Determining how and how often asexual lineages emerge within sexual species is central to our understanding of sex-asex transitions and the long-term maintenance of sex. Asexuality can arise "by transmission" from an existing asexual lineage to a new one, through different types of crosses. The occurrence of these crosses, cryptic sex, variation in ploidy and recombination within asexuals greatly complicates the study of sex-asex transitions, as they preclude the use of standard phylogenetic methods and genetic distance metrics. In this study we show how to overcome these challenges by developing new approaches to investigate the origin of the various asexual lineages of the brine shrimp Artemia parthenogenetica. We use a large sample of asexuals, including all known polyploids, and their sexual relatives. We combine flow cytometry with mitochondrial and nuclear DNA data. We develop new genetic distance measures and methods to compare various scenarios describing the origin of the different lineages. We find that all diploid and polyploid A. parthenogenetica likely arose within the last 80,000 years through successive and nested hybridization events that involved backcrosses with different sexual species. All A. parthenogenetica have the same common ancestor and therefore likely carry the same asexuality gene(s) and reproduce by automixis. These findings radically change our view of sex-asex transitions in this group, and show the importance of considering asexuality "by transmission" scenarios. The methods developed are applicable to many other asexual taxa.