchers circumvent this by using data on cleared offences (Johnson, 2014), low clearance rates and clearance biases limit the generalizability and applicability of research results to crimes committed by unknown offenders.
Triangulating data sources might prove valuable to offset the inherent biases of one particular data type, for example by setting up offender-based study designs. To illustrate, interviews with incarcerated offenders revealed that offenders deliberately disperse activity as time goes on in order to decrease the risk of detection or apprehension, an observation that is in line with OFT predictions (Summers et al., 2010). Additionally, the use of DNA data holds great potential for studying the spatiotemporal behaviour of individual (unknown) offenders in general De Moor et al., 2018;Lammers, 2014;Lammers and Bernasco, 2013), and predictions from OFT in particular.
Finally, recent extensions of OFT might prove valuable for developing criminological theory, with some contemporary issues showing similarity to issues in criminology. Criminological research into offenders' spatial decision-making increasingly accounts for between-offender differences (for example, Frith et al., 2017;Townsley and Sidebottom, 2010;Townsley et al., 2016). Similarly, studies in animal ecology increasingly acknowledge diet variation amongst members of the same species (individual specialization; for example, Bolnick et al., 2003;Tinker et al., 2012). Theoretical and methodological innovations from these studies might provide valuable insights for crime researchers. In particular, OFT offers a framework for explaining and quantifying between-individual differences in prey selection (Araújo et al., 2011;Bolnick et al., 2003). For example, individual specialization in prey selection may arise owing to ecological opportunities, competition for shared resources, or predation risk. Each hypothesis yields different qualitative and quantitative predictions that can be evaluated by custom metrics (Almeida-Neto and Ulrich, 2011;Almeida-Neto et al., 2008;Roughgarden, 1972;Simpson, 1949).
Unavoidably, this study suffers from limitations. Although objective selection criteria for the included studies were used, they were applied by a single author only and were not subjected to inter-rater reliability assessment procedures. In addition, it is possible that bias occurred due to our choice of just two bibliographic databases. The decision to include only empirical research resulted in the loss of some interesting theoretical work on crime-foraging (Burgason and Walker, 2013) and a number of OFT-inspired ABM studies of crime (Brantingham and Tita, 2008;Malleson, 2012;Malleson et al., 2012Malleson et al., , 2013Pitcher and Johnson, 2011). Although these studies were not the focus of this review, they could inspire future crime researchers. For example, Burgason and Walker (2013) articulate how crime researchers might establish the optimization components central to a foraging-inspired model of Internet sexual offenders, and Brantingham and Tita (2008) demonstrate how OFT-inspired mathematical models and ABMs generate quantitative predictions of offender movement. Keeping these limitations in mind, the divergent focus of the selected foraging studies, combined with the observation that OFT is still peripheral to criminology, leads us to believe that this review was adequate to provide a comprehensive overview of the current state of the field.
In conclusion, OFT's introduction in environmental criminology has generated a large volume of novel empirical research, illustrating that OFT can inspire criminological research and offer a framework to improve our understanding of offender decision-making. Nevertheless, the extent to which theory development has benefitted from these applications of OFT to crime research remains limited. We rarely observed theoretical innovation in any of the identified studies. In most OFT-inspired crime research, OFT was used as an interpretative framework for understanding the spatiotemporal patterns produced by repeat and near-repeat victimization, leaving other promising applications of OFT to crime and crime control unexplored. Despite a decade of OFT-inspired research, our conclusion echoes Bernasco's (2009) conclusion that there remains much potential for future OFT-inspired research. We recommend future researchers to prioritize solidifying OFT's theoretical foundation in criminology and exploring anchor points between behavioural ecology, evolutionary theory, and crime science. Additionally, contemporary extensions to OFT and tools developed for the study of animal foraging decisions, in particular specialization in prey choice, show great potential for application to criminal foraging problems. By taking advantage of theoretical and methodological advances in the foraging literature, a greater understanding of offender decision-making may develop.

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/ or publication of this article: Christophe Vandeviver's contribution to this work was supported in part by the Research Foundation -Flanders (FWO) Postdoctoral Fellowship funding scheme