Adaptive networks consist of a collection of nodes with learning abilities that interact with each other locally in order to solve distributed processing and distributed inference problems in real-time. Various algorithms and performance analyses have been put forward for such networks, such as the adapt-then-combine (ATC) and combine-then-adapt (CTA) diffusion algorithms, the probabilistic diffusion algorithm, and diffusion with adaptive weights over the links. In this paper, we add mobility as another dimension and study the behavior of the network when the nodes move in pursuit/avoidance of a target. Mobility leads naturally to an adaptive topology with changing neighborhoods. Mobility also imposes physical constraints on the proximity among the nodes and on the velocity and location of the center of the network. We develop adaptation algorithms that exhibit self-organization properties and apply them to the modeling of collective behavior in biological systems, such as fish schooling. The results help provide an explanation for the agile adjustment of network patterns of fish schools in the presence of predators.