Many species reproduce both sexually and asexually producing genetically unique and clonal recruits. The relative contribution of sexual and asexual reproduction is mostly considered a consequence of natural selection, for example, disfavouring sexual propagules during invasions. Here, we present a novel model for the invasion of species into a new habitat. The model is fully neutral with respect to the dispersal and the survival of sexual and asexual recruits. In addition to local dispersal through sexual and asexual reproduction, long-distance dispersal is implemented through a non-zero probability for long-range relocations. We parameterized our model using empirical data on the distribution of asexually and sexually recruited individuals of the recently established macroalga Fucus radicans over its current area of distribution, the 8000 year old Baltic Sea. As a solely stochastic alternative mechanism to natural selection, our simulation results suggest local abundance of one sex, that during a persistent phase of establishment will result in a heterogeneous distribution of sexual and asexual recruits. Specifically, the model suggests an initial general dominance of one or a few clones, and this pattern is observed in Fucus radicans as well as in several other species with recent colonization histories.