Connectivity relates to the coupling of landforms (e.g. hillslopes and channels) and the transfer of water and sediment between them. The degree to which parts of a catchment are connected depends largely on the morphological complexity of the catchment's landscape. Landscapes can have very different and distinct morphologies, such as terraces, V-shaped valleys or broad floodplains. The objective of this study is to better understand and quantify the relation between landscape complexity and catchment connectivity. We hypothesize that connectivity decreases with increasing landscape morphological complexity. To quantify the connectivity–complexity relationship virtual digital elevation models (DEMs) with distinct morphologies were used as inputs into the landscape evolution model LAPSUS to simulate the sediment connectivity of each landscape. Additionally, the hypothesis was tested on six common real DEMs with widely different morphologies. Finally, the effects of different rainfall time series on catchment response were explored. Simulation results confirm the hypothesis and quantify the non-linear relation. Results from the exploration of sediment connectivity in response to sequences of rainfall events indicate that feedback between erosion and deposition are more important for certain landscape morphologies than for others: for a given rainfall input, a more effective sediment connectivity and erosion response may be expected from rolling or V-shaped catchments than from dissected or stepped landscapes. Awareness of the differences in the behaviour and response of different morphologies to catchment processes provides valuable information for the effective management of landscapes and ecosystems through efficiently designed soil and water conservation measures. Copyright © 2013 John Wiley & Sons, Ltd.