Since seeds are the principle means by which plants move across the landscape, the final fate of seeds plays a fundamental role in the assemblage, functioning and dynamics of plant communities. Once seeds land on the soil surface after being dispersed from the parent plant, they can be moved horizontally by surface runoff. In arid and semiarid patchy ecosystems, where seeds are scattered into a very heterogeneous environment and intense rainfalls occur, the transport of seeds by runoff to new sites may be an opportunity for seeds to reach more favourable sites for seed germination and seedling survival. Although seed transport by runoff may be of vital importance for the recruitment of plants in these ecosystems, it has received little attention in the scientific literature, especially among soil scientists. The main goals of this review paper are (1) to offer an updated conceptual model of seed fate with a focus on seed destiny in and on the soil; (2) to review studies on seed fate in overland flow and the ecological implications seed transport by runoff has for the origin, spatial patterning and maintenance of patches in arid and semiarid patchy ecosystems; and finally (3) to point out directions for future research.

This review shows that seed fate in overland flow may result either in the export of seeds from the system (seed loss) or in the spatial redistribution of seeds within the system through short-distance seed movements (seed displacement). Seed transport by runoff depends on rainfall, slope and soil characteristics. Susceptibility of seed removal varies highly between species and is mainly related to seed traits, including seed size, seed shape, presence of appendages, and ability of a seed to secrete mucilage. Although initially considered as a risk of seed loss, seed removal by runoff has recently been described as an ecological driver that shapes plant composition from the first phases of the plant life by favouring species with seeds able to resist erosion and by selecting for plant traits that prevent seed loss. Moreover, the interaction of seed transport by overland flow with the high seed trapping capacity of vegetated patches results in a "patch-to-patch" transport of seeds that plays a relevant role in vegetation establishment and patterning in arid and semiarid patchy ecosystems.

Overall, this review shows how the knowledge about seed fate in overland flow can be used to explain a number of important characteristics of whole plant communities. It also underlines important gaps in knowledge that should be filled in. Future lines of research are proposed in order to broaden our understanding of the origin, maintenance and dynamics of patchiness in arid and semiarid ecosystems and to improve restoration success of intensively eroded ecosystems. Among the most exciting challenges, empirical studies are needed to understand the relevance of short-distance seed displacements in the origin and maintenance of patchiness, addressing the feedbacks between structure and function and abiotic and biotic components, in order to validate existing models about the dynamics of arid and semiarid ecosystems and help to predict future changes under the scenarios of climate change.