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 method to detect diversity-dependent 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 maximum likelihood method based on the non-spatial diversity-dependence model can detect local diversity-dependence, by applying it to phylogenies, simulated with a spatial stochastic model of local-diversity-dependent 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 non-spatial model. Moreover, estimates of intrinsic speciation rate, extinction rate and ecological limit strongly depend on dispersal rate. We conclude that the non-spatial diversity-dependent 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.