Antagonistic networks are known to be structured in the wild, but knowledge on how this structure may change as a response to environmental perturbations is scarce. We describe a natural bipartite network between bacteria and lytic bacteriophages, and investigate how it is affected by environmental productivity in the form of different resource levels for the bacteria. We report that low amounts of resource decrease phage generality and lead to less robust and less stable communities. We discuss how resource levels in nature may alter the structure of complex communities.