Beginning with Loftin (1986), scholars of crime have described homicide in general, and gun-related homicide in particular as diffusion processes with contagion or epidemic properties (Reiss et al. 1993; Fagan et al. 2007; Patel et al. 2012). Within this paradigm, a variety of different contagion theories have been proposed, all positing that acts of violence increase the odds of further violence, though they differ in the mechanism and time-scale of violence transmission. Early work by Blumstein (1995) subsequently expanded by Fagan et al. (2007) articulated a macro-historical version of contagion theory wherein changing illegal markets led to multi-year increases in gun violence. Other scholars have suggested that violence propagates through social networks of connected individuals (Papachristos et al. 2016). Most scholars, however, have theorized contagion on a much shorter time scale with individual incidents leading to elevated risk of retaliatory shootings concentrated in the communities and lives of individuals connected to earlier incidents. This criminological and public health perspective, beyond its importance to the discipline, also provides a theoretical foundation for policy interventions such as violence interruption programs (Skogan et al. 2009; Webster et al. 2012), designed to disrupt the transmission of gun violence between specific individuals and within particular gun violence hotspots.

Empirical studies of the spatiotemporal properties of crime have reported robust evidence of space-time clustering of property crime (Johnson 2008; Mohler et al. 2011; Short et al. 2010; Townsley et al. 2003) and violent crime (Cohen and Tita 1999; Morenoff et al. 2001; Tita and Cohen 2004; Ratcliffe and Rengert 2008; Braga et al. 2010; Rosenfeld et al. 1999). Cohen and Tita (1999) and Tita and Cohen (2004) report evidence of spatial spillover of homicide and shots fired from census tracts with increasing rates to adjacent tracts, but only during peak crime periods. Messner et al. (1999) report non-random clustering of homicides at the county level, and Ratcliffe and Rengert (2008) reports evidence of a non-random spatiotemporal clustering at the block-level. Both interpret non-random space/time clustering as potential evidence of violence diffusion. However, scholars have yet to determine whether gun violence actually diffuses in space and time, consistent with an epidemic or similar contagion process, or merely clusters in space and time, consistent with endemic gun violence concentrated in certain locations at certain times. This limitation is due, at least in part, to the fact that existing space/time tests were designed to detect departures from complete spatiotemporal randomness rather than distinguishing between different types of non-random clustering (Mohler 2013; Ornstein and Hammond 2017).

Given the high levels of observed gun violence in many US cities (Braga et al. 2010), including retaliatory shootings embedded in social networks that are themselves embedded in neighborhoods characterized by concentrated poverty (Morenoff et al. 2001; Tita and Ridgeway 2007; Papachristos 2009), gun violence could conceivably become contagious with violence triggering more violence (Fagan et al. 2007; Patel et al. 2012). Lending empirical support for this possibility, other human behaviors, including self-directed violence, have been shown to diffuse readily (de Tarde 1903; Coleman et al. 1957; Christakis and Fowler 2007) and evidence of diffusion of violence in social networks has been recently reported (Rosenfeld et al. 1999; Papachristos 2009; Short et al. 2014; Papachristos et al. 2016; Green et al. 2017).

At the same time, detailed examinations of homicide circumstances and motivations have revealed that much fatal gun violence is spontaneous (Metropolitan Police Department 2006; Philadelphia Police Department 2014; Chicago Police Department 2012), resulting from arguments and failed drug transactions (Tita et al. 2003). The existence of non-retaliatory shootings alone, if they were randomly distributed in space-time, would simply add noise to estimates of the diffusion of any retaliatory shootings. However, if a sufficient fraction of all gun discharges in a city result from non-retaliatory shootings that are themselves clustered in space-time, then endemic gun violence with little or no diffusion in space or time could be confused for an epidemic or infectious process using conventional space/time interaction tests.1

Distinguishing between these two interpretations is important on both theoretical and policy grounds. Theoretically, diffusing gun violence would provide support for models of gun violence that emphasize its contagious/infectious features and suggest the need for additional studies focusing on the exact individual-level and mobility-based mechanisms through which elevated risk is transmitted through space and time. Non-random clustering without diffusion, on the other hand, highlights the role of social structure and place in determining the observed distributions. Similarly, the policy implications of these two interpretations can be quite different. Diffusion models have recently formed the theoretical basis for violence interruption programs targeting individuals at heightened risk of perpetration or victimization. Non-diffusion models, by contrast, suggest the need for place-based interventions that address persistent underlying structures (Braga 2005; Weisburd et al. 2012).

To test these alternative possibilities and to more precisely describe the spatiotemporal point process of contemporary gun violence, we examine a dataset composed of data from an acoustic gunshot locator system (AGLS) installed in Washington, DC, a city with a long history of gang and gun violence. Using this data, which overcomes the incomplete measurement of gun violence in conventional reported crime data, and refined space-time interaction tests, we observe that while gun violence does diffuse over space and time, this diffusion is quite minimal—limited in space to 126 m and in time to 10 min–and thus much more likely to be consistent with a discrete gun fight, lasting for a matter of minutes, than with a diffusing, “infectious” process linking violent events across hours, days, or weeks. We then replicate these results using conventional calls for service (CFS) data on reported gunfire incidents. As such, these results provide little support for contagion models of violence diffusion in space and time; instead, this finding supports models predicting stochastic space/time clustering of gun violence (Braga et al. 2010).