Collective adaptive systems may be broadly defined as ensembles of autonomous agents, whose interaction may lead to the emergence of global features and patterns. Formal verification may provide strong guarantees about the emergence of these features, but may suffer from scalability issues caused by state space explosion. Compositional verification, whereby the state space of a system is generated by combining (an abstraction of) those of its components, has shown to be a promising countermeasure to the state space explosion problem. Therefore, in this work we apply these techniques to the problem of verifying collective adaptive systems with stigmergic interaction. Specifically, we automatically encode these systems into networks of LNT processes, apply a static value analysis to prune the state space of individual agents, and then reuse compositional verification procedures provided by the CADP toolbox. We demonstrate the effectiveness of our approach by verifying a collection of representative systems.