Improving or declining: What are the consequences for changes in local crime?*.

Whereas existing ecology of crime research frequently uses a cross‐sectional design, an open question is whether theories underlying such studies will operate similarly in longitudinal research. Using latent trajectory models and longitudinal data in half‐mile egohoods from the Southern California region over a 10‐year period (2000–2010), we explore this question and assess whether the changes in key measures of social disorganization theory are related to changes in violent or property crime through three possible relationships: 1) a monotonic relationship, 2) an asymmetric relationship, and 3) a perturbation relationship in which any change increases crime. We find evidence that measures can exhibit any of these three possible relationships, highlighting the importance of not assuming monotonic relationships. Most frequently observed are asymmetric relationships, which we posit are simultaneously capturing more than one theoretical process of neighborhoods and crime. Specific findings include asymmetric relationships between change in concentrated disadvantage, racial/ethnic minority composition, or population and violent crime, as well as relationships between change in Asian composition or population and property crime. We consider how this strategy opens a needed area of future research assessing how measures for other theories operate as environments change. [ABSTRACT FROM AUTHOR]