  There is a significant amount of online human activity which is either
clandestine or illicit in nature, and hence where individuals operate under
fear of exposure or capture. Yet there is little theoretical understanding of
what models best describe the resulting dynamics. Here we address this gap, by
analyzing the evolutionary dynamics of the supporters behind the 95 pro-ISIS
online communities (i.e. self-organized social media groups) that appeared
recently on a global social media site. We show that although they do not
follow a conventional (i.e. size-based) preferential attachment (PA) model,
their dynamical evolution can be explained by a new variant that we introduce
here, which we refer to as active attraction model (AA). This AA model takes
into account the locality and group heterogeneity which undoubtedly feature in
humans' online behavior under pressure, but which are not contained in
conventional PA models. The AA model captures both group-specific and
macroscopic observations over all size ranges -- as opposed to just the tail
for large groups or groups' initial growth -- suggesting that heterogeneity and
locality play a crucial role in the dynamics of online extremist support. We
derive approximate expressions for the group size distributions in two simple
systems that involve simultaneously the mechanisms of group joining (governed
by either PA or AA), group leaving, and account banning, and show how these
processes influence the group size distributions. We believe this work will
serve in helping understand a broad spectrum of online human activities which
are either clandestine or illicit in nature, and hence where individuals
operate under fear of exposure or capture.
