Neutral models characterize evolutionary or ecological patterns expected in the absence of specific causal processes, such as natural selection or ecological interactions. In this study, we describe and evaluate three neutral models that can, in principle, help to explain the apparent 'twigginess' of asexual lineages on phylogenetic trees without involving the negative consequences predicted for the absence of recombination and genetic exchange between individuals. Previously, such phylogenetic twiggyness of asexual lineages has been uncritically interpreted as evidence that asexuality is associated with elevated extinction rates and thus represents an evolutionary dead end. Our first model uses simple phylogenetic simulations to illustrate that, with sexual reproduction as the ancestral state, low transition rates to stable asexuality, or low rates of ascertained ‘speciation’ in asexuals, can generate twiggy distributions of asexuality, in the absence of high extinction rates for asexual lineages. The second model, developed by Janko et al. (2008), shows that a dynamic equilibrium between origins and neutral losses of asexuals can, under some conditions, generate a relatively low mean age of asexual lineages. The third model posits that the risk of extinction for asexual lineages may be higher than that of sexuals simply because asexuals inhabit higher latitudes or altitudes, and not due to effects of their reproductive systems. Such neutral models are useful in that they allow quantitative evaluation of whether empirical data, such as phylogenetic and phylogeographic patterns of sex and asexuality, indeed support the idea that asexually reproducing lineages persist over shorter evolutionary periods than sexual lineages, due to such processes as mutation accumulation, slower rates of adaptive evolution, or relatively lower levels of genetic variability.