Collective efficacy (CE) - the combination of social ties between local residents and their shared willingness to actively engage in social control - has become widely recognised as one of the central ecological theories of crime and place. However, despite a substantial evidence base that has demonstrated the negative link between collective and crime rates, we still know little about the formation of CE or how its spatial distribution is determined by a neighbourhood’s inner structure. 

In this study we address this gap by presenting a novel convolution model that allows for a mathematical investigation of how a neighbourhood’s internal resources lead to spatial variations in CE, and in turn crime, as well as providing insights into the transitions between different regions of CE. With the theory of planned behaviour, we show how individual CE can lead to emergent CE behaviour and clustering at neighbourhood level. We find that the size and shape of the neighbourhood of the influence on an individual's efficacy is critical in the shape of the clustering behaviour of CE.