Standard models of population dynamics focus on the interaction, survival, and extinction of the competing species individually. Real ecological systems, however, are characterized by an abundance of species (or strategies, in the terminology of evolutionary-game theory) that form intricate, complex interaction networks. The description of the ensuing dynamics may be aided by studying associations of certain strategies rather than individual ones. Here we show how such a higher-level description can bear fruitful insight. Motivated from different strains of colicinogenic Escherichia coli bacteria, we investigate a four-strategy system which contains a three-strategy cycle and a neutral alliance of two strategies. We find that the stochastic, spatial model exhibits a mobility-dependent selection of either the three-strategy cycle or of the neutral pair. We analyze this intriguing phenomenon numerically and analytically.