Phylogenetic and phylogeographic studies suggest that a majority of asexual organisms are evolutionarily recent offshoots of extant sexual taxa and that old clonal lineages tend to be isolated from their sexual and younger asexual counterparts. These observations have often been interpreted as support for the long-term disadvantages of asexuality resulting from the mechanisms of clonal decay. Although clonal decay is likely to be an important mechanism that limits the temporal and spatial distribution of asexual lineages, we argue here that contemporary phylogenetic analyses, which are mostly restricted to simple comparisons of "recent" and "ancient" clones, need to be tested against an appropriate null model of neutrality. We use computer simulations to show that many empirical observations of the distribution of asexuality do not in fact reject a null model of the neutral turnover of clones spawned by sexual relatives. In particular, neutral clonal turnover results in qualitatively similar pattern of clonal spatial distribution and age structure, as does a process that includes clonal decay. Although there are important quantitative differences between predictions made by the two models, we show that published empirical data are still inadequate to distinguish between them. Further work on sexual-asexual complexes is therefore required before clonal turnover can be rejected as a parsimonious explanation of the spatial distribution and age structure of asexual lineages.