Biological networks change dynamically as protein components are synthesized and degraded. Understanding the time-dependence and, in a multicellular organism, tissue-dependence of a network leads to insight beyond a view that collapses time-varying interactions into a single static map. Conventional algorithms are limited to analyzing evolving networks by reducing them to a series of unrelated snapshots.Here we introduce an approach that groups proteins according to shared interaction patterns through a dynamical hierarchical stochastic block model. Protein membership in a block is permitted to evolve as interaction patterns shift over time and space, representing the spatial organization of cell types in a multicellular organism. The spatiotemporal evolution of the protein components are inferred from transcript profiles, using Arabidopsis root development (5 tissues, 3 temporal stages) as an example.The new model requires essentially no parameter tuning, out-performs existing snapshot-based methods, identifies protein modules recruited to specific cell types and developmental stages, and could have broad application to social networks and other similar dynamic systems.