Recent studies have suggested that spatial patterns of intraspecific diversity can be influenced by density-dependent processes, which can inhibit effective migration of new lineages to established populations. How mechanisms such as dispersal and disturbance influence these processes is, however, still poorly understood. We hypothesised that (1) species with leptokurtic dispersal (frequent on small scales but rare on larger scales) would show no spatial structure on small scales and strong structure on large scales, and (2) disturbance would influence the chance of genetic turnover in a population. We tested these hypotheses using empirical genetic (mtDNA) data from field observations of a model taxon (the buoyant, forest-forming kelp Durvillaea, which exhibits leptokurtic dispersal distribution), and by conducting simulation analyses. Our data supported the first hypothesis, with no spatial structure detected on fine (metres) scales despite evidence of strong structure on larger (tens to hundreds of kilometres) scales. The second hypothesis was also supported, with simulations showing that disturbance increased the rate at which structure developed, and reduced the time to fixation (monopolisation by a single lineage). The chance of any lineage reaching fixation was directly related to its initial proportion in the population, and this relationship was unaffected by changes in disturbance size or dispersal capacity. We conclude that, in the absence of selection, extirpation is typically a prerequisite for population-genetic “turnover”, with remnant (refugial) individuals otherwise outnumbering immigrants. Synthesis. Disturbance plays a critical role in releasing density-dependent blocks to colonisation, and thus enables lineage turnover within species. Our results indicate that although both disturbance size and dispersal capacity play important roles in the formation of spatial structure within species, unless a population is totally extirpated, establishment of genetic lineages from elsewhere (turnover) is unlikely even for species that can disperse well.