Resistance genes are a major tool for managing crop diseases. The crop breeder networks that exchange resistance genes and deploy them in elite varieties help to determine the global landscape of resistance and epidemics, and comprise an important system for maintaining food security. These networks function as complex adaptive systems, with associated strengths and vulnerabilities, and implications for policies to support resistance gene deployment strategies. Extensions of epidemic network analysis can be used to evaluate the multilayer agricultural networks that support and influence crop breeding networks. We evaluate the general structure of crop breeding networks for cassava, potato, rice, and wheat, which illustrate a range of public and private configurations. These systems must adapt to global change in climate and land use, the emergence of new diseases, and disruptive breeding technologies. Principles for maintaining system resilience can be applied to global resistance gene deployment. For example, both diversity and redundancy in the roles played by individual crop breeding groups (public versus private, global versus local) may support societal goals for crop production. Another principle is management of connectivity, where enhanced connectivity among crop breeders may benefit global resistance gene deployment, but increase risks to the durability of resistance genes without effective policies regarding deployment.