<p>Movement across fragmented landscapes has profound implications for biodiversity and ecosystem function. In this study, we develop and analyse a discrete-time metapopulation model that captures the effects of landscape heterogeneity and incorporates both density-dependent and costly dispersal. Each region’s population dynamics are modelled using bounded population maps, while dispersal proportions are described by nonlinear functions. Our framework extends traditional metapopulation models, which typically focus on constant and/or costless dispersal, by providing a more ecologically realistic basis for understanding persistence in fragmented environments. We begin by detailing the modelling framework, then state sufficient conditions for the local and global stability of the extinction equilibrium and the existence of a positive equilibrium, while also identifying a region where such an equilibrium lies. We further provide a condition for uniform strong persistence in terms of both the total and minimum population sizes. Through an extensive numerical study, within a source-sink context, we explore some of the model’s qualitative dynamics. In particular, we show that introducing density-dependent dispersal can stabilise systems that are otherwise oscillatory under passive dispersal or destabilise systems that are otherwise stable. We demonstrate that connecting sources to sinks or multiple sources via density-dependent dispersal can result in a reduction of the long-term average population size. We finally conduct bifurcation analyses to explore parameter sensitivity, revealing the complex dynamics our model can capture. This includes transitions between extinction and convergence to positive equilibria, as well as the emergence of periodic behaviour, chaotic-type dynamics, and bubbling effects, depending on the interplay between density-dependent dispersal and intrinsic growth rates. Throughout, we discuss the implications of these findings for pest management and conservation, emphasising the need for nuanced, context-dependent strategies that account for the nonlinear effects of dispersal on metapopulation dynamics.</p>