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One of the current challenges in evolutionary ecology is understanding the long-term persistence of contemporary-evolving predator-prey interactions across space and time. To address this, we developed an extension of a multi-locus, multi-trait eco-evolutionary individual-based model that incorporates several interacting species in explicit landscapes. We simulated eco-evolutionary dynamics of multiple species food webs with different degrees of connectance across soil-moisture islands. A broad set of parameter combinations led to the local extinction of species, but some species persisted, and this was associated with (1) high connectance and omnivory and (2) ongoing evolution, due to multi-trait genetic variability of the embedded species. Furthermore, persistence was highest at intermediate island distances, likely because of a balance between predation-induced extinction (strongest at short island distances) and the coupling of island diversity by top predators, which by travelling among islands exert global top-down control of biodiversity. In the simulations with high genetic variation, we also found widespread trait evolutionary changes indicative of eco-evolutionary dynamics. We discuss how the ever-increasing computing power and high-resolution data availability will soon allow researchers to start bridging the in vivo-in silico gap. [ABSTRACT FROM AUTHOR]