To understand why and how species invade ecosystems, ecologists have made heavy use of observations of species colonization on islands. The theory of island biogeography, developed in the 1960s by R.H. MacArthur and E.O. Wilson, has had a tremendous impact on how ecologists understand the link between species diversity and characteristics of the habitat such as isolation and size. Recent developments have described how the inclusion of information on trophic interactions can further inform our understanding of island biogeography dynamics. Here, we extend the trophic theory of island biogeography to assess whether certain food web properties on the mainland affect colonization/extinction dynamics of species on islands. Our results highlight that both food web connectance and size on the mainland increase species diversity on islands. We also highlight that more heavily tailed degree distributions in the mainland food web correlate with less frequent but potentially more important extinction cascades on islands. The average shortest path to a basal species on islands follows a hump-shaped curve as a function of realized species richness, with food chains slightly longer than on the mainland at intermediate species richness. More modular mainland webs are also less persistent on islands. We discuss our results in the context of global changes and from the viewpoint of community assembly rules, aiming at pinpointing further theoretical developments needed to make the trophic theory of island biogeography even more useful for fundamental and applied ecology.