CRIME DIVERSITY*

• DOI: http://doi.org/10.1111/1745-9125.12116
• Published date: 01 November 2016
• Date: 01 November 2016
• Author: P. JEFFREY BRANTINGHAM

CRIME DIVERSITY∗

P. JEFFREY BRANTINGHAM

Department of Anthropology, University of California, Los Angeles

KEYWORDS: neutral models, ecology, environmental criminology, mathematical mod-

eling, crime pattern theory

Large geographic areas should host a greater diversity of crime compared with small

geographic areas. This proposition is reasonable given that larger geographic areas

should not only support more crime but also contain a greater diversity of crimino-

genic settings. This article uses a neutral model to characterize crime richness as a

function of area. The model starts with two neutral assumptions: 1) that all environ-

ments are statistically equivalent and exert no influence on what types of crimes occur

there; and 2) that different crime types occur independently of one another. The model

produces rigorous predictions for the mean and variance in crime richness with in-

creasing area. Tests of the model against a sample of 172,055 crimes occurring in Los

Angeles during the year 2013 are qualitatively consistent with neutral expectations. The

model is made quantitatively consistent by constant scaling. Resampling experiments

show that at most 20 percent of the mean crime richness is attributable to nonrandom

clustering and assortment of crime types. A modified neutral model allowing for vari-

ation crime concentration is consistent with observed variance in crime richness. The

results suggest that very general and largely neutral laws may be driving crime diversity

in space.

Environmental criminology is based broadly on the idea that the crime manifest in a

place is closely connected to the environmental conditions of that place (Brantingham

and Brantingham, 1978, 1981; Eck and Weisburd, 1995). Considerable ambiguity still

exists, however, surrounding the mechanisms that give rise to such connections, espe-

cially when examining the occurrence of unique crime types in the context of place. In

a manner paralleling the debate over offender specialization (Blumstein et al., 1988;

Deane, Armstrong, and Felson, 2005; McGloin et al., 2011; Osgood and Schreck, 2007),

the tie between a unique crime type and an environment may be explained as offender

decision-making in response to either very general or very specific environmental cues

or opportunities (Brantingham and Brantingham, 1978, 1981; Weisburd et al., 1992;

Wikstr ¨

om et al., 2012). In the former case, general environmental cues are necessary

for the occurrence of crime, but these cues place few constraints on exactly what type

of crime might occur there (Keizer, Lindenberg, and Steg, 2008; Kinney et al., 2008). In

the latter case, environmental cues are not only necessary for the occurrence of crime

∗This work was supported in part by ARO MURI Grant W911NF-11-1-0332. Special thanks go to

the Los Angeles Police Department, Mathew Valasik (LSU), and Martin Short (Georgia Tech).

This article greatly benefitted from the careful readings of three anonymous referees.

Direct correspondence to P. Jeffrey Brantingham, Department of Anthropology, University of

California, Los Angeles, 341 Haines Hall, Los Angeles, CA 90095 (e-mail: branting@ucla.edu).

C2016 American Society of Criminology doi: 10.1111/1745-9125.12116

CRIMINOLOGY Volume 54 Number 4 553–586 2016 553

554 BRANTINGHAM

but also narrowly specify which crime types are possible (Clarke and Cornish, 1985).

Here it is assumed that there is a close fit between the requirements to complete a

particular type of crime and the opportunities presented by the environment (Taylor and

Gottfredson, 1986). Indeed, the absence of a specific environmental cue or opportunity

may be sufficient to exclude some crime types from occurring at all.

Which of these mechanisms is more plausible, or whether some mixture of generalized

and specialized environmental cues drives crime, is of great importance both theoreti-

cally and as a matter of policy and practice. Again paralleling the debate over offender

specialization (Osgood and Schreck, 2007), offending in response to very generalized

environmental cues suggests that generic, universal models may be sufficient to explain

the spatial patterning of any crime type across all environments (Weisburd, 2015). By

contrast, if crimes are tied to environments in intricate and mutually dependent ways,

then generalizations beyond individual crime types or even the individual events and

the places where they occur may be problematic (Cornish and Clarke, 1986; Weisburd

et al., 1992). On the policy front, generalized connections between crime and place

suggest that generic environmental interventions may be both widely applicable and

scalable (Jeffery, 1977). On the other hand, if unique crime types are committed in ways

that are closely calibrated to a unique set of environmental cues or opportunities, then

situational, problem-oriented solutions may be required for each environmental setting

(Clarke, 1997; Eck and Spelman, 1988; Goldstein, 1979). The idea of problem-oriented

policing may be widely applicable, but actual interventions do not readily scale.

The proposition that crime types are well fit to the environment holds important

microscopic implications about the decision-making of offenders (e.g., Bernasco and

Nieuwbeerta, 2005; Townsley et al., 2015; Wikstr ¨

om et al., 2012). It also leads to

novel macroscopic predictions (e.g., Schreck, McGloin, and Kirk, 2009). Specifically,

larger geographic areas should be expected to host a more diverse set of crime types

compared with smaller geographic areas. Such macroscopic patterning can arise both

if the environmental cues that support crime are very general and if they are very

specific. If general environmental cues drive crime, then larger geographic areas should

contain more unique crime types simply by virtue of the size of the area sampled. By

contrast, if specific environmental cues drive crime, then larger geographic areas should

also contain more unique crime types because larger areas will generally encompass

a more heterogeneous mixture of environmental settings. The primary goal of this

article is to document empirically macroscopic patterns of crime diversity and provide a

mathematically grounded explanation for these patterns.

The situation outlined earlier parallels closely one well known in ecology. The

attributes of organisms are thought to be well fit to the environments they inhabit,

with evolution by means of natural selection being the primary mechanism whereby

adaptations develop (Bock, 1980). Whether adaptations develop in response to general

environmental conditions such as temperature, or specific resources such as an essential

nutrient, large areas are expected to contain more unique species than are small areas.

In contrast to the case with crime diversity, however, strong empirical evidence describes

patterns of biodiversity across spatial scales. Decades of research in ecology have shown

not only that species diversity increases as a function of the size of the geographic area

sampled but also that this pattern of increase is very regular, although usually nonlinear

(Arrhenius, 1921; Fisher, Corbet, and Williams, 1943; He and Hubbell, 2011; Hubbell,

CRIME DIVERSITY 555

2001; Huston, 1979; MacArthur and Wilson, 1967; Simberloff, 1974). This so-called

“species–area relationship” is observed in almost all environments and across radically

different functional groups of organisms (Ferenc et al., 2014; Hobbs et al., 2012; Murgui,

2007; Pedr ´

os-Ali ´

o, 2012). Indeed, species–area relationships are one of a small handful

of universal patterns in ecology that hint at fundamental laws regulating biodiversity

(Hubbell, 2001; Leibold et al., 2004). Here I find many of the same regularities in

crime-type–area relationships, raising the possibility that similarly broad mechanisms are

at play in regulating the diversity of crime (see also Weisburd, 2015). The findings have

important implications not only for the study of crime and place but also for broader

issues in crime pattern theory and environmental criminology.

The structure of this article is as follows. The first section defines what is meant by

crime diversity and why it may be important. The approach I take deviates from existing

methods in criminology in considering patterns expressed across a wide spectrum of crime

types. By following practice in ecology, I distinguish between crime richness, which is sim-

ply a count of the number of unique crime types found in a sample, and crime evenness,

which refers the patterns of abundance among different unique crime types (see Piquero

et al., 1999). Here the focus is on crime richness. As a target measure, richness is blind to

detailed characteristics of specific crime types. The co-occurrence of homicide and theft

is counted in the same way as the co-occurrence of narcotics violations and theft, even

though theory might suggest there is a stronger functional connection between narcotics

violations and theft than that between homicide and theft (Anglin and Speckart, 1988;

Wright and Decker, 1994). It is argued that crime richness is relevant to ecosystem func-

tion, with areas supporting a greater range of crime types being functionally worse off.

The second section places crime diversity in the context of crime pattern theory

(Brantingham and Brantingham, 1978, 1981, 1984; see also Wikstr ¨

om et al., 2012).

Crime pattern theory posits that the spatial occurrence of crime stems from motivated

offenders deploying a multistage decision process in response to environmental cues or

opportunities. Those cues can be either very general or very specific and, thus, place few

or many constraints on the types of crime that might occur, respectively. Both general

and specific cues might underlie patterns of increasing crime diversity as a function of

the size of the area observed. The third section seeks to disentangle the role of general

and specific environmental cues or opportunities by drawing on models from theoretical

ecology for guidance. The approach taken is explicitly neutral (Gotelli and Graves,

1996; Hubbell, 2001). This section starts by introducing key assumptions underlying

neutral modeling. These assumptions are likely to be met with considerable outrage

(see Rosindell, Hubbell, and Etienne, 2011), although the goal is to improve explanation

(Weisburd and Piquero, 2008). The fourth section follows with a formal mathematical

model for characterizing crime diversity generated by neutral processes (Arrhenius,

1921; Coleman, 1981; Connor and McCoy, 1979). The passive sampling model, as it is

termed, assumes that crime types are placed randomly and independently in space. The

occurrence of a crime type in any given area is determined only by the relative size of

that area and the global abundance of that crime type. No dependencies between crime

types or crime types and environments are assumed. Patterns of crime diversity as a

function of area are modeled as the result of neutral stochastic processes alone. The

neutral approach is used to set rigorous mathematical expectations for crime diversity

patterns that should be easy to reject if the model is a poor fit for the processes at hand.