Whether there are ecological limits to species diversification is a hotly debated topic. Molecular phylogenies show slowdowns in lineage accumulation, suggesting that speciation rates decline with increasing diversity. A maximum-likelihood (ML) method to detect diversity-dependent (DD) diversification from phylogenetic branching times exists, but it assumes that diversity-dependence is a global phenomenon and therefore ignores that the underlying species interactions are mostly local, and not all species in the phylogeny co-occur locally. Here, we explore whether this ML method based on the nonspatial diversity-dependence model can detect local diversity-dependence, by applying it to phylogenies, simulated with a spatial stochastic model of local DD speciation, extinction, and dispersal between two local communities. We find that type I errors (falsely detecting diversity-dependence) are low, and the power to detect diversity-dependence is high when dispersal rates are not too low. Interestingly, when dispersal is high the power to detect diversity-dependence is even higher than in the nonspatial model. Moreover, estimates of intrinsic speciation rate, extinction rate, and ecological limit strongly depend on dispersal rate. We conclude that the nonspatial DD approach can be used to detect diversity-dependence in clades of species that live in not too disconnected areas, but parameter estimates must be interpreted cautiously.