Most of earth's biodiversity is comprised of interactions among species, yet it is unclear what causes variation in interaction diversity across space and time. We define interaction diversity as the richness and relative abundance of interactions linking species together at scales from localized, measurable webs to entire ecosystems. Large-scale patterns suggest that two basic components of interaction diversity differ substantially and predictably between different ecosystems: overall taxonomic diversity and host specificity of consumers. Understanding how these factors influence interaction diversity, and quantifying the causes and effects of variation in interaction diversity are important goals for community ecology. While previous studies have examined the effects of sampling bias and consumer specialization on determining patterns of ecological networks, these studies were restricted to two trophic levels and did not incorporate realistic variation in species diversity and consumer diet breadth. Here, we developed a food web model to generate tri-trophic ecological networks, and evaluated specific hypotheses about how the diversity of trophic interactions and species diversity are related under different scenarios of species richness, taxonomic abundance, and consumer diet breadth. We investigated the accumulation of species and interactions and found that interactions accumulate more quickly; thus, the accumulation of novel interactions may require less sampling effort than sampling species in order to get reliable estimates of either type of diversity. Mean consumer diet breadth influenced the correlation between species and interaction diversity significantly more than variation in both species richness and taxonomic abundance. However, this effect of diet breadth on interaction diversity is conditional on the number of observed interactions included in the models. The results presented here will help develop realistic predictions of the relationships between consumer diet breadth, interaction diversity, and species diversity within multi-trophic communities, which is critical for the conservation of biodiversity in this period of accelerated global change.