A central question in ecology with great importance for management, conservation and biological control is how changing connectivity affects the persistence and dynamics of interacting species. Researchers in many disciplines have used large systems of coupled oscillators to model the behaviour of a diverse array of fluctuating systems in nature. In the well-studied regime of weak coupling, synchronization is favoured by increases in coupling strength and large-scale network structures (for example `small worlds') that produce short cuts and clustering. Here we show that, by contrast, randomizing the structure of dispersal networks in a model of predators and prey tends to favour asynchrony and prolonged transient dynamics, with resulting effects on the amplitudes of population fluctuations. Our results focus on synchronization and dynamics of clusters in models, and on timescales, more appropriate for ecology, namely smaller systems with strong interactions outside the weak-coupling regime, rather than the better-studied cases of large, weakly coupled systems. In these smaller systems, the dynamics of transients and the effects of changes in connectivity can be well understood using a set of methods including numerical reconstructions of phase dynamics, examinations of cluster formation and the consideration of important aspects of cyclic dynamics, such as amplitude.