Understanding the principles that govern the assembly of microbial communities across earth's biomes is a major challenge in modern microbial ecology. This pursuit is complicated by the difficulties of mapping functional roles and interactions onto communities with immense taxonomic diversity and of identifying the scale at which microbes interact . To address this challenge, here, we focused on the bacterial communities that colonize and degrade particulate organic matter in the ocean [2-4]. We show that the assembly of these communities can be simplified as a linear combination of functional modules. Using synthetic polysaccharide particles immersed in natural bacterioplankton assemblages [1, 5], we showed that successional particle colonization dynamics are driven by the interaction of two types of modules: a first type made of narrowly specialized primary degraders, whose dynamics are controlled by particle polysaccharide composition, and a second type containing substrate-independent taxa whose dynamics are controlled by interspecific interactions-in particular, cross-feeding via organic acids, amino acids, and other metabolic byproducts. We show that, as a consequence of this trophic structure, communities can assemble modularly-i.e., by a simple sum of substrate-specific primary degrader modules, one for each complex polysaccharide in the particle, connected to a single broad-niche range consumer module. Consistent with this model, a linear combination of the communities on single-polysaccharide particles accurately predicts community composition on mixed-polysaccharide particles. Our results suggest that the assembly of heterotrophic communities that degrade complex organic materials follows simple design principles that could be exploited to engineer heterotrophic microbiomes.