Ecological networks represent the backbone of biodiversity. As species diversify over macro-evolutionary time-scales, the structure of these networks changes; this happens because species are gained and lost, and therefore add or remove interactions in their communities. The mechanisms underlying such dynamic changes in ecological network structure, however, remain poorly understood. Here we show that several types of ecological interactions share common evolutionary mechanisms that can be parametrised based on extant interaction data. In particular, we found that a model mimicking birth-death processes for species interactions describes the structure of extant networks remarkably well. Moreover, the various types of ecological interactions we considered--seed dispersal, herbivory, parasitism, bacteriophagy, and pollination--only differed in the position they occupy in the parameters' multi-dimensional space. Notably, we found no clustering of parameters values between antagonistic and mutualistic interactions. Our results provide a common modelling framework for the evolution of ecological networks that we anticipate will contribute to the greater consideration of the explicit role played by species interactions in models of macro-evolution and adaptive radiations.