Assessing deep-time mechanisms affecting the assembly of ecological networks is key to understanding biodiversity changes on broader time scales. We combined analyses of diversification rates with interaction network descriptors from 468 bird species belonging to 29 seed-dispersal networks to show that bird species that contribute most to the network structure of plant-frugivorous interactions belong to lineages that show higher macroevolutionary stability. This association is stronger in warmer, wetter, less seasonal environments. We infer that the macroevolutionary sorting mechanism acts through the regional pool of species by sorting species based on the available relative differences in diversification rates, rather than absolute rates. Our results illustrate how the interplay between interaction patterns and diversification dynamics may shape the organization and long-term dynamics of ecological networks.