P>1. Sex ratios in unisexual bryophytes are most often female biased, whereas male-biased sex ratios predominate in unisexual seed plants. This 'bryophyte paradox', i.e. that sex ratios are biased in favour of the sex associated with the highest reproductive costs, has remained unexplained. 2. Analysis of sex-ratio patterns via the influence of sex distribution on population growth rates (lambda) has not previously been carried out for bryophytes. We used this method to model how variation in sex ratio and sporophyte frequency influences lambda in the clonal bryophyte Hylocomium splendens. We obtained lambda by matrix modelling of synthetic experimental populations derived from demographic field data, using a linear two-sex model. 3. In our set of experimental populations lambda varied between 1.13 and 1.27 in response to variation in sex ratio and sporophyte frequency, with the highest lambda obtained for the combination of a very low sporophyte frequency and a slightly female-biased sex ratio. 4. Our results explain the female-biased sex ratio of H. splendens by the slightly lower survival of and production of vegetative offspring by males than by non-sporophytic females. 5. Synthesis. According to our models, female dominance is the predicted outcome of low to moderate fertilization success and male performance intermediate between that of sporophytic and of non-sporophytic females. Our results therefore explain how a female-biased sex ratio can be maintained despite higher costs of reproduction in females than in males. In dioecious bryophytes, males and females must grow in close contact for fertilization to take place. Better performance of male ramets than of the female ramets they fertilize also explains how male clones can expand into female clones. A similar performance hierarchy of males and females may occur in unisexual clonal seed plants, but more efficient fertilization systems by pollination prevents the selective advantage of unfertilized females from being realized. This explains why vascular plant populations tend to be male biased. We hypothesise difference in fertilization distance range between sperm and pollen as a simple explanation why ramet level sex ratios are in general male dominated in clonal seed plants and female dominated in clonal bryophytes.