1As much dispersal research has focused on the eco-evolutionary dynamics of dispersal rates, it remains 2 unclear what shape evolutionarily stable dispersal kernels must be expected to have. Yet, detailed 3 knowledge about dispersal kernels, quantifying the statistical distribution of dispersal distances, is of 4 pivotal importance for understanding biogeographic diversity, predicting species invasions, and explaining 5 range shifts. We therefore examine the evolution of dispersal kernels in an individual-based model of a 6 population of sessile organisms, such as trees or corals. Specifically, we analyze the influence of three 7 potentially important factors on the shape of dispersal kernels: distance-dependent competition, distance-8 dependent dispersal costs, and maternal investment reducing an offspring's dispersal costs through a 9 trade-off with maternal fecundity. We find that without maternal investment, competition and dispersal 10 costs lead to unimodal kernels, with increasing dispersal costs reducing the kernel's width and tail weight.
11Unexpectedly, maternal investment inverts this effect: kernels become bimodal at high dispersal costs.
12This increases a kernel's width and tail weight, and thus the fraction of long-distance dispersers, at the 13 expense of simultaneously increasing the fraction of non-dispersers. We finally demonstrate the qualitative 14 robustness of our results against variations in a majority of tested parameter combinations.